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1
Johnson, Blair A., and Edwin A. Cowen. "Turbulent boundary layers absent mean shear." Journal of Fluid Mechanics 835 (November 27, 2017): 217–51. http://dx.doi.org/10.1017/jfm.2017.742.
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We perform an experimental study to investigate the turbulent boundary layer above a stationary solid glass bed in the absence of mean shear. High Reynolds number $(Re_{\unicode[STIX]{x1D706}}\sim 300)$ horizontally homogeneous isotropic turbulence is generated via randomly actuated synthetic jet arrays (RASJA – Variano & Cowen J. Fluid Mech. vol. 604, 2008, pp. 1–32). Each of the arrays is controlled by a spatio-temporally varying algorithm, which in turn minimizes the formation of secondary mean flows. One array consists of an $8\times 8$ grid of jets, while the other is a $16\times 16$ array. Particle image velocimetry measurements are used to study the isotropic turbulent region and the boundary layer formed beneath as the turbulence encounters a stationary wall. The flow is characterized with statistical metrics including the mean flow and turbulent velocities, turbulent kinetic energy, integral scales and the turbulent kinetic energy transport equation, which includes the energy dissipation rate, production and turbulent transport. The empirical constant in the Tennekes (J. Fluid Mech. vol. 67, 1975, pp. 561–567) model of Eulerian frequency spectra is calculated based on the dissipation results and temporal frequency spectra from acoustic Doppler velocimetry measurements. We compare our results to prior literature that addresses mean shear free turbulent boundary layer characterizations via grid-stirred tank experiments, moving-bed experiments, rapid-distortion theory and direct numerical simulations in a forced turbulent box. By varying the operational parameters of the randomly actuated synthetic jet array, we also find that we are able to control the turbulence levels, including integral length scales and dissipation rates, by changing the mean on-times in the jet algorithm.
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Thole, K. A., and D. G. Bogard. "High Freestream Turbulence Effects on Turbulent Boundary Layers." Journal of Fluids Engineering 118, no. 2 (June 1, 1996): 276–84. http://dx.doi.org/10.1115/1.2817374.
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High freestream turbulence levels significantly alter the characteristics of turbulent boundary layers. Numerous studies have been conducted with freestreams having turbulence levels of 7 percent or less, but studies using turbulence levels greater than 10 percent have been essentially limited to the effects on wall shear stress and heat transfer. This paper presents measurements of the boundary layer statistics for the interaction between a turbulent boundary layer and a freestream with turbulence levels ranging from 10 to 20 percent. The boundary layer statistics reported in this paper include mean and rms velocities, velocity correlation coefficients, length scales, and power spectra. Although the freestream turbulent eddies penetrate into the boundary layer at high freestream turbulence levels, as shown through spectra and length scale measurements, the mean velocity profile still exhibits a log-linear region. Direct measurements of total shear stress (turbulent shear stress and viscous shear stress) confirm the validity of the log-law at high freestream turbulence levels. Velocity defects in the outer region of the boundary layer were significantly decreased resulting in negative wake parameters. Fluctuating rms velocities were only affected when the freestream turbulence levels exceeded the levels of the boundary layer generated rms velocities. Length scales and power spectra measurements showed large scale turbulent eddies penetrate to within y+ = 15 of the wall.
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Fontaine, Ryan A., Gregory S. Elliott, Joanna M. Austin, and Jonathan B. Freund. "Very near-nozzle shear-layer turbulence and jet noise." Journal of Fluid Mechanics 770 (March 27, 2015): 27–51. http://dx.doi.org/10.1017/jfm.2015.119.
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One of the principal challenges in the prediction and design of low-noise nozzles is accounting for the near-nozzle turbulent mixing layers at the high Reynolds numbers of engineering conditions. Even large-eddy simulation is a challenge because the locally largest scales are so small relative to the nozzle diameter. Model-scale experiments likewise typically have relatively thick near-nozzle shear layers, which potentially hampers their applicability to high-Reynolds-number design. To quantify the sensitivity of the far-field sound to nozzle turbulent-shear-layer conditions, a family of diameter $D$ nozzles is studied in which the exit turbulent boundary layer momentum thickness is varied from $0.0042D$ up to $0.021D$ for otherwise identical flow conditions. Measurements include particle image velocimetry (PIV) to within $0.04D$ of the exit plane and far-field acoustic spectra. The influence of the initial turbulent-shear-layer thickness is pronounced, though it is less significant than the well-known sensitivity of the far-field sound to laminar versus turbulent shear-layer exit conditions. For thicker shear layers, the nominally missing region, where the corresponding thinner shear layer would develop, leads to the noise difference. The nozzle-exit momentum thickness successfully scales the high-frequency radiated sound for nozzles of different sizes and exhaust conditions. Yet, despite this success, the detailed turbulence statistics show distinct signatures of the different nozzle boundary layers from the different nozzles. Still, the different nozzle shear-layer thicknesses and shapes have a similar downstream development, which is consistent with a linear stability analysis of the measured velocity profiles.
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Pei, Binbin, FangBo Li, Zhengyuan Luo, Liang Zhao, and Bofeng Bai. "Dynamics of mixing flow with double-layer density stratification: Enstrophy and vortical structures." Physics of Fluids 34, no. 10 (October 2022): 104107. http://dx.doi.org/10.1063/5.0121554.
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Previous studies on stratified shear layers involving two streams with different densities have been conducted under the Boussinesq approximation, while the combined effect of stratified instability and mean shear in relation to multi-layer density stratification induced by scalar fields remains an unresolved fundamental question. In this paper, the shear-driven mixing flow involving initial double-layer density interfaces due to the compositional differences are numerically investigated, in which the mean shear interacts with Rayleigh–Taylor instability (RTI). Since its critical role in dynamics of shear layers and scalar transport, we focus on the evolution of entrophy and vortical structures. We find that the dynamics of mixing layers are determined by the mean shear and the distance between the initial density stratification. The mean shear and the Kelvin–Helmholtz instability dominate the evolution of shear layers at the initial stage. The increase in mean shear, therefore, is favorable for turbulent mixing, irrespective of effect of RTI. However, once the transition of turbulence occurs, the mean shear becomes weaker and RTI becomes prominent. This promotes the destruction of hairpin vortex and generation of vortex tube. In addition, the interaction of mean shear with RTI becomes weaker with increasing distance between initial density stratification. Furthermore, the viscous dissipation of enstrophy is larger than enstrophy production in the turbulent region due to the effect of RTI. The baroclinic term has the larger contribution in the turbulent region than near the turbulent/non-turbulent interface, which is different from the results of stably stratified flow under the Boussinesq approximation.
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Sleath, J. F. A. "Coastal Bottom Boundary Layers." Applied Mechanics Reviews 48, no. 9 (September 1, 1995): 589–600. http://dx.doi.org/10.1115/1.3023147.
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Turbulent boundary layers in oscillatory flow are reviewed. These boundary layers show a thin inner layer with similar characteristics to wall layers in steady flow. Above this, there is an outer layer which has some characteristics which are the same as those of steady flow outer layers and other characteristics which are different. One difference is that the defect velocity profile does not scale on the shear velocity alone. Also, over rough beds, the turbulence intensity in the outer layer falls off with height in a similar way to oscillating grid turbulence. Transition from laminar to turbulent flow is also reviewed. Combined oscillatory and steady flows are only briefly touched on.
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Watanabe, Tomoaki, Carlos B. da Silva, and Koji Nagata. "Non-dimensional energy dissipation rate near the turbulent/non-turbulent interfacial layer in free shear flows and shear free turbulence." Journal of Fluid Mechanics 875 (July 18, 2019): 321–44. http://dx.doi.org/10.1017/jfm.2019.462.
