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1
Teixeira, M. A. C., and C. B. da Silva. "Turbulence dynamics near a turbulent/non-turbulent interface." Journal of Fluid Mechanics 695 (February 13, 2012): 257–87. http://dx.doi.org/10.1017/jfm.2012.17.
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AbstractThe characteristics of the boundary layer separating a turbulence region from an irrotational (or non-turbulent) flow region are investigated using rapid distortion theory (RDT). The turbulence region is approximated as homogeneous and isotropic far away from the bounding turbulent/non-turbulent (T/NT) interface, which is assumed to remain approximately flat. Inviscid effects resulting from the continuity of the normal velocity and pressure at the interface, in addition to viscous effects resulting from the continuity of the tangential velocity and shear stress, are taken into account by considering a sudden insertion of the T/NT interface, in the absence of mean shear. Profiles of the velocity variances, turbulent kinetic energy (TKE), viscous dissipation rate ($\varepsilon $), turbulence length scales, and pressure statistics are derived, showing an excellent agreement with results from direct numerical simulations (DNS). Interestingly, the normalized inviscid flow statistics at the T/NT interface do not depend on the form of the assumed TKE spectrum. Outside the turbulent region, where the flow is irrotational (except inside a thin viscous boundary layer),$\varepsilon $decays as${z}^{\ensuremath{-} 6} $, where$z$is the distance from the T/NT interface. The mean pressure distribution is calculated using RDT, and exhibits a decrease towards the turbulence region due to the associated velocity fluctuations, consistent with the generation of a mean entrainment velocity. The vorticity variance and$\varepsilon $display large maxima at the T/NT interface due to the inviscid discontinuities of the tangential velocity variances existing there, and these maxima are quantitatively related to the thickness$\delta $of the viscous boundary layer (VBL). For an equilibrium VBL, the RDT analysis suggests that$\delta \ensuremath{\sim} \eta $(where$\eta $is the Kolmogorov microscale), which is consistent with the scaling law identified in a very recent DNS study for shear-free T/NT interfaces.
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Hannoun, Imad A., Harindra J. S. Fernando, and E. John List. "Turbulence structure near a sharp density interface." Journal of Fluid Mechanics 189 (April 1988): 189–209. http://dx.doi.org/10.1017/s0022112088000965.
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The effects of a sharp density interface and a rigid flat plate on oscillating-grid induced shear-free turbulence were investigated experimentally. A two-component laser-Doppler velocimeter was used to measure turbulence intensities in and above the density interface (with matched refractive indices) and near the rigid flat plate. Energy spectra, velocity correlations, and kinetic energy fluxes were also measured. Amplification of the horizontal turbulent velocity, coupled with a sharp reduction in the vertical turbulent velocity, was observed near both the density interface and the flat plate. These findings are in agreement with some previous results pertaining to shear-free turbulence near rigid walls (Hunt & Graham 1978) and near density interfaces (Long 1978). The results imply that, near the density interface, the turbulent kinetic energy in the vertical velocity component is only a small fraction of the total turbulent kinetic energy and indicate that the effects of the anisotropy created by the density interface or the flat plate are confined to the large turbulence scales.
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Popot, Jean-Lue. "Turbulent interface." Biochimie 80, no. 5-6 (May 1998): 355–56. http://dx.doi.org/10.1016/s0300-9084(00)80002-4.
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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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Li, Sicheng, Yanguang Long, and Jinjun Wang. "Turbulent/non-turbulent interface for laminar boundary flow over a wall-mounted fence." Physics of Fluids 34, no. 12 (December 2022): 125113. http://dx.doi.org/10.1063/5.0128609.
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The turbulent/non-turbulent interface plays an important role in the exchange of mass, momentum, and energy between turbulent and nonturbulent flows. However, the role played by the interface in the separation and reattachment flow remains poorly understood. This study, thus, investigates the geometrical and dynamic properties of the interface in the separation and reattachment flow induced by a wall-mounted fence by using particle image velocimetry in a water tunnel. The flow undergoes laminar separation, reattachment, and the recovery of the boundary layer. Finally, the fully developed turbulent boundary layer is established. The geometrical and dynamic properties of the interface vary consistently with the vortex structure. The geometrical properties change most quickly above the reattachment point, where the dynamic properties are maximal. Before the reattachment point, the shear motion of the fluid contributes significantly to the interface properties. As a result, the interface thickness does not scale with the size of the nearby vortex until reattachment. Additionally, quasiperiodic shedding vortices significantly affect the interface properties. Remarkable bulges and troughs of the interface form corresponding to the spatial arrangement of the shedding vortices. In addition, the conditional averaged dynamic quantities peak along the interface coordinate as the turbulence intensity is enhanced by the shedding vortex. This study provides a new perspective of the turbulent/non-turbulent interface, improves our understanding of turbulent diffusion in the separation and reattachment flow, and clarifies how the separated flow and shedding vortices affect the interface properties.
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Lee, Jin, Hyung Jin Sung, and Tamer A. Zaki. "Signature of large-scale motions on turbulent/non-turbulent interface in boundary layers." Journal of Fluid Mechanics 819 (April 18, 2017): 165–87. http://dx.doi.org/10.1017/jfm.2017.170.