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The non-dimensional dissipation rate $C_{\unicode[STIX]{x1D700}}=\unicode[STIX]{x1D700}L/u^{\prime 3}$, where $\unicode[STIX]{x1D700}$, $L$ and $u^{\prime }$ are the viscous energy dissipation rate, integral length scale of turbulence and root-mean-square of the velocity fluctuations, respectively, is computed and analysed within the turbulent/non-turbulent interfacial (TNTI) layer using direct numerical simulations of a planar jet, mixing layer and shear free turbulence. The TNTI layer that separates the turbulent and non-turbulent regions exists at the edge of free shear turbulent flows and turbulent boundary layers, and comprises both the viscous superlayer and turbulent sublayer regions. The computation of $C_{\unicode[STIX]{x1D700}}$ is made possible by the introduction of an original procedure, based on local volume averages within spheres of radius $r$, combined with conditional sampling as a function of the location with respect to the TNTI layer. The new procedure allows for a detailed investigation of the scale dependence of several turbulent quantities near the TNTI layer. An important achievement of this procedure consists in permitting the computation of the turbulent integral scale within the TNTI layer, which is shown to be approximately constant. Both the non-dimensional dissipation rate and turbulent Reynolds number $Re_{\unicode[STIX]{x1D706}}$ vary in space within the TNTI layer, where two relations are observed: $C_{\unicode[STIX]{x1D700}}\sim Re_{\unicode[STIX]{x1D706}}^{-1}$ and $C_{\unicode[STIX]{x1D700}}\sim Re_{\unicode[STIX]{x1D706}}^{-2}$. Specifically, whereas the viscous superlayer and part of the turbulent sublayer display $C_{\unicode[STIX]{x1D700}}\sim Re_{\unicode[STIX]{x1D706}}^{-2}$, the remaining of the turbulent sublayer exhibits $C_{\unicode[STIX]{x1D700}}\sim Re_{\unicode[STIX]{x1D706}}^{-1}$, which is consistent with non-equilibrium turbulence (Vassilicos, Annu. Rev. Fluid Mech. vol. 47, 2015, pp. 95–114).
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Muppidi, Suman, and Krishnan Mahesh. "Direct numerical simulations of roughness-induced transition in supersonic boundary layers." Journal of Fluid Mechanics 693 (January 6, 2012): 28–56. http://dx.doi.org/10.1017/jfm.2011.417.
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AbstractDirect numerical simulations are used to study the laminar to turbulent transition of a Mach 2.9 supersonic flat plate boundary layer flow due to distributed surface roughness. Roughness causes the near-wall fluid to slow down and generates a strong shear layer over the roughness elements. Examination of the mean wall pressure indicates that the roughness surface exerts an upward impulse on the fluid, generating counter-rotating pairs of streamwise vortices underneath the shear layer. These vortices transport near-wall low-momentum fluid away from the wall. Along the roughness region, the vortices grow stronger, longer and closer to each other, and result in periodic shedding. The vortices rise towards the shear layer as they advect downstream, and the resulting interaction causes the shear layer to break up, followed quickly by a transition to turbulence. The mean flow in the turbulent region shows a good agreement with available data for fully developed turbulent boundary layers. Simulations under varying conditions show that, where the shear is not as strong and the streamwise vortices are not as coherent, the flow remains laminar.
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Gan, X., M. Kilic, and J. M. Owen. "Flow Between Contrarotating Disks." Journal of Turbomachinery 117, no. 2 (April 1, 1995): 298–305. http://dx.doi.org/10.1115/1.2835659.
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The paper describes a combined experimental and computational study of laminar and turbulent flow between contrarotating disks. Laminar computations produce Batchelor-type flow: Radial outflow occurs in boundary layers on the disks and inflow is confined to a thin shear layer in the midplane; between the boundary layers and the shear layer, two contrarotating cores of fluid are formed. Turbulent computations (using a low-Reynolds-number k–ε turbulence model) and LDA measurements provide no evidence for Batchelor-type flow, even for rotational Reynolds numbers as low as 2.2 × 104. While separate boundary layers are formed on the disks, radial inflow occurs in a single interior core that extends between the two boundary layers; in the core, rotational effects are weak. Although the flow in the core was always found to be turbulent, the flow in the boundary layers could remain laminar for rotational Reynolds numbers up to 1.2 × 105. For the case of a superposed outflow, there is a source region in which the radial component of velocity is everywhere positive; radially outward of this region, the flow is similar to that described above. Although the turbulence model exhibited premature transition from laminar to turbulent flow in the boundary layers, agreement between the computed and measured radial and tangential components of velocity was mainly good over a wide range of nondimensional flow rates and rotational Reynolds numbers.
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Brown, Garry L., and Anatol Roshko. "Turbulent shear layers and wakes." Journal of Turbulence 13 (January 2012): N51. http://dx.doi.org/10.1080/14685248.2012.723805.
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CARSTENSEN, STEFAN, B. MUTLU SUMER, and JØRGEN FREDSØE. "Coherent structures in wave boundary layers. Part 1. Oscillatory motion." Journal of Fluid Mechanics 646 (March 8, 2010): 169–206. http://dx.doi.org/10.1017/s0022112009992825.
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This work concerns oscillatory boundary layers over smooth beds. It comprises combined visual and quantitative techniques including bed shear stress measurements. The experiments were carried out in an oscillating water tunnel. The experiments reveal two significant coherent flow structures: (i) Vortex tubes, essentially two-dimensional vortices close to the bed extending across the width of the boundary-layer flow, caused by an inflectional-point shear layer instability. The imprint of these vortices in the bed shear stress is a series of small, insignificant kinks and dips. (ii) Turbulent spots, isolated arrowhead-shaped areas close to the bed in an otherwise laminar boundary layer where the flow ‘bursts’ with violent oscillations. The emergence of the turbulent spots marks the onset of turbulence. Turbulent spots cause single or multiple violent spikes in the bed shear stress signal, which has profound implications for sediment transport (in both the laboratory and the field). The experiments also show that similar coherent flow structures exist in the case of combined oscillatory flow and current.
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Elsinga, G. E., and C. B. da Silva. "How the turbulent/non-turbulent interface is different from internal turbulence." Journal of Fluid Mechanics 866 (March 5, 2019): 216–38. http://dx.doi.org/10.1017/jfm.2019.85.
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The average patterns of the velocity and scalar fields near turbulent/non-turbulent interfaces (TNTI), obtained from direct numerical simulations (DNS) of planar turbulent jets and shear free turbulence, are assessed in the strain eigenframe. These flow patterns help to clarify many aspects of the flow dynamics, including a passive scalar, near a TNTI layer, that are otherwise not easily and clearly assessed. The averaged flow field near the TNTI layer exhibits a saddle-node flow topology associated with a vortex in one half of the interface, while the other half of the interface consists of a shear layer. This observed flow pattern is thus very different from the shear-layer structure consisting of two aligned vortical motions bounded by two large-scale regions of uniform flow, that typically characterizes the average strain field in the fully developed turbulent regions. Moreover, strain dominates over vorticity near the TNTI layer, in contrast to internal turbulence. Consequently, the most compressive principal straining direction is perpendicular to the TNTI layer, and the characteristic 45-degree angle displayed in internal shear layers is not observed at the TNTI layer. The particular flow pattern observed near the TNTI layer has important consequences for the dynamics of a passive scalar field, and explains why regions of particularly high scalar gradient (magnitude) are typically found at TNTIs separating fluid with different levels of scalar concentration. Finally, it is demonstrated that, within the fully developed internal turbulent region, the scalar gradient exhibits an angle with the most compressive straining direction with a peak probability at around 20$^{\text{o}}$. The scalar gradient and the most compressive strain are not preferentially aligned, as has been considered for many years. The misconception originated from an ambiguous definition of the positive directions of the strain eigenvectors.
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Molinari, John, Patrick Duran, and David Vollaro. "Low Richardson Number in the Tropical Cyclone Outflow Layer." Journal of the Atmospheric Sciences 71, no. 9 (August 28, 2014): 3164–79. http://dx.doi.org/10.1175/jas-d-14-0005.1.
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Abstract Dropsondes from the NOAA G-IV aircraft were used to examine the presence of low bulk Richardson numbers RB in tropical cyclones. At least one 400-m layer above z = 7.5 km exhibited RB < 1 in 96% of the sondes and RB ≤ 0.25 in 35% of the sondes. The latter represent almost certain turbulence. Sondes from major Hurricane Ivan (2004) were examined in detail. Turbulent layers fell into three broad groups. The first was found below cloud base near the edge of the central dense overcast (CDO) where relative humidity fell below 40%. Near-zero static stability existed within the turbulent layer with stability and shear maxima above it. This structure strongly resembled that seen previously from sublimation of precipitation beneath cloud base. The second type of turbulent layer was located within CDO clouds in the upper troposphere and was due almost entirely to near-zero static stability. This most likely arose as a result of cooling via longwave flux divergence below CDO top. The third type of turbulent layer existed well outside the CDO and was produced by large local vertical wind shear. The shear maxima associated with the beneath-cloud and outside-CDO turbulent layers produced a sharp transition from weak inflow below to strong outflow above. The results suggest that the CDO creates its own distinctive stability profile that strongly influences the distribution of turbulence and the transition to outflow in tropical cyclones.