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The effect of large-scale motions (LSMs) on the turbulent/non-turbulent (T/NT) interface is examined in a turbulent boundary layer. Using flow fields from direct numerical simulation, the shape of the interface and near-interface statistics are evaluated conditional on the position of the LSM. The T/NT interface is identified using the vorticity magnitude and a streak detection algorithm is adopted to identify and track the LSMs. Two-point correlation and spectral analysis of variations in the interface height show that the spatial undulation of the interface is longer in streamwise wavelength than the boundary-layer thickness, and grows with the Reynolds number in a similar manner to the LSMs. The average variation in the interface height was evaluated conditional on the position of the LSMs. The result provides statistical evidence that the interface is locally modulated by the LSMs in both the streamwise and spanwise directions. The modulation is different when the coherent structure is high- versus low-speed motion: high-speed structures lead to a wedge-shaped deformation of the T/NT interface, which causes an anti-correlation between the angles of the interface and the internal shear layer. On the other hand, low-speed structures are correlated with crests in the interface. Finally, the sudden changes in turbulence statistics across the interface are in line with the changes in the population of low-speed structures, which consist of slower mean streamwise velocity and stronger turbulence than the high-speed counterparts.
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Borrell, Guillem, and Javier Jiménez. "Properties of the turbulent/non-turbulent interface in boundary layers." Journal of Fluid Mechanics 801 (July 26, 2016): 554–96. http://dx.doi.org/10.1017/jfm.2016.430.
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The turbulent/non-turbulent interface is analysed in a direct numerical simulation of a boundary layer in the Reynolds number range$Re_{{\it\theta}}=2800{-}6600$, with emphasis on the behaviour of the relatively large-scale fractal intermittent region. This requires the introduction of a new definition of the distance between a point and a general surface, which is compared with the more usual vertical distance to the top of the layer. Interfaces are obtained by thresholding the enstrophy field and the magnitude of the rate-of-strain tensor, and it is concluded that, while the former are physically relevant features, the latter are not. By varying the threshold, a topological transition is identified as the interface moves from the free stream into the turbulent core. A vorticity scale is defined which collapses that transition for different Reynolds numbers, roughly equivalent to the root-mean-squared vorticity at the edge of the boundary layer. Conditionally averaged flow variables are analysed as functions of the new distance, both within and outside the interface. It is found that the interface contains a non-equilibrium layer whose thickness scales well with the Taylor microscale, enveloping a self-similar layer spanning a fixed fraction of the boundary-layer thickness. Interestingly, the straining structure of the flow is similar in both regions. Irrotational pockets within the turbulent core are also studied. They form a self-similar set whose size decreases with increasing depth, presumably due to breakup by the turbulence, but the rate of viscous diffusion is independent of the pocket size. The raw data used in the analysis are freely available from our web page (http://torroja.dmt.upm.es).
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Ferrey, P., and B. Aupoix. "Behaviour of turbulence models near a turbulent/non-turbulent interface revisited." International Journal of Heat and Fluid Flow 27, no. 5 (October 2006): 831–37. http://dx.doi.org/10.1016/j.ijheatfluidflow.2006.03.022.
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Moeng, C.-H., B. Stevens, and P. P. Sullivan. "Where is the Interface of the Stratocumulus-Topped PBL?" Journal of the Atmospheric Sciences 62, no. 7 (July 1, 2005): 2626–31. http://dx.doi.org/10.1175/jas3470.1.
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Abstract Various locally defined (not horizontal mean) interfaces between the stratocumulus-topped PBL and the free atmosphere are investigated using a fine-resolution large-eddy simulation with a vertical grid spacing of about 4 m. The local cloud-top height is found to be always below the height where the maximum gradient of the local sounding occurs, and the maximum-gradient height is always below the interface where PBL air can reach via turbulent motions. The distances between these local interfaces are of significant amount, a few tens of meters on average. Air between the cloud-top and maximum-gradient interfaces is fully turbulent, unsaturated, but rather moist. Air between the maximum-gradient and turbulent-mixing interfaces consists of turbulent motions that are intermittent in space and time. The simulated flow shows no clearly defined interface that separates cloudy, turbulent air mass from clear, nonturbulent air above, even locally.
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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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Wang, T., P. Li, J. S. Bai, G. Tao, B. Wang, and L. Y. Zou. "Large-eddy simulation of the Richtmyer–Meshkov instability." Canadian Journal of Physics 93, no. 10 (October 2015): 1124–30. http://dx.doi.org/10.1139/cjp-2014-0652.
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The subgrid-scale (SGS) terms of turbulence transport are modelled by the stretched-vortex SGS stress model, and a large-eddy simulation code multi-viscous fluid and turbulence (MVFT) is developed to investigate the MVFT problems. Then one AWE shock tube experiment of interface instability is simulated numerically by MVFT code, which reproduces the development process of the interface. The obtained numerical images of interface evolution and wave structures in flow field are consistent with the experimental results. The evolution of perturbed interface and propagation of shock waves in flow field and their interactions are analyzed in detail. The statistics features of turbulence mixing in the form of finer quantities, such as the turbulent kinetic energy, enstrophy, density variance, and turbulent mass flux are investigated, which also proves that the SGS model has a key role in large-eddy simulation. The turbulent kinetic energy and enstrophy decay with time as a power law.
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Gampert, Markus, Jonas Boschung, Fabian Hennig, Michael Gauding, and Norbert Peters. "The vorticity versus the scalar criterion for the detection of the turbulent/non-turbulent interface." Journal of Fluid Mechanics 750 (June 10, 2014): 578–96. http://dx.doi.org/10.1017/jfm.2014.280.