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KIT, E. L. G., E. J. STRANG, and H. J. S. FERNANDO. "Measurement of turbulence near shear-free density interfaces." Journal of Fluid Mechanics 334 (March 10, 1997): 293–314. http://dx.doi.org/10.1017/s0022112096004442.
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The results of an experimental study carried out to investigate the structure of turbulence near a shear-free density interface are presented. The experimental configuration consisted of a two-layer fluid medium in which the lower layer was maintained in a turbulent state by an oscillating grid. The measurements included the root-mean-square (r.m.s.) turbulent velocities, wavenumber spectra, dissipation of turbulent kinetic energy and integral lengthscales. It was found that the introduction of a density interface to a turbulent flow can strongly distort the structure of turbulence near the interface wherein the horizontal velocity components are amplified and the vertical component is damped. The modification of r.m.s velocities is essentially limited to distances smaller than about an integral lengthscale. Inspection of spectra shows that these distortions are felt only at small wavenumbers of the order of the integral scale and a range of low-wavenumbers of the inertial subrange; the distortions become pronounced as the interface is approached. Comparison of the horizontal velocity data with the rapid distortion theory (RDT) analyses of Hunt & Graham (1978) and Hunt (1984) showed a qualitative agreement near the interface and a quantitative agreement away from the interface. On the other hand, the RDT predictions for the vertical component were in general agreement with the data. The near-interface horizontal velocity data, however, showed quantitative agreement with a model proposed by Hunt (1984) based on nonlinear vortex dynamics near the interface. The effects due to interfacial waves appear to be important for distances less than about 10% of the integral lengthscale. As a consequence of the non-zero energy flux divergence, the introduction of a density interface to oscillating grid turbulence increases the rate of dissipation in the turbulent layer except near the interface, where a sharp drop occurs. The present measurements provide useful information on the structure of turbulence in shear-free boundary layers, such as atmospheric and oceanic convective boundary layers, thus improving modelling capabilities for such flows.
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Watanabe, Tomoaki, and Koji Nagata. "Energetics and vortex structures near small-scale shear layers in turbulence." Physics of Fluids 34, no. 9 (September 2022): 095114. http://dx.doi.org/10.1063/5.0099959.
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Vortices and kinetic energy distributions around small-scale shear layers are investigated with direct numerical simulations of isotropic turbulence. The shear layers are examined with the triple decomposition of a velocity gradient tensor. The shear layers subject to a biaxial strain appear near vortices with rotation, which induce energetic flow that contributes to the shear. A similar configuration of rotating motions near the shear layers is observed in a multi-scale random velocity field, which is free from the dynamics of turbulence. Therefore, the mechanism that sustains shearing motion is embedded as a kinematic nature in random velocity fields. However, the biaxial strain is absent near the shear layers in random velocity because rotating motions appear right next to the shear layers. When a random velocity field begins to evolve following the Navier–Stokes equations, the shear layers are immediately tilted to the nearby rotating motions. This misalignment is a key for the vortex to generate the compressive strain of the biaxial strain around the shear layer. As the configuration of shearing and rotating motions arises from the kinematic nature, the shear layers with the biaxial strain are formed within a few times the Kolmogorov timescale once the random velocity field begins to evolve. The analysis with high-pass filtered random velocity suggests that this shear layer evolution is caused by small-scale turbulent motions. These results indicate that the kinematic nature of shear and rotation in velocity fluctuations has a significant role in the formation of shear layers in turbulence.
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Mislevy, S. P., and T. Wang. "The Effects of Adverse Pressure Gradients on Momentum and Thermal Structures in Transitional Boundary Layers: Part 2—Fluctuation Quantities." Journal of Turbomachinery 118, no. 4 (October 1, 1996): 728–36. http://dx.doi.org/10.1115/1.2840928.
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The effects of adverse pressure gradients on the thermal and momentum characteristics of a heated transitional boundary layer were investigated with free-stream turbulence ranging from 0.3 to 0.6 percent. Boundary layer measurements were conducted for two constant-K cases, K1 = −0.51 × 10−6 and K2 = −1.05 × 10−6. The fluctuation quantities, u′, ν′, t′, the Reynolds shear stress (uν), and the Reynolds heat fluxes (νt and ut) were measured. In general, u′/U∞, ν′/U∞, and νt have higher values across the boundary layer for the adverse pressure-gradient cases than they do for the baseline case (K = 0). The development of ν′ for the adverse pressure gradients was more actively involved than that of the baseline. In the early transition region, the Reynolds shear stress distribution for the K2 case showed a near-wall region of high-turbulent shear generated at Y+ = 7. At stations farther downstream, this near-wall shear reduced in magnitude, while a second region of high-turbulent shear developed at Y+ = 70. For the baseline case, however, the maximum turbulent shear in the transition region was generated at Y+ = 70, and no near-wall high-shear region was seen. Stronger adverse pressure gradients appear to produce more uniform and higher t′ in the near-wall region (Y+ < 20) in both transitional and turbulent boundary layers. The instantaneous velocity signals did not show any clear turbulent/nonturbulent demarcations in the transition region. Increasingly stronger adverse pressure gradients seemed to produce large non turbulent unsteadiness (or instability waves) at a similar magnitude as the turbulent fluctuations such that the production of turbulent spots was obscured. The turbulent spots could not be identified visually or through conventional conditional-sampling schemes. In addition, the streamwise evolution of eddy viscosity, turbulent thermal diffusivity, and Prt, are also presented.
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Volino, R. J., and T. W. Simon. "Boundary Layer Transition Under High Free-Stream Turbulence and Strong Acceleration Conditions: Part 2—Turbulent Transport Results." Journal of Heat Transfer 119, no. 3 (August 1, 1997): 427–32. http://dx.doi.org/10.1115/1.2824115.
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Measurements from heated boundary layers along a concave-curved test wall subject to high (initially 8 percent) free-stream turbulence intensity and strong (K = (ν/U∞2 dU∞/dx, as high as 9 × 10−6) acceleration are presented and discussed. Conditions for the experiments were chosen to simulate those present on the downstream half of the pressure side of a gas turbine airfoil. Turbulence statistics, including the turbulent shear stress, the turbulent heat flux, and the turbulent Prandtl number are presented. The transition zone is of extended length in spite of the high free-stream turbulence level. Turbulence quantities are strongly suppressed below values in unaccelerated turbulent boundary layers. Turbulent transport quantities rise with the intermittency, as the boundary layer proceeds through transition. Octant analysis shows a similar eddy structure in the present flow as was observed in transitional flows under low free-stream turbulence conditions. To the authors’ knowledge, this is the first detailed documentation of a high-free-stream-turbulence boundary layer flow in such a strong acceleration field.
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Park, Seung-Bu, Jong-Jin Baik, and Beom-Soon Han. "Role of Wind Shear in the Decay of Convective Boundary Layers." Atmosphere 11, no. 6 (June 12, 2020): 622. http://dx.doi.org/10.3390/atmos11060622.
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The role of wind shear in the decay of the convective boundary layer (CBL) is systematically investigated using a series of large-eddy simulations. Nine CBLs with weak, intermediate, and strong wind shear are simulated, and their decays after stopping surface heat flux are investigated. After the surface heat flux is stopped, the boundary-layer-averaged turbulent kinetic energy (TKE) stays constant for almost one convective time scale and then decreases following a power law. While the decrease persists until the end of the simulation in the buoyancy-dominated (weak-shear) cases, the TKE in the other cases decreases slowly or even increases to a level which can be maintained by wind shear. In the buoyancy-dominated cases, convective cells occur, and they decay and oscillate over time. The oscillation of vertical velocity is not distinct in the other cases, possibly because wind shear disturbs the reversal of vertical circulations. The oscillations are detected again in the profiles of vertical turbulent heat flux in the buoyancy-dominated cases. In the strong-shear cases, mechanical turbulent eddies are generated, which transport heat downward in the lower boundary layers when convective turbulence decays significantly. The time series of vertical velocity skewness demonstrates the shear-dependent flow characteristics of decaying CBLs.
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Watanabe, Tomoaki, James J. Riley, Koji Nagata, Keigo Matsuda, and Ryo Onishi. "Hairpin vortices and highly elongated flow structures in a stably stratified shear layer." Journal of Fluid Mechanics 878 (September 4, 2019): 37–61. http://dx.doi.org/10.1017/jfm.2019.577.
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Turbulent structures in stably stratified shear layers are studied with direct numerical simulation. Flow visualization confirms the existence of hairpin vortices and highly elongated structures with positive and negative velocity fluctuations, whose streamwise lengths divided by the layer thickness are $O(10^{0})$ and $O(10^{1})$, respectively. The flow at the wavelength related to these structures makes a large contribution to turbulent kinetic energy. These structures become prominent in late time, but with small buoyancy Reynolds numbers indicating suppression of turbulent mixing. Active turbulent mixing associated with the hairpin vortices, however, does occur. The structures and the vertical profile of the integral shear parameter show connections between stable stratified shear layers and wall-bounded shear flows.
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Ji (季索清), Suoqing, S. Peng Oh, and Phillip Masterson. "Simulations of radiative turbulent mixing layers." Monthly Notices of the Royal Astronomical Society 487, no. 1 (May 9, 2019): 737–54. http://dx.doi.org/10.1093/mnras/stz1248.
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ABSTRACTRadiative turbulent mixing layers should be ubiquitous in multi-phase gas with shear flow. They are a potentially attractive explanation for the high ions such as O vi seen in high-velocity clouds and the circumgalactic medium (CGM) of galaxies. We perform 3D magnetohydrohynamics (MHD) simulations with non-equilibrium (NEI) and photoionization modelling, with an eye towards testing simple analytic models. Even purely hydrodynamic collisional ionization equilibrium (CIE) calculations have column densities much lower than observations. Characteristic inflow and turbulent velocities are much less than the shear velocity, and the layer width $h \propto t_{\mathrm{cool}}^{1/2}$ rather than h ∝ tcool. Column densities are not independent of density or metallicity as analytic scalings predict, and show surprisingly weak dependence on shear velocity and density contrast. Radiative cooling, rather than Kelvin–Helmholtz instability, appears paramount in determining the saturated state. Low pressure due to fast cooling both seeds turbulence and sets the entrainment rate of hot gas, whose enthalpy flux, along with turbulent dissipation, energizes the layer. Regardless of initial geometry, magnetic fields are amplified and stabilize the mixing layer via magnetic tension, producing almost laminar flow and depressing column densities. NEI effects can boost column densities by factors of a few. Suppression of cooling by NEI or photoionization can, in principle, also increase O vi column densities, but, in practice, is unimportant for CGM conditions. To explain observations, sightlines must pierce hundreds or thousands of mixing layers, which may be plausible if the CGM exists as a ‘fog’ of tiny cloudlets.
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Umlauf, Lars. "The Description of Mixing in Stratified Layers without Shear in Large-Scale Ocean Models." Journal of Physical Oceanography 39, no. 11 (November 1, 2009): 3032–39. http://dx.doi.org/10.1175/2009jpo4006.1.
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Abstract Large-scale geophysical flows often exhibit layers with negligible vertical shear and infinite gradient Richardson number Ri. It is well known that these layers may be regions of active mixing, even in the absence of local shear production of turbulence because, among other processes, turbulence may be supplied by vertical turbulent transport from neighboring regions. This observation is contrasted by the behavior of most turbulence parameterizations used in ocean climate modeling, predicting the collapse of mixing of mass and matter if the Richardson number exceeds a critical threshold. Here, the performance of a simple model without critical Richardson number is evaluated, taking into account the diffusion of turbulence into layers without shear production and therefore avoiding the suppression of mixing at large values of Ri. The model is based on the framework of second-moment turbulence closures, focusing on the consistent modeling of the turbulent length scale for strongly stratified turbulence. Results are compared to eddy-resolving simulations of stratified shear flows that have recently become available. The model is simple enough for inclusion in ocean climate models.
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Barrett, Michael J., and D. Keith Hollingsworth. "On the Calculation of Length Scales for Turbulent Heat Transfer Correlation." Journal of Heat Transfer 123, no. 5 (December 18, 2000): 878–83. http://dx.doi.org/10.1115/1.1391277.
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Turbulence length scale calculation methods were critically reviewed for their usefulness in boundary layer heat transfer correlations. Using the variance of the streamwise velocity and the dissipation spectrum, a rigorous method for calculating an energy-based integral scale was introduced. A principal advantage of the new method is the capability to calculate length scales in a low-Reynolds-number turbulent boundary layer. The method was validated with data from grid-generated, free-shear-layer, and wall-bounded turbulence. Length scales were calculated in turbulent boundary layers with momentum thickness Reynolds numbers from 400 to 2100 and in flows with turbulent Reynolds numbers as low as 90.
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Perera, M. J. A. M., H. J. S. Fernando, and D. L. Boyer. "Turbulent mixing at an inversion layer." Journal of Fluid Mechanics 267 (May 25, 1994): 275–98. http://dx.doi.org/10.1017/s0022112094001187.
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A series of laboratory experiments was carried out to examine the interaction between stratification and turbulence at an inversion layer, with the objective of gaining insight into certain wave–turbulence encounters in the atmosphere. A three-layer stratified fluid system, consisting of a (thick) strongly stratified inversion layer, sandwiched between an upper turbulent layer and a lower non-turbulent weakly stratified layer, was employed. Oscillating-grid-induced shear-free turbulence was used in the upper layer. During the experiments, a fourth (interfacial) layer developed in the region between the inversion and the turbulent layer, and most of the wave–turbulence interactions were confined to this layer. Detailed measurements of the vertical velocity structure, internal-wave parameters and mixing characteristics were made in the stratified layers and, whenever possible, the results were compared to available theoretical predictions.
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MacKinnon, J. A., and M. C. Gregg. "Spring Mixing: Turbulence and Internal Waves during Restratification on the New England Shelf." Journal of Physical Oceanography 35, no. 12 (December 1, 2005): 2425–43. http://dx.doi.org/10.1175/jpo2821.1.
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Abstract Integrated observations are presented of water property evolution and turbulent microstructure during the spring restratification period of April and May 1997 on the New England continental shelf. Turbulence is shown to be related to surface mixed layer entrainment and shear from low-mode near-inertial internal waves. The largest turbulent diapycnal diffusivity and associated buoyancy fluxes were found at the bottom of an actively entraining and highly variable wind-driven surface mixed layer. Away from surface and bottom boundary layers, turbulence was systematically correlated with internal wave shear, though the nature of that relationship underwent a regime shift as the stratification strengthened. During the first week, while stratification was weak, the largest turbulent dissipation away from boundaries was coincident with shear from mode-1 near-inertial waves generated by passing storms. Wave-induced Richardson numbers well below 0.25 and density overturning scales of several meters were observed. Turbulent dissipation rates in the region of peak shear were consistent in magnitude with several dimensional scalings. The associated average diapycnal diffusivity exceeded 10−3 m2 s−1. As stratification tripled, Richardson numbers from low-mode internal waves were no longer critical, though turbulence was still consistently elevated in patches of wave shear. Kinematically, dissipation during this period was consistent with the turbulence parameterization proposed by MacKinnon and Gregg, based on a reinterpretation of wave–wave interaction theory. The observed growth of temperature gradients was, in turn, consistent with a simple one-dimensional model that vertically distributed surface heat fluxes commensurate with calculated turbulent diffusivities.
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Johnston, J. P., and K. A. Flack. "Review—Advances in Three-Dimensional Turbulent Boundary Layers With Emphasis on the Wall-Layer Regions." Journal of Fluids Engineering 118, no. 2 (June 1, 1996): 219–32. http://dx.doi.org/10.1115/1.2817367.
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Current information concerning three-dimensional turbulent boundary layers is discussed. Several topics are presented including (i) a detailed description of eleven experiments published since 1990. In nine cases cross flows are controlled by pressure gradients imposed from the freestream, but in two cases the cross flows are wall-shear-driven. The other topics include (ii) an examination of state of the art in measurement techniques; (iii) a look at some issues and ideas in turbulence modeling; and (iv) an introduction to new work on the visualization and description of quasicoherent structures (high/low-speed streaks and turbulent vortices) in three-dimensional turbulent boundary layers.
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Gat, Ilana, Georgios Matheou, Daniel Chung, and Paul E. Dimotakis. "Incompressible variable-density turbulence in an external acceleration field." Journal of Fluid Mechanics 827 (August 24, 2017): 506–35. http://dx.doi.org/10.1017/jfm.2017.490.