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AbstractBased on a direct numerical simulation (DNS) of a temporally evolving mixing layer, we present a detailed study of the turbulent/non-turbulent (T/NT) interface that is defined using the two most common procedures in the literature, namely either a vorticity or a scalar criterion. The different detection approaches are examined qualitatively and quantitatively in terms of the interface position, conditional statistics and orientation of streamlines and vortex lines at the interface. Computing the probability density function (p.d.f.) of the mean location of the T/NT interface from vorticity and scalar allows a detailed comparison of the two methods, where we observe a very good agreement. Furthermore, conditional mean profiles of various quantities are evaluated. In particular, the position p.d.f.s for both criteria coincide and are found to follow a Gaussian distribution. The terms of the governing equations for vorticity and passive scalar are conditioned on the distance to the interface and analysed. At the interface, vortex stretching is negligible and the displacement of the vorticity interface is found to be determined by diffusion, analogous to the scalar interface. In addition, the orientation of vortex lines at the vorticity and the scalar based T/NT interface are analyzed. For both interfaces, vorticity lines are perpendicular to the normal vector of the interface, i.e. parallel to the interface isosurface.
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da Silva, Carlos Bettencourt, and Ricardo José Nunes dos Reis. "The role of coherent vortices near the turbulent/non-turbulent interface in a planar jet." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, no. 1937 (February 28, 2011): 738–53. http://dx.doi.org/10.1098/rsta.2010.0300.
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The role of coherent vortices near the turbulent/non-turbulent (T/NT) interface in a turbulent plane jet is analysed by a direct numerical simulation (DNS). The coherent vortices near the jet edge consist of large-scale vortical structures (LSVSs) maintained by the mean shear and intense vorticity structures (IVSs) created by the background fluctuating turbulence field. The radius of the LSVS is equal to the Taylor micro-scale R lsvs ≈ λ , while the radius of the IVS is of the order of the Kolmogorov micro-scale R ivs ∼ η . The LSVSs are responsible for the observed vorticity jump at the T/NT interface, being of the order of the Taylor micro-scale. The coherent vortices in the proximity of the T/NT interface are preferentially aligned with the tangent to the T/NT interface and are responsible for the viscous dissipation of kinetic energy near the T/NT interface and to the characteristic shape of the enstrophy viscous diffusion observed at that location.
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Zhou, Y., and J. C. Vassilicos. "Related self-similar statistics of the turbulent/non-turbulent interface and the turbulence dissipation." Journal of Fluid Mechanics 821 (May 25, 2017): 440–57. http://dx.doi.org/10.1017/jfm.2017.262.
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The scalings of the local entrainment velocity$v_{n}$of the turbulent/non-turbulent interface and of the turbulence dissipation rate are closely related to each other in an axisymmetric and self-similar turbulent wake. The turbulence dissipation scaling implied by the Kolmogorov equilibrium cascade phenomenology is consistent with a Kolmogorov scaling of$v_{n}$whereas the non-equilibrium dissipation scaling reported for various turbulent flows in Vassilicos (Annu. Rev. Fluid Mech., vol. 47, 2015, pp. 95–114), Dairayet al.(J. Fluid Mech., vol. 781, 2015, pp. 166–195), Goto & Vassilicos (Phys. Lett. A, vol. 379 (16), 2015, pp. 1144–1148) and Obligadoet al.(Phys. Rev. Fluids, vol. 1 (4), 2016, 044409) is consistent with a different scaling of $v_{n}$. We present results from a direct numerical simulation of a spatially developing axisymmetric and self-similar turbulent wake which supports this conclusion and the assumptions that it is based on.
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Dessler, A. J. "Editorial: A turbulent interface." Geophysical Research Letters 13, no. 1 (January 1986): 1. http://dx.doi.org/10.1029/gl013i001p00001.
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Yu, R., X. S. Bai, and A. N. Lipatnikov. "A direct numerical simulation study of interface propagation in homogeneous turbulence." Journal of Fluid Mechanics 772 (April 29, 2015): 127–64. http://dx.doi.org/10.1017/jfm.2015.211.
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A 3D direct numerical simulation (DNS) study of the evolution of a self-propagating interface in forced constant-density statistically stationary homogeneous isotropic turbulence was performed by solving Navier–Stokes and level-set equations under a wide range of conditions that cover various (from 0.1 to 2.0) ratios of the interface speed $S_{L}$ to the r.m.s. turbulent velocity $U^{\prime }$ and various (50, 100 and 200) turbulent Reynolds numbers $\mathit{Re}$. By analysing computed data, the following issues were addressed: (i) dependence of the speed and thickness of the fully developed statistically planar mean front that envelops the interface on $U^{\prime }/S_{L}$ and $\mathit{Re}$, (ii) dependence of the fully developed mean turbulent flux of a scalar $c$ that characterizes the state of the fluid ($c=0$ and 1 ahead and behind the interface respectively) on $U^{\prime }/S_{L}$ and $\mathit{Re}$, (iii) evolution of the mean front speed, its thickness, and the mean scalar flux during the front development after embedding a planar interface into the forced turbulence and (iv) relation between canonical and conditioned moments of the velocity, velocity gradient and pressure gradient fields.
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Breda, M., and O. R. H. Buxton. "Behaviour of small-scale turbulence in the turbulent/non-turbulent interface region of developing turbulent jets." Journal of Fluid Mechanics 879 (September 20, 2019): 187–216. http://dx.doi.org/10.1017/jfm.2019.676.
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Tomographic particle image velocimetry experiments were conducted in the near and intermediate fields of two different types of jet, one fitted with a circular orifice and another fitted with a repeating-fractal-pattern orifice. Breda & Buxton (J. Vis., vol. 21 (4), 2018, pp. 525–532; Phys. Fluids, vol. 30, 2018, 035109) showed that this fractal geometry suppressed the large-scale coherent structures present in the near field and affected the rate of entrainment of background fluid into, and subsequent development of, the fractal jet, relative to the round jet. In light of these findings we now examine the modification of the turbulent/non-turbulent interface (TNTI) and spatial evolution of the small-scale behaviour of these different jets, which are both important factors behind determining the entrainment rate. This evolution is examined in both the streamwise direction and within the TNTI itself where the fluid adapts from a non-turbulent state, initially through the direct action of viscosity and then through nonlinear inertial processes, to the state of the turbulence within the bulk of the flow over a short distance. We show that the suppression of the coherent structures in the fractal jet leads to a less contorted interface, with large-scale excursions of the inner TNTI (that between the jet’s azimuthal shear layer and the potential core) being suppressed. Further downstream, the behaviour of the TNTI is shown to be comparable for both jets. The velocity gradients develop into a canonical state with streamwise distance, manifested as the development of the classical tear-drop shaped contours of the statistical distribution of the velocity-gradient-tensor invariants $\mathit{Q}$ and $\mathit{R}$. The velocity gradients also develop spatially through the TNTI from the irrotational boundary to the bulk flow; in particular, there is a strong small-scale anisotropy in this region. This strong inhomogeneity of the velocity gradients in the TNTI region has strong consequences for the scaling of the thickness of the TNTI in these spatially developing flows since both the Taylor and Kolmogorov length scales are directly computed from the velocity gradients.
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Wu, Xiaohua, James M. Wallace, and Jean-Pierre Hickey. "Boundary layer turbulence and freestream turbulence interface, turbulent spot and freestream turbulence interface, laminar boundary layer and freestream turbulence interface." Physics of Fluids 31, no. 4 (April 2019): 045104. http://dx.doi.org/10.1063/1.5093040.
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Norscini, Claudia, Thomas Cartier-Michaud, Guilhem Dif-Pradalier, Xavier Garbet, Philippe Ghendrih, Virginie Grandgirard, and Yanick Sarazin. "Interface transport barriers in magnetized plasmas." Plasma Physics and Controlled Fusion 64, no. 5 (March 31, 2022): 055007. http://dx.doi.org/10.1088/1361-6587/ac5a07.
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Abstract We address the formation of Interface Transport Barriers using a generic turbulent transport model, reduced to 2D, and used to investigate interchange turbulence in magnetized plasmas. The generation of a transport barrier at the edge-scrape off layer (SOL) plasma interface is governed by a zonation regime in the edge region with closed-field lines. The barrier is triggered by a gap in the turbulent spectrum between zero, the zonal flow wave vector, and the wave vector of the spectrum maximum. This gap is controlled by the energy injection wave vector of the interchange instability and the Rhine scale that bounds the inverse cascade. Increasing the magnitude of the turbulence drive at a given gap reinforces the transport barrier. In the interface transport barrier regime, edge relaxation bursts of turbulence regenerate the zonal flows that are eroded by damping processes such as collisions. The duration of the quiescent phase between the quasi-periodic relaxation events is then governed by the ion collision frequency. Such an interface transport barrier can play the role of a seed barrier prior to a full bifurcation to improved confinement.
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BISSET, DAVID K., JULIAN C. R. HUNT, and MICHAEL M. ROGERS. "The turbulent/non-turbulent interface bounding a far wake." Journal of Fluid Mechanics 451 (January 25, 2002): 383–410. http://dx.doi.org/10.1017/s0022112001006759.
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The velocity fields of a turbulent wake behind a flat plate obtained from the direct numerical simulations of Moser et al. (1998) are used to study the structure of the flow in the intermittent zone where there are, alternately, regions of fully turbulent flow and non-turbulent velocity fluctuations on either side of a thin randomly moving interface. Comparisons are made with a wake that is ‘forced’ by amplifying initial velocity fluctuations. A temperature field T, with constant values of 1.0 and 0 above and below the wake, is transported across the wake as a passive scalar. The value of the Reynolds number based on the centreplane mean velocity defect and half-width b of the wake is Re ≈ 2000.The thickness of the continuous interface is about 0.07b, whereas the amplitude of fluctuations of the instantaneous interface displacement yI(t) is an order of magnitude larger, being about 0.5b. This explains why the mean statistics of vorticity in the intermittent zone can be calculated in terms of the probability distribution of yI and the instantaneous discontinuity in vorticity across the interface. When plotted as functions of y−yI the conditional mean velocity 〈U〉 and temperature 〈T〉 profiles show sharp jumps at the interface adjacent to a thick zone where 〈U〉 and 〈T〉 vary much more slowly.Statistics for the conditional vorticity and velocity variances, available in such detail only from DNS data, show how streamwise and spanwise components of vorticity are generated by vortex stretching in the bulges of the interface. While mean Reynolds stresses (in the fixed reference frame) decrease gradually in the intermittent zone, conditional stresses are roughly constant and then decrease sharply towards zero at the interface. Flow fields around the interface, analysed in terms of the local streamline pattern, confirm and explain previous results that the advancement of the vortical interface into the irrotational flow is driven by large-scale eddy motion.Terms used in one-point turbulence models are evaluated both conventionally and conditionally in the interface region, and the current practice in statistical models of approximating entrainment by a diffusion process is assessed.
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Shrinivas, Ajay B., and Gary R. Hunt. "Confined turbulent entrainment across density interfaces." Journal of Fluid Mechanics 779 (August 14, 2015): 116–43. http://dx.doi.org/10.1017/jfm.2015.366.