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Dynamics and mixing of a variable-density turbulent flow subject to an externally imposed acceleration field in the zero-Mach-number limit are studied in a series of direct numerical simulations. The flow configuration studied consists of alternating slabs of high- and low-density fluid in a triply periodic domain. Density ratios in the range of $1.05\leqslant R\equiv \unicode[STIX]{x1D70C}_{1}/\unicode[STIX]{x1D70C}_{2}\leqslant 10$ are investigated. The flow produces temporally evolving shear layers. A perpendicular density–pressure gradient is maintained in the mean as the flow evolves, with multi-scale baroclinic torques generated in the turbulent flow that ensues. For all density ratios studied, the simulations attain Reynolds numbers at the beginning of the fully developed turbulence regime. An empirical relation for the convection velocity predicts the observed entrainment-ratio and dominant mixed-fluid composition statistics. Two mixing-layer temporal evolution regimes are identified: an initial diffusion-dominated regime with a growth rate ${\sim}t^{1/2}$ followed by a turbulence-dominated regime with a growth rate ${\sim}t^{3}$. In the turbulent regime, composition probability density functions within the shear layers exhibit a slightly tilted (‘non-marching’) hump, corresponding to the most probable mole fraction. The shear layers preferentially entrain low-density fluid by volume at all density ratios, which is reflected in the mixed-fluid composition.
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Lyn, D. A., and W. Rodi. "The flapping shear layer formed by flow separation from the forward corner of a square cylinder." Journal of Fluid Mechanics 267 (May 25, 1994): 353–76. http://dx.doi.org/10.1017/s0022112094001217.
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The turbulent shear layer and the associated recirculation region on the sidewall formed in flow separation from the forward corner of a square cylinder have been studied with one-component laser-Doppler velocimetry. Because of vortex shedding, the flow is approximately periodic, and is treated as a separated flow undergoing largeamplitude forcing at the shedding frequency. Phase (ensemble)-averaged velocities and turbulence intensities were obtained, and a close relationship in phase and amplitude between phase-averaged turbulence intensities and gradients of phase-averaged velocity is found in much of the flow region. The similarity behaviour of the phase-averaged profiles in the shear layer as well as the streamwise growth of the shear layer are investigated. While phase-averaged velocity profiles collapse well in similarity coordinates, normalized turbulence intensities exhibit systematic deviations from similarity. Shear-layer growth also departs markedly from the linear growth law of unforced plane mixing layers. The effect of the recirculation is suggested as a possible explanation for some of these deviations. Similarities to and differences from steady and forced mixing layers, steady separated flows with recirculation, and unsteady boundary layers are discussed.
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Schetz, Joseph A. "Turbulent Shear Layers in Supersonic Flow." AIAA Journal 36, no. 5 (May 1998): 879–80. http://dx.doi.org/10.2514/2.455.
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Benham, Graham P., Alfonso A. Castrejon-Pita, Ian J. Hewitt, Colin P. Please, Rob W. Style, and Paul A. D. Bird. "Turbulent shear layers in confining channels." Journal of Turbulence 19, no. 6 (April 20, 2018): 431–45. http://dx.doi.org/10.1080/14685248.2018.1459630.
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Jović, Srba. "Recovery of reattached turbulent shear layers." Experimental Thermal and Fluid Science 17, no. 1-2 (May 1998): 57–62. http://dx.doi.org/10.1016/s0894-1777(97)10049-8.
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Alboussière, T., V. Uspenski, and R. Moreau. "Quasi-2D MHD turbulent shear layers." Experimental Thermal and Fluid Science 20, no. 1 (September 1999): 19–24. http://dx.doi.org/10.1016/s0894-1777(99)00023-0.
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WONG, A. B. D., R. W. GRIFFITHS, and G. O. HUGHES. "Shear layers driven by turbulent plumes." Journal of Fluid Mechanics 434 (May 10, 2001): 209–41. http://dx.doi.org/10.1017/s002211200100355x.
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A turbulent plume from a continuous source of buoyancy in a long tank is shown to generate a series of quasi-steady counterflowing horizontal shear layers throughout the tank. Both the horizontal flow velocity and the depth of the shear layers are observed to decrease with distance above/below the plume outflow. The shear layers are supported by the stable density stratification produced by the plume and are superimposed on the vertical advection and entrainment inflow that make up the so-called ‘filling box’ circulation. Thus, at some depths, the surrounding water flows away from the plume instead of being entrained, although we see no evidence of ‘detrainment’ of dense plume water. Given the stratification produced by the plume at large times, the timescale for the velocity structure to adjust to changes in forcing is proportional to the time for long internal gravity waves to travel the length of the tank. The shear layers are interpreted in terms of internal normal modes that are excited by, and which in turn determine, the horizontal plume outflow. The sixth and seventh baroclinic modes typically dominate because at the level of the plume outflow their phase speed is approximately equal and opposite to the vertical advection in the ‘filling box’. Also, the approximate balance between phase speed and advection is found to hold throughout the tank, resulting in the observed quasi-steady flow structure. Viscosity causes the horizontal velocity in the shear layers to decrease with distance above/below the plume outflow, and is thought to be responsible for a low-frequency oscillation in the flow structure that is observed during experiments.
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Geurts, Bernard J. "Mixing efficiency in turbulent shear layers." Journal of Turbulence 2 (January 2001): N17. http://dx.doi.org/10.1088/1468-5248/2/1/017.
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Hunt, J. C. R. "Studying turbulence using direct numerical simulation: 1987 Center for Turbulence Research NASA Ames/Stanford Summer Programme." Journal of Fluid Mechanics 190 (May 1988): 375–92. http://dx.doi.org/10.1017/s0022112088001363.
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This paper is an account of a summer programme for the study of the ideas and models of turbulent flows, using the results of direct numerical stimulations of the Navier-Stokes equations. These results had been obtained on the computers and stored as accessible databases at the Center for Turbulence Research (CTR) of NASA Ames Research Center and Stanford University. At this first summer programme, some 32 visiting researchers joined those at the CTR to test hypotheses and models in five aspects of turbulence research: turbulence decomposition, bifurcation and chaos; two-point closure (or k-space) modelling; structure of turbulent boundary layers; Reynolds-stress modelling; scalar transport and reacting flows.A number of new results emerged including: computation of space and space-time correlations in isotropic turbulence can be related to each other and modelled in terms of the advection of small scales by large-scale motion; the wall layer in turbulent boundary layers is dominated by shear layers which protrude into the outer layers, and have long lifetimes; some aspects of the ejection mechanism for these layers can be described in terms of the two-dimensional finite-amplitude Navier-Stokes solutions; a self-similar form of the two-point, cross-correlation data of the turbulence in boundary layers (when normalized by the r.m.s. value at the furthest point from the wall) shows how both the blocking of eddies by the wall and straining by the mean shear control the lengthscales; the intercomponent transfer (pressure-strain) is highly localized in space, usually in regions of concentrated vorticity; conditioned pressure gradients are linear in the conditioning of velocity and independent of vorticity in homogeneous shear flow; some features of coherent structures in the boundary layer are similar to experimental measurements of structures in mixing-layers, jets and wakes.The availability of comprehensive velocity and pressure data certainly helps the investigation of concepts and models. But a striking feature of the summer programme was the diversity of interpretation of the same computed velocity fields. There are few signs of any convergence in turbulence research! But with new computational facilities the divergent approaches can at least be related to each other.
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Gu, Li, Hang Yuan, Qiu Lan Li, Zi Nan Jiao, and Lan Lan Wang. "Section Turbulent Distribution of the Stratified Shear Flow in the Braided River." Applied Mechanics and Materials 665 (October 2014): 459–63. http://dx.doi.org/10.4028/www.scientific.net/amm.665.459.
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The turbulent characteristics of stratified shear flow in braided rivers with different velocities in upper and lower layers are not clear at present. The physical model of a typical braided river was conducted to study its sectional turbulence intensity distribution. The model has a mid-bar between two symmetrical anabranches. The transverse distribution, the vertical distribution and the whole section distribution of turbulent intensity were analyzed. The strong turbulent intensity occurred in the interface of upper and lower layers and the boundary zone of the high velocity and low velocity near outer bank. As the flow moved downstream, the strong area of turbulent intensity had a trend moving from the outer bank to the inner bank, and then the turbulent intensity decreased and mixed uniformly.
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WU, XIAOHUA, and KYLE D. SQUIRES. "Numerical investigation of the turbulent boundary layer over a bump." Journal of Fluid Mechanics 362 (May 10, 1998): 229–71. http://dx.doi.org/10.1017/s0022112098008982.