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In pursuit of a universal law for the rate of entrainment across a density interface driven by the impingement of a localised turbulent flow, the role of the confinement, wherein the environment is within the confines of a box, has to date been overlooked. Seeking to unravel the effects of confinement, we develop a phenomenological model describing the quasi-steady rate at which buoyant fluid is turbulently entrained across a density interface separating two uniform layers within the confines of a box. The upper layer is maintained by a turbulent plume, and the localised impingement of a turbulent fountain with the interface drives entrainment of fluid from the upper layer into the lower layer. The plume and fountain rise from sources at the base of the box and are non-interacting. Guided by previous observations, our model characterises the dynamics of fountain–interface interaction and the steady secondary flow in the environment that is induced by the perpetual cycle of vertical excursions of the interface. We reveal that the dimensionless entrainment flux across the interface $E_{i}$ is governed not only by an interfacial Froude number $\mathit{Fr}_{i}$ but also by a ‘confinement’ parameter ${\it\lambda}_{i}$, which characterises the length scale of interfacial turbulence relative to the depth of the upper layer. By deducing the range of ${\it\lambda}_{i}$ that may be regarded as ‘small’ and ‘large’, we shed new light on the effects of confinement on interfacial entrainment. We establish that for small ${\it\lambda}_{i}$, a weak secondary flow has little influence on $E_{i}$, which follows a quadratic power law $E_{i}\propto \mathit{Fr}_{i}^{2}$. For large ${\it\lambda}_{i}$, a strong secondary flow significantly influences $E_{i}$, which then follows a cubic power law $E_{i}\propto \mathit{Fr}_{i}^{3}$. Drawing on these results, and showing that for previous experimental studies ${\it\lambda}_{i}$ exhibits wide variation, we highlight underlying physical reasons for the significant scatter in the existing measurements of the rate of interfacial entrainment. Finally, we explore the implications of our results for guiding appropriate choices of box geometry for experimentally and numerically examining interfacial entrainment.
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Lorke, Andreas, and Frank Peeters. "Toward a Unified Scaling Relation for Interfacial Fluxes." Journal of Physical Oceanography 36, no. 5 (May 1, 2006): 955–61. http://dx.doi.org/10.1175/jpo2903.1.
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Abstract Interfacial fluxes, that is, gas exchange at the water–atmosphere interface and benthic fluxes at the sediment–water interface, are often parameterized in terms of wind speed or turbulent friction velocity, with numerous empirical relationships obtained from individual experiments. The present study attempts to combine the general outcome of such experiments at both interfaces into a universal scaling relation for the thicknesses of the viscous and diffusive sublayers in terms of the Kolmogorov and Batchelor length scales, respectively. Transfer velocities can then be described in terms of the Schmidt number of the respective tracer and in terms of the turbulence dissipation rate. Applying law-of-the-wall scaling to convert dissipation rates into an appropriate friction velocity estimate results in a mechanistic description of the transfer velocity, which is comparable to common empirical parameterizations. It is hypothesized, however, that the dissipation rate and hence the directly estimated level of turbulence provide a more appropriate variable for the parameterization of interfacial fluxes than wind speed or turbulent friction velocity inferred from law-of-the-wall scaling.
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Fan, Wenyuan, and Henryk Anglart. "Progress in Phenomenological Modeling of Turbulence Damping around a Two-Phase Interface." Fluids 4, no. 3 (July 18, 2019): 136. http://dx.doi.org/10.3390/fluids4030136.
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The presence of a moving interface in two-phase flows challenges the accurate computational fluid dynamics (CFD) modeling, especially when the flow is turbulent. For such flows, single-phase-based turbulence models are usually used for the turbulence modeling together with certain modifications including the turbulence damping around the interface. Due to the insufficient understanding of the damping mechanism, the phenomenological modeling approach is always used. Egorov’s model is the most widely-used turbulence damping model due to its simple formulation and implementation. However, the original Egorov model suffers from the mesh size dependency issue and uses a questionable symmetric treatment for both liquid and gas phases. By introducing more physics, this paper introduces a new length scale for Egorov’s model, making it independent of mesh sizes in the tangential direction of the interface. An asymmetric treatment is also developed, which leads to more physical predictions for both the turbulent kinetic energy and the velocity field.
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WESTERWEEL, J., C. FUKUSHIMA, J. M. PEDERSEN, and J. C. R. HUNT. "Momentum and scalar transport at the turbulent/non-turbulent interface of a jet." Journal of Fluid Mechanics 631 (July 17, 2009): 199–230. http://dx.doi.org/10.1017/s0022112009006600.
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Conditionally sampled measurements with particle image velocimetry (PIV) of a turbulent round submerged liquid jet in a laboratory have been taken at Re = 2 × 103 between 60 and 100 nozzle diameters from the nozzle in order to investigate the dynamics and transport processes at the continuous and well-defined bounding interface between the turbulent and non-turbulent regions of flow. The jet carries a fluorescent dye measured with planar laser-induced fluorescence (LIF), and the surface discontinuity in the scalar concentration is identified as the fluctuating turbulent jet interface. Thence the mean outward ‘boundary entrainment’ velocity is derived and shown to be a constant fraction (about 0.07) of the the mean jet velocity on the centreline. Profiles of the conditional mean velocity, mean scalar and momentum flux show that at the interface there are clear discontinuities in the mean axial velocity and mean scalar and a tendency towards a singularity in mean vorticity. These actual or asymptotic discontinuities are consistent with the conditional mean momentum and scalar transport equations integrated across the interface. Measurements of the fluxes of turbulent kinetic energy and enstrophy are consistent with computations by Mathew & Basu (Phys. Fluids, vol. 14, 2002, pp. 2065–2072) in showing that for a jet flow (without forcing) the entrainment process is dominated by small-scale eddying at the highly sheared interface (‘nibbling’), with large-scale engulfing making a small (less than 10%) contribution consistent with concentration measurements showing that the interior of the jet is well mixed. (Turbulent jets differ greatly from the free shear layer in this respect.) To explain the difference between velocity and scalar profiles, their conditional mean gradients are defined in terms of a local eddy viscosity and eddy diffusivity and the momentum and scalar fluxes inside the interface. Since the eddy diffusivity is larger than the eddy viscosity, the scalar profile is flatter inside the interface so that the scalar discontinuity is relatively greater than the mean velocity discontinuity. Theoretical arguments, following Hunt, Eames & Westerweel (in Proc. of the IUTAM Symp. on Computational Physics and New Perspectives in Turbulence, ed. Y. Kaneda, vol. 4, 2008, pp. 331–338, Springer), are proposed for how the vortex sheet develops, how the internal structure of the interface layer relates to the inhomogeneous rotational and irrotational motions on each side and why the dominant entrainment process of jets and wakes differs from that of free shear layers.
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Silva, Tiago S., Marco Zecchetto, and Carlos B. da Silva. "The scaling of the turbulent/non-turbulent interface at high Reynolds numbers." Journal of Fluid Mechanics 843 (March 21, 2018): 156–79. http://dx.doi.org/10.1017/jfm.2018.143.
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The scaling of the turbulent/non-turbulent interface (TNTI) at high Reynolds numbers is investigated by using direct numerical simulations (DNS) of temporal turbulent planar jets (PJET) and shear free turbulence (SFT), with Reynolds numbers in the range $142\leqslant Re_{\unicode[STIX]{x1D706}}\leqslant 400$. For $Re_{\unicode[STIX]{x1D706}}\gtrsim 200$ the thickness of the TNTI ($\unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D714}}$), like that of its two sublayers – the viscous superlayer (VSL, $\unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D708}}$) and the turbulent sublayer (TSL, $\unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D70E}}$) – all scale with the Kolmogorov micro-scale $\unicode[STIX]{x1D702}$, while the particular scaling constant depends on the sublayer. Specifically, for $Re_{\unicode[STIX]{x1D706}}\gtrsim 200$ while the VSL is always of the order of $\unicode[STIX]{x1D702}$, with $4\leqslant \langle \unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D708}}\rangle /\unicode[STIX]{x1D702}\leqslant 5$, the TSL and the TNTI are typically equal to $10\unicode[STIX]{x1D702}$, with $10.4\leqslant \langle \unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D70E}}\rangle /\unicode[STIX]{x1D702}\leqslant 12.5$, and $15.4\leqslant \langle \unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D714}}\rangle /\unicode[STIX]{x1D702}\leqslant 16.8$, respectively.
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HASEGAWA, SUSUMU, KATSUNOBU NISHIHARA, and HITOSHI SAKAGAMI. "NUMERICAL SIMULATION OF MIXING BY RAYLEIGH-TAYLOR INSTABILITY AND ITS FRACTAL STRUCTURES." Fractals 04, no. 03 (September 1996): 241–50. http://dx.doi.org/10.1142/s0218348x96000339.
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Turbulent interface caused by the 2-dimensional Rayleigh-Taylor instability is investigated by direct numerical simulation. It is shown that the interface becomes fractal spontaneously in the case where there are initially multimode perturbations on the interface. The generalized dimensions and the singularity spectrum are obtained by applying the multifractal theory to the turbulent interface. The fractal dimension of the line interface is found to be 1.7–1.8, which is greater than that of turbulent/nonturbulent interface in a turbulent flow. Time evolution of the fractal dimensions of the interface is also investigated.
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Watanabe, Tomoaki, Yasuhiko Sakai, Kouji Nagata, Yasumasa Ito, and Toshiyuki Hayase. "Vortex stretching and compression near the turbulent/non-turbulent interface in a planar jet." Journal of Fluid Mechanics 758 (October 13, 2014): 754–85. http://dx.doi.org/10.1017/jfm.2014.559.
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AbstractVortex stretching and compression, which cause enstrophy production by inviscid processes, are investigated near the turbulent/non-turbulent (T/NT) interface in a planar jet by using a direct numerical simulation (DNS). The enstrophy production is investigated by analysing the relationship among a vorticity vector, strain-rate eigenvectors and strain-rate eigenvalues. The statistics are calculated individually for three different interface orientations. The vorticity near the T/NT interface is oriented in the tangential direction to the interface. The enstrophy production is affected by the interface orientation because the intensity of vortex stretching depends on the interface orientation, and the alignment between the vorticity vector and the strain-rate eigenvectors is confined by the interface. The enstrophy production near the T/NT interface is analysed by considering the motion of turbulent fluid relative to that of the interface. The results show that the alignment between the interface and the strain-rate eigenvectors changes depending on the velocity field near the T/NT interface. When the turbulent fluid moves toward the T/NT interface, the enstrophy is generated by vortex stretching without being greatly affected by vortex compression. In contrast, when the turbulent fluid relatively moves away from the T/NT interface, large enstrophy reduction frequently occurs by vortex compression. Thus, it is shown that the velocity field near the T/NT interface affects the enstrophy production near the interface through the alignment between the vorticity and the strain-rate eigenvectors.
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BRIGGS, DAVID A., JOEL H. FERZIGER, JEFFREY R. KOSEFF, and STEPHEN G. MONISMITH. "Turbulent mixing in a shear-free stably stratified two-layer fluid." Journal of Fluid Mechanics 354 (January 10, 1998): 175–208. http://dx.doi.org/10.1017/s0022112097007672.