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Large-eddy simulation (LES) has been used to calculate the flow of a statistically two-dimensional turbulent boundary layer over a bump. Subgrid-scale stresses in the filtered Navier–Stokes equations were closed using the dynamic eddy viscosity model. LES predictions for a range of grid resolutions were compared to the experimental measurements of Webster et al. (1996). Predictions of the mean flow and turbulence intensities are in good agreement with measurements. The resolved turbulent shear stress is in reasonable agreement with data, though the peak is over-predicted near the trailing edge of the bump. Analysis of the flow confirms the existence of internal layers over the bump surface upstream of the summit and along the downstream trailing at plate, and demonstrates that the quasi-step increases in skin friction due to perturbations in pressure gradient and surface curvature selectively enhance near-wall shear production of turbulent stresses and are responsible for the formation of the internal layers. Though the flow experiences a strong adverse pressure gradient along the rear surface, the boundary layer is unique in that intermittent detachment occurring near the wall is not followed by mean-flow separation. Certain turbulence characteristics in this region are similar to those previously reported in instantaneously separating boundary layers. The present investigation also explains the driving mechanism for the surprisingly rapid return to equilibrium over the trailing flat plate found in the measurements of Webster et al. (1996), i.e. the simultaneous uninterrupted development of an inner energy-equilibrium region and the monotonic decay of elevated turbulence shear production away from the wall. LES results were also used to examine response of the dynamic eddy viscosity model. While subgrid-scale dissipation decreases/increases as the turbulence is attenuated/enhanced, the ratio of the (averaged) forward to reverse energy transfers predicted by the model is roughly constant over a significant part of the layer. Model predictions of backscatter, calculated as the percentage of points where the model coefficient is negative, show a rapid recovery downstream similar to the mean-flow and turbulence quantities.
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Volino, Ralph J., and Terrence W. Simon. "Spectral Measurements in Transitional Boundary Layers on a Concave Wall Under High and Low Free-Stream Turbulence Conditions." Journal of Turbomachinery 122, no. 3 (August 1, 1997): 450–57. http://dx.doi.org/10.1115/1.1303075.
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The relationship between free-stream turbulence and boundary layer behavior has been investigated using spectral measurements. The power spectral densities of turbulence quantities in transitional and fully turbulent boundary layers were computed and compared to the power spectra of the same quantities measured in the free stream. Comparisons were made using the “transfer function.” The transfer function is the ratio of two spectra at each frequency in the spectra. Comparisons were done in flows with low (0.6 percent) and high (8 percent) free-stream turbulence intensities. Evidence was gathered that suggests that relatively low-frequency, large-scale eddies in the free stream buffet the boundary layer, causing boundary layer unsteadiness at the same low frequencies. These fluctuations are present in both transitional and fully turbulent boundary layers. They are seen under both high and low free-stream turbulence conditions, although they are stronger in the high-turbulence case. Examination of the turbulent shear stress suggests that the low-frequency fluctuations enhance transport in the boundary layer but they are not so effective in promoting eddy transport as are turbulent eddies produced and residing within the boundary layer. In the fully-turbulent boundary layer, higher-frequency fluctuations are added to the low-frequency unsteadiness. These higher-frequency fluctuations, not seen in the transitional boundary layer, are associated with turbulence production in the boundary layer and appear not to be directly related to free-stream unsteadiness. [S0889-504X(00)00403-7]
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Naqavi, Iftekhar Z., James C. Tyacke, and Paul G. Tucker. "Direct numerical simulation of a wall jet: flow physics." Journal of Fluid Mechanics 852 (August 8, 2018): 507–42. http://dx.doi.org/10.1017/jfm.2018.503.
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A direct numerical simulation (DNS) of a plane wall jet is performed at a Reynolds number of $Re_{j}=7500$. The streamwise length of the domain is long enough to achieve self-similarity for the mean flow and the Reynolds shear stress. This is the highest Reynolds number wall jet DNS for a large domain achieved to date. The high resolution simulation reveals the unsteady flow field in great detail and shows the transition process in the outer shear layer and inner boundary layer. Mean flow parameters of maximum velocity decay, wall shear stress, friction coefficient and jet spreading rate are consistent with several other studies reported in the literature. Mean flow, Reynolds normal and shear stress profiles are presented with various scalings, revealing the self-similar behaviour of the wall jet. The Reynolds normal stresses do not show complete similarity for the given Reynolds number and domain length. Previously published inner layer budgets based on LES are inaccurate and those that have been measured are only available in the outer layer. The current DNS provides fully balanced, explicitly calculated budgets for the turbulence kinetic energy, Reynolds normal stresses and Reynolds shear stress in both the inner and outer layers. The budgets are scaled with inner and outer variables. The inner-scaled budgets in the near wall region show great similarity with turbulent boundary layers. The only remarkable difference is for the turbulent diffusion in the wall-normal Reynolds stress and Reynolds shear stress budgets. The outer layer interacts with the inner layer through turbulent diffusion and the excess energy from the wall-normal direction is transferred to the spanwise direction.
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Ali, Sk Zeeshan, and Subhasish Dey. "Origin of the scaling laws of developing turbulent boundary layers." Physics of Fluids 34, no. 7 (July 2022): 071402. http://dx.doi.org/10.1063/5.0096255.
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In this Perspective article, we seek the origin of the scaling laws of developing turbulent boundary layers over a flat plate from the perspective of the phenomenological theory of turbulence. The scaling laws of the boundary-layer thickness and the boundary shear stress in rough and smooth boundary-layer flows are established. In a rough boundary-layer flow, the boundary-layer thickness (scaled with the boundary roughness) and the boundary shear stress (scaled with the dynamic pressure) obey the “2/(1− σ)” and “(1+ σ)/(1− σ)” scaling laws, respectively, with the streamwise distance (scaled with the boundary roughness). Here, σ is the spectral exponent. In a smooth boundary-layer flow, the boundary-layer thickness (scaled with the viscous length scale) and the boundary shear stress (scaled with the dynamic pressure) obey the “8/(5 − 3 σ)” and “3(1+ σ)/(5 − 3 σ)” scaling laws, respectively, with the Reynolds number characterized by the streamwise distance.
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Briggs, D. A., J. H. Ferziger, J. R. Koseff, and S. G. Monismith. "Entrainment in a shear-free turbulent mixing layer." Journal of Fluid Mechanics 310 (March 10, 1996): 215–41. http://dx.doi.org/10.1017/s0022112096001784.
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Results from a direct numerical simulation of a shear-free turbulent mixing layer are presented. The mixing mechanisms associated with the turbulence are isolated. In the first set of simulations, the turbulent mixing layer decays as energy is exchanged between the layers. Energy spectra with E(k) ∼ k2 and E(k) ∼ k4 dependence at low wavenumber are used to initialize the flow to investigate the effect of initial conditions. The intermittency of the mixing layer is quantified by the skewness and kurtosis of the velocity fields: results compare well with the shearless mixing layer experiments of Veeravalli & Warhaft (1989). Eddies of size of the integral scale (k3/2/∈) penetrate the mixing layer intermittently, transporting energy and causing the layer to grow. The turbulence in the mixing layer can be characterized by eddies with relatively large vertical kinetic energy and vertical length scale. In the second set of simulations, a forced mixing layer is created by continuously supplying energy in a local region to maintain a stationary kinetic energy profile. Assuming the spatial decay of r.m.s. velocity is of the form u &∞ yn, predictions of common two-equation turbulence models yield values of n ranging from -1.25 to -2.5. An exponent of -1.35 is calculated from the forced mixing layer simulation. In comparison, oscillating grid experiments yield decay exponents between n = -1 (Hannoun et al. 1989) and n = -1.5 (Nokes 1988). Reynolds numbers of 40 and 58, based on Taylor microscale, are obtained in the decaying and forced simulations, respectively. Components of the turbulence models proposed by Mellor & Yamada (1986) and Hanjalić & Launder (1972) are analysed. Although the isotropic models underpredict the turbulence transport, more complicated anisotropic models do not represent a significant improvement. Models for the pressure-strain tensor, based on the anisotropy tensor, performed adequately.
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Wu, Xuesong, and Xiuling Zhuang. "Nonlinear dynamics of large-scale coherent structures in turbulent free shear layers." Journal of Fluid Mechanics 787 (December 16, 2015): 396–439. http://dx.doi.org/10.1017/jfm.2015.646.