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Direct numerical simulation is used to examine turbulent mixing in a shear-free stably stratified fluid. Energy is continuously supplied to a small region to maintain a well-developed kinetic energy profile, as in an oscillating grid flow (Briggs et al. 1996; Hopfinger & Toly 1976; Nokes 1988). A microscale Reynolds number of 60 is maintained in the source region. The turbulence forms a well-mixed layer which diffuses from the source into the quiescent fluid below. Turbulence transport at the interface causes the mixed layer to grow under weakly stratified conditions. When the stratification is strong, large-scale turbulent transport is inactive and pressure transport becomes the principal mechanism for the growth of the turbulence layer. Down-gradient buoyancy flux is present in the large scales; however, far from the source, weak counter-gradient fluxes appear in the medium to small scales. The production of internal waves and counter-gradient fluxes rapidly reduces the mixing when the turbulent Froude number is lower than unity. When the stratification is weak, the turbulence is strong enough to break up the density interface and transport fluid parcels of different density over large vertical distances. As the stratification intensifies, turbulent eddies flatten against the interface creating anisotropy and internal waves. The dominant entrainment mechanism is then scouring. Mixing efficiency, defined as the ratio of buoyancy flux to available kinetic energy, exhibits a similar dependence on Froude number to other stratified flows (Holt et al. 1992; Lienhard & Van Atta 1990). However, using the anisotropy of the turbulence to define an alternative mixing efficiency and Froude number improves the correlation and allows local scaling.
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Voermans, J. J., M. Ghisalberti, and G. N. Ivey. "The variation of flow and turbulence across the sediment–water interface." Journal of Fluid Mechanics 824 (July 6, 2017): 413–37. http://dx.doi.org/10.1017/jfm.2017.345.
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A basic framework characterising the interaction between aquatic flows and permeable sediment beds is presented here. Through the permeability Reynolds number ($Re_{K}=\sqrt{K}u_{\ast }/\unicode[STIX]{x1D708}$, where$K$is the sediment permeability,$u_{\ast }$is the shear velocity and$\unicode[STIX]{x1D708}$is the fluid viscosity), the framework unifies two classical flow typologies, namely impermeable boundary layer flows ($Re_{K}\ll 1$) and highly permeable canopy flows ($Re_{K}\gg 1$). Within this range, the sediment–water interface (SWI) is identified as a transitional region, with$Re_{K}$in aquatic systems typically$O(0.001{-}10)$. As the sediments obstruct conventional measurement techniques, experimental observations of interfacial hydrodynamics remain extremely rare. The use of refractive index matching here allows measurement of the mean and turbulent flow across the SWI and thus direct validation of the proposed framework. This study demonstrates a strong relationship between the structure of the mean and turbulent flow at the SWI and$Re_{K}$. Hydrodynamic characteristics, such as the interfacial turbulent shear stress, velocity, turbulence intensities and turbulence anisotropy tend towards those observed in flows over impermeable boundaries as$Re_{K}\rightarrow 0$and towards those seen in flows over highly permeable boundaries as$Re_{K}\rightarrow \infty$. A value of$Re_{K}\approx 1{-}2$is seen to be an important threshold, above which the turbulent stress starts to dominate the fluid shear stress at the SWI, the penetration depths of turbulence and the mean flow into the sediment bed are comparable and similarity relationships developed for highly permeable boundaries hold. These results are used to provide a new perspective on the development of interfacial transport models at the SWI.
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Chandrasekhara, M. S., and B. R. Ramaprian. "Intermittency and Length Scale Distributions in a Plane Turbulent Plume." Journal of Fluids Engineering 112, no. 3 (September 1, 1990): 367–69. http://dx.doi.org/10.1115/1.2909413.
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Previous studies have shown that normalized Reynolds shear stress and turbulent heat fluxes in asymptotic plane turbulent plumes are significantly higher than in asymptotic plane turbulent jets. This paper describes an attempt to relate this increase to the length scales in the flow. Hot/cold interface intermittency and integral-length-scale distributions were measured in both these flows. The interface-intermittency distributions were found to be bell-shaped in the plume in contrast to a nearly top-hat shape in a jet, thus providing confirmation of the role of buoyancy in generating larger scales in plumes. These larger scales cause the integral length of turbulence in the plume to increase by nearly 15 percent relative to the non-buoyant jet.
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Wu, Zhao, Tamer A. Zaki, and Charles Meneveau. "High-Reynolds-number fractal signature of nascent turbulence during transition." Proceedings of the National Academy of Sciences 117, no. 7 (February 5, 2020): 3461–68. http://dx.doi.org/10.1073/pnas.1916636117.
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Transition from laminar to turbulent flow occurring over a smooth surface is a particularly important route to chaos in fluid dynamics. It often occurs via sporadic inception of spatially localized patches (spots) of turbulence that grow and merge downstream to become the fully turbulent boundary layer. A long-standing question has been whether these incipient spots already contain properties of high-Reynolds-number, developed turbulence. In this study, the question is posed for geometric scaling properties of the interface separating turbulence within the spots from the outer flow. For high-Reynolds-number turbulence, such interfaces are known to display fractal scaling laws with a dimension D≈7/3, where the 1/3 excess exponent above 2 (smooth surfaces) follows from Kolmogorov scaling of velocity fluctuations. The data used in this study are from a direct numerical simulation, and the spot boundaries (interfaces) are determined by using an unsupervised machine-learning method that can identify such interfaces without setting arbitrary thresholds. Wide separation between small and large scales during transition is provided by the large range of spot volumes, enabling accurate measurements of the volume–area fractal scaling exponent. Measurements show a dimension of D=2.36±0.03 over almost 5 decades of spot volume, i.e., trends fully consistent with high-Reynolds-number turbulence. Additional observations pertaining to the dependence on height above the surface are also presented. Results provide evidence that turbulent spots exhibit high-Reynolds-number fractal-scaling properties already during early transitional and nonisotropic stages of the flow evolution.