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Fully developed turbulent free shear layers exhibit a high degree of order, characterized by large-scale coherent structures in the form of spanwise vortex rollers. Extensive experimental investigations show that such organized motions bear remarkable resemblance to instability waves, and their main characteristics, including the length scales, propagation speeds and transverse structures, are reasonably well predicted by linear stability analysis of the mean flow. In this paper, we present a mathematical theory to describe the nonlinear dynamics of coherent structures. The formulation is based on the triple decomposition of the instantaneous flow into a mean field, coherent fluctuations and small-scale turbulence but with the mean-flow distortion induced by nonlinear interactions of coherent fluctuations being treated as part of the organized motion. The system is closed by employing a gradient type of model for the time- and phase-averaged Reynolds stresses of fine-scale turbulence. In the high-Reynolds-number limit, the nonlinear non-equilibrium critical-layer theory for laminar-flow instabilities is adapted to turbulent shear layers by accounting for (1) the enhanced non-parallelism associated with fast spreading of the mean flow, and (2) the influence of small-scale turbulence on coherent structures. The combination of these factors with nonlinearity leads to an interesting evolution system, consisting of coupled amplitude and vorticity equations, in which non-parallelism contributes the so-called translating critical-layer effect. Numerical solutions of the evolution system capture vortex roll-up, which is the hallmark of a turbulent mixing layer, and the predicted amplitude development mimics the qualitative feature of oscillatory saturation that has been observed in a number of experiments. A fair degree of quantitative agreement is obtained with one set of experimental data.
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Schultz, Michael P. "Turbulent Boundary Layers on Surfaces Covered With Filamentous Algae." Journal of Fluids Engineering 122, no. 2 (February 8, 2000): 357–63. http://dx.doi.org/10.1115/1.483265.
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Turbulent boundary layer measurements have been made on surfaces covered with filamentous marine algae. These experiments were conducted in a closed return water tunnel using a two-component, laser Doppler velocimeter (LDV). The mean velocity profiles and parameters, as well as the axial and wall-normal turbulence intensities and Reynolds shear stress, are compared with flows over smooth and sandgrain rough walls. Significant increases in the skin friction coefficient for the algae-covered surfaces were measured. The boundary layer and integral thickness length scales were also increased. The results indicate that profiles of the turbulence quantities for the smooth and sandgrain rough walls collapse when friction velocity and boundary layer thickness are used as normalizing parameters. The algae-covered surfaces, however, exhibited a significant increase in the wall-normal turbulence intensity and the Reynolds shear stress, with only a modest increase in the axial turbulence intensity. The peak in the Reynolds shear stress profiles for the algae surfaces corresponded to the maximum extent of outward movement of the algae filaments. [S0098-2202(00)01902-7]
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Womack, Kristofer M., Charles Meneveau, and Michael P. Schultz. "Comprehensive shear stress analysis of turbulent boundary layer profiles." Journal of Fluid Mechanics 879 (September 27, 2019): 360–89. http://dx.doi.org/10.1017/jfm.2019.673.
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Motivated by the need for accurate determination of wall shear stress from profile measurements in turbulent boundary layer flows, the total shear stress balance is analysed and reformulated using several well-established semi-empirical relations. The analysis highlights the significant effect that small pressure gradients can have on parameters deduced from data even in nominally zero pressure gradient boundary layers. Using the comprehensive shear stress balance together with the log-law equation, it is shown that friction velocity, roughness length and zero-plane displacement can be determined with only velocity and turbulent shear stress profile measurements at a single streamwise location for nominally zero pressure gradient turbulent boundary layers. Application of the proposed analysis to turbulent smooth- and rough-wall experimental data shows that the friction velocity is determined with accuracy comparable to force balances (approximately 1 %–4 %). Additionally, application to boundary layer data from previous studies provides clear evidence that the often cited discrepancy between directly measured friction velocities (e.g. using force balances) and those derived from traditional total shear stress methods is likely due to the small favourable pressure gradient imposed by a fixed cross-section facility. The proposed comprehensive shear stress analysis can account for these small pressure gradients and allows more accurate boundary layer wall shear stress or friction velocity determination using commonly available mean velocity and shear stress profile data from a single streamwise location.
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Mashayek, A., C. P. Caulfield, and W. R. Peltier. "Role of overturns in optimal mixing in stratified mixing layers." Journal of Fluid Mechanics 826 (August 8, 2017): 522–52. http://dx.doi.org/10.1017/jfm.2017.374.
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Turbulent mixing plays a major role in enabling the large-scale ocean circulation. The accuracy of mixing rates estimated from observations depends on our understanding of basic fluid mechanical processes underlying the nature of turbulence in a stratified fluid. Several of the key assumptions made in conventional mixing parameterizations have been increasingly scrutinized in recent years, primarily on the basis of adequately high resolution numerical simulations. We add to this evidence by compiling results from a suite of numerical simulations of the turbulence generated through stratified shear instability processes. We study the inherently intermittent and time-dependent nature of wave-induced turbulent life cycles and more specifically the tight coupling between inherently anisotropic scales upon which small-scale isotropic turbulence grows. The anisotropic scales stir and stretch fluid filaments enhancing irreversible diffusive mixing at smaller scales. We show that the characteristics of turbulent mixing depend on the relative time evolution of the Ozmidov length scale $L_{O}$ compared to the so-called Thorpe overturning scale $L_{T}$ which represents the scale containing available potential energy upon which turbulence feeds and grows. We find that when $L_{T}\sim L_{O}$, the mixing is most active and efficient since stirring by the largest overturns becomes ‘optimal’ in the sense that it is not suppressed by ambient stratification. We argue that the high mixing efficiency associated with this phase, along with observations of $L_{O}/L_{T}\sim 1$ in oceanic turbulent patches, together point to the potential for systematically underestimating mixing in the ocean if the role of overturns is neglected. This neglect, arising through the assumption of a clear separation of scales between the background mean flow and small-scale quasi-isotropic turbulence, leads to the exclusion of an highly efficient mixing phase from conventional parameterizations of the vertical transport of density. Such an exclusion may well be significant if the mechanism of shear-induced turbulence is assumed to be representative of at least some turbulent events in the ocean. While our results are based upon simulations of shear instability, we show that they are potentially more generic by making direct comparisons with $L_{T}-L_{O}$ data from ocean and lake observations which represent a much wider range of turbulence-inducing physical processes.
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Beresh, Steven J., Justin L. Wagner, and Katya M. Casper. "Compressibility effects in the shear layer over a rectangular cavity." Journal of Fluid Mechanics 808 (October 26, 2016): 116–52. http://dx.doi.org/10.1017/jfm.2016.540.
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The influence of compressibility on the shear layer over a rectangular cavity of variable width has been studied in a free stream Mach number range of 0.6–2.5 using particle image velocimetry data in the streamwise centre plane. As the Mach number increases, the vertical component of the turbulence intensity diminishes modestly in the widest cavity, but the two narrower cavities show a more substantial drop in all three components as well as the turbulent shear stress. This contrasts with canonical free shear layers, which show significant reductions in only the vertical component and the turbulent shear stress due to compressibility. The vorticity thickness of the cavity shear layer grows rapidly as it initially develops, then transitions to a slower growth rate once its instability saturates. When normalized by their estimated incompressible values, the growth rates prior to saturation display the classic compressibility effect of suppression as the convective Mach number rises, in excellent agreement with comparable free shear layer data. The specific trend of the reduction in growth rate due to compressibility is modified by the cavity width.
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Williams, Owen, Tristen Hohman, Tyler Van Buren, Elie Bou-Zeid, and Alexander J. Smits. "The effect of stable thermal stratification on turbulent boundary layer statistics." Journal of Fluid Mechanics 812 (January 11, 2017): 1039–75. http://dx.doi.org/10.1017/jfm.2016.781.
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The effects of stable thermal stratification on turbulent boundary layers are experimentally investigated for smooth and rough walls. For weak to moderate stability, the turbulent stresses are seen to scale with the wall shear stress, compensating for changes in fluid density in the same manner as done for compressible flows. This suggests little change in turbulent structure within this regime. At higher levels of stratification turbulence no longer scales with the wall shear stress and turbulent production by mean shear collapses, but without the preferential damping of near-wall motions observed in previous studies. We suggest that the weakly stable and strongly stable (collapsed) regimes are delineated by the point where the turbulence no longer scales with the local wall shear stress, a significant departure from previous definitions. The critical stratification separating these two regimes closely follows the linear stability analysis of Schlichting (Z. Angew. Math. Mech., vol. 15 (6), 1935, pp. 313–338) for both smooth and rough surfaces, indicating that a good predictor of critical stratification is the gradient Richardson number evaluated at the wall. Wall-normal and shear stresses follow atmospheric trends in the local gradient Richardson number scaling of Sorbjan (Q. J. R. Meteorol. Soc., vol. 136, 2010, pp. 1243–1254), suggesting that much can be learned about stratified atmospheric flows from the study of laboratory scale boundary layers at relatively low Reynolds numbers.
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DEY, SUBHASISH, TUSHAR K. NATH, and SUJIT K. BOSE. "Submerged wall jets subjected to injection and suction from the wall." Journal of Fluid Mechanics 653 (April 27, 2010): 57–97. http://dx.doi.org/10.1017/s0022112010000182.
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This paper presents an experimental study on turbulent flow characteristics in submerged plane wall jets subjected to injection (upward seepage) and suction (downward seepage) from the wall. The vertical distributions of time-averaged velocity components, turbulence intensity components and Reynolds shear stress at different horizontal distances are presented. The horizontal distributions of wall shear stress determined from the Reynolds shear stress profiles are also furnished. The flow field exhibits a decay of the jet velocity over a horizontal distance. The wall shear stress and the rate of decay of the jet velocity increase in the presence of injection and decrease with suction. Based on the two-dimensional Reynolds-averaged Navier–Stokes equations of a steady turbulent flow, the velocity and Reynolds shear stress distributions in the fully developed zone subjected to no seepage, injection and suction are theoretically computed. The response of the turbulent flow characteristics to injection and suction is analysed from the point of view of similarity characteristics, growth of the length scale and decay of the velocity and turbulence characteristics scales. The significant observation is that the velocity, Reynolds shear stress and turbulence intensities in the fully developed zone are reasonably similar under both injection and suction on applying the appropriate scaling laws. An analysis of the third-order moments of velocity fluctuations reveals that the inner layer of the jet is associated with the arrival of low-speed fluid streaks causing an effect of retardation. On the other hand, the upper layer of the jet is associated with the arrival of high-speed fluid streaks causing an effect of acceleration. Injection influences the near-wall distributions of the third-order moments by increasing the upward turbulent advection of the streamwise Reynolds normal stress. In contrast, suction influences the near-wall distributions of the third-order moments by increasing the downward turbulent advection of the streamwise Reynolds normal stress. Also, injection and suction change the vertical turbulent flux of the vertical Reynolds normal stress in a similar way. The streamwise turbulent energy flux travels towards the jet origin within the jet layer, while it travels away from the origin within the inner layer of the circulatory flow. The turbulent energy budget suggests that the turbulent and pressure energy diffusions oppose each other, and the turbulent dissipation lags the turbulent production. The quadrant analysis of velocity fluctuations reveals that the inward and outward interactions are the primary contributions to the Reynolds shear stress production in the inner and outer layers of the jet, respectively. However, injection induces feeble ejections in the vicinity of the wall.
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Fortova, S. V. "Numerical Simulation of Turbulence Flows in Shear Layer." Archives of Metallurgy and Materials 59, no. 3 (October 28, 2014): 1155–58. http://dx.doi.org/10.2478/amm-2014-0201.
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Abstract For various problems of continuum mechanics described by the equations of hyperbolic type, the comparative analysis of scenarios of development of turbulent flows in shear layers is carried out. It is shown that the development of the hydrodynamic instabilities leads to a vortex cascade that corresponds to the development stage of the vortices in the energy and the inertial range during the transition to the turbulent flow stage. It is proved that for onset of turbulence the spatial problem definition is basic. At the developed stage of turbulence the spectral analysis of kinetic energy is carried out and the Kolmogorov “-5/3” power law is confirmed.
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Schwarz, Andreas C., Michael W. Plesniak, and S. N. B. Murthy. "Turbulent Boundary Layers Subjected to Multiple Strains." Journal of Fluids Engineering 121, no. 3 (September 1, 1999): 526–32. http://dx.doi.org/10.1115/1.2823500.
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Turbomachinery flows can be extremely difficult to predict, due to a multitude of effects, including interacting strain rates, compressibility, and rotation. The primary objective of this investigation was to study the influence of multiple strain rates (favorable streamwise pressure gradient combined with radial pressure gradient due to convex curvature) on the structure of the turbulent boundary layer. The emphasis was on the initial region of curvature, which is relevant to the leading edge of a stator vane, for example. In order to gain better insight into the dynamics of complex turbulent boundary layers, detailed velocity measurements were made in a low-speed water tunnel using a two-component laser Doppler velocimeter. The mean and fluctuating velocity profiles showed that the influence of the strong favorable pressure augmented the stabilizing effects of convex curvature. The trends exhibited by the primary Reynolds shear stress followed those of the mean turbulent bursting frequency, i.e., a decrease in the bursting frequency coincided with a reduction of the peak Reynolds shear stress. It was found that the effects of these two strain rates were not superposable, or additive in any simple manner. Thus, the dynamics of the large energy-containing eddies and their interaction with the turbulence production mechanisms must be considered for modeling turbulent flows with multiple strain rates.
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Thorpe, S. A. "Layers and internal waves in uniformly stratified fluids stirred by vertical grids." Journal of Fluid Mechanics 793 (March 16, 2016): 380–413. http://dx.doi.org/10.1017/jfm.2016.121.
Full textAbstract:
Laboratory experiments in which uniformly stratified fluids are stirred by horizontally moving vertical grids, or arrays of vertical rods, are reviewed to examine their consistency and to compare their findings, particularly those relating to the generation of layers. Selected experiments are of three types, those in which (a) turbulence spreads from a horizontally confined region where it is continuously generated by an oscillating grid; (b) grid stirring is maintained throughout a rectangular tank; or (c) a ‘cloud’ of turbulence decays after a short period of horizontally localized grid mixing. In all the experiments turbulence is generated over the full vertical extent of the tank. In the experiments of types (a) and (c) layers of comparable scale are observed to intrude into the ambient fluid from the turbulent region. In the type (b) experiments, layers form only when the time interval between the passage of the grid through the stratified fluid is sufficiently long, allowing turbulence to decay substantially between grid strokes. Two mechanisms are found to be dominant in the production of layers. In experiments of type (a) and (c) overturning eddies in the turbulent region of scale significantly larger than the Ozmidov length scale collapse and spread, intruding and forming layers in the adjoining laminar region. Internal shear waves propagating ahead of the intrusions have a vertical wavelength that is approximately twice the layer height. In type (b) experiments, layers are formed through a process described by Holford & Linden (Dyn. Atmos. Oceans, vol. 30, 1999a, pp. 173–198): the bending of vortices shed by the grid bars. The height of the layers is approximately half the vertical wavelength of internal shear waves that travel at the speed of the grid. It is proposed that the flow field of the shear waves bends the vortices, resulting in diapycnal mixing that forms the layers. The relationship of layers and internal shear waves in the experiments is therefore as follows: in type (a) and (c) experiments internal waves are generated by layers intruding from the turbulent region into the quiescent stratified region, but in experiments of type (b) internal waves drive and dictate the height of the layers; layers are generated as a consequence of vortex bending by internal waves. There is insufficient evidence to establish whether zigzag instability, either of vortex pairs or of vortex streets shed by a moving grid, accounts for the layers in any of the three types of grid experiments. The Phillips and Posmentier instability may reinforce layers formed by other processes. The generation of pancake vortices or vortical mode motion is left for later review.
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Dutta, G., M. C. Ajay Kumar, P. Vinay Kumar, P. V. Rao, B. Bapiraju, and H. Aleem Basha. "High resolution observations of turbulence in the troposphere and lower stratosphere over Gadanki." Annales Geophysicae 27, no. 6 (June 11, 2009): 2407–15. http://dx.doi.org/10.5194/angeo-27-2407-2009.
Full textAbstract:
Abstract. High resolution (150 m) wind measurements from 13–17 July 2004 by Mesosphere-Stratosphere-Troposphere (MST) radar and 15–16 July 2004 by Lower Atmospheric Wind Profiler (LAWP) have been used to study the time variation of turbulence intensity. Layers of higher turbulence are observed in the lower stratosphere on 15–16 July which give rise to mixing in the region. Enhancement in short-period gravity wave activity and turbulent layers are observed after 22:00 LT which could be due to a dry convection event that occurred at that time. The breakdown of the convectively generated high frequency waves seems to have given rise to the turbulence layers. Wind shear is found to be high above the easterly jet, but very poor correlation is observed between square of wind shear and turbulence parameters in the region. The heights of the turbulent layers in the lower stratosphere do not correlate with levels of minimum Richardson number. A monochromatic inertia gravity wave could be identified during 13–17 July 2004. A non-linear interaction between the waves of different scales as proposed by Hines (1992) might also be responsible for the breakdown and generation of turbulence layers.