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Ali, S. Firasat, and E. A. Ibrahim. "Coincidence of turbulent-nonturbulent interface and hot-cold interface in a plane turbulent wake." Mechanics Research Communications 23, no. 1 (January 1996): 91–102. http://dx.doi.org/10.1016/0093-6413(95)00082-8.
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HUNT, J. C. R., D. D. STRETCH, and S. E. BELCHER. "Viscous coupling of shear-free turbulence across nearly flat fluid interfaces." Journal of Fluid Mechanics 671 (February 24, 2011): 96–120. http://dx.doi.org/10.1017/s0022112010005525.
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The interactions between shear-free turbulence in two regions (denoted as + and − on either side of a nearly flat horizontal interface are shown here to be controlled by several mechanisms, which depend on the magnitudes of the ratios of the densities, ρ+/ρ−, and kinematic viscosities of the fluids, μ+/μ−, and the root mean square (r.m.s.) velocities of the turbulence, u0+/u0−, above and below the interface. This study focuses on gas–liquid interfaces so that ρ+/ρ− ≪ 1 and also on where turbulence is generated either above or below the interface so that u0+/u0− is either very large or very small. It is assumed that vertical buoyancy forces across the interface are much larger than internal forces so that the interface is nearly flat, and coupling between turbulence on either side of the interface is determined by viscous stresses. A formal linearized rapid-distortion analysis with viscous effects is developed by extending the previous study by Hunt & Graham (J. Fluid Mech., vol. 84, 1978, pp. 209–235) of shear-free turbulence near rigid plane boundaries. The physical processes accounted for in our model include both the blocking effect of the interface on normal components of the turbulence and the viscous coupling of the horizontal field across thin interfacial viscous boundary layers. The horizontal divergence in the perturbation velocity field in the viscous layer drives weak inviscid irrotational velocity fluctuations outside the viscous boundary layers in a mechanism analogous to Ekman pumping. The analysis shows the following. (i) The blocking effects are similar to those near rigid boundaries on each side of the interface, but through the action of the thin viscous layers above and below the interface, the horizontal and vertical velocity components differ from those near a rigid surface and are correlated or anti-correlated respectively. (ii) Because of the growth of the viscous layers on either side of the interface, the ratio uI/u0, where uI is the r.m.s. of the interfacial velocity fluctuations and u0 the r.m.s. of the homogeneous turbulence far from the interface, does not vary with time. If the turbulence is driven in the lower layer with ρ+/ρ− ≪ 1 and u0+/u0− ≪ 1, then uI/u0− ~ 1 when Re (=u0−L−/ν−) ≫ 1 and R = (ρ−/ρ+)(v−/v+)1/2 ≫ 1. If the turbulence is driven in the upper layer with ρ+/ρ− ≪ 1 and u0+/u0− ≫ 1, then uI/u0+ ~ 1/(1 + R). (iii) Nonlinear effects become significant over periods greater than Lagrangian time scales. When turbulence is generated in the lower layer, and the Reynolds number is high enough, motions in the upper viscous layer are turbulent. The horizontal vorticity tends to decrease, and the vertical vorticity of the eddies dominates their asymptotic structure. When turbulence is generated in the upper layer, and the Reynolds number is less than about 106–107, the fluctuations in the viscous layer do not become turbulent. Nonlinear processes at the interface increase the ratio uI/u0+ for sheared or shear-free turbulence in the gas above its linear value of uI/u0+ ~ 1/(1 + R) to (ρ+/ρ−)1/2 ~ 1/30 for air–water interfaces. This estimate agrees with the direct numerical simulation results from Lombardi, De Angelis & Bannerjee (Phys. Fluids, vol. 8, no. 6, 1996, pp. 1643–1665). Because the linear viscous–inertial coupling mechanism is still significant, the eddy motions on either side of the interface have a similar horizontal structure, although their vertical structure differs.
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GERASHCHENKO, S., G. GOOD, and Z. WARHAFT. "Entrainment and mixing of water droplets across a shearless turbulent interface with and without gravitational effects." Journal of Fluid Mechanics 668 (January 26, 2011): 293–303. http://dx.doi.org/10.1017/s002211201000577x.
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We describe experiments of the entrainment and mixing of water (sub-Kolmogorov scale) droplets across a turbulent–non-turbulent interface (TNI) as well a turbulent–turbulent interface (TTI) in shearless grid turbulence, over a time scale in which evaporation is insignificant. The flow is produced by means of a splitter plate with an active grid and water sprays on one side and screens or an active grid on the other side. The Taylor microscale Reλ on the turbulent side is 275 and the average dissipation scale Stokes number, Stη ≈ 0.2, and based on the integral scale, Stl ≈ 0.003. By changing the orientation of the grid system, gravitational effects may be excluded or included. We show that in the absence of gravity, for the Stokes number range studied (0.06 ≤ Stη ≤ 1.33), the droplet distribution does not change across the interface. With gravity, the larger drops are selectively mixed and this is more pronounced for the TNI than for the TTI. The particle concentration distribution is an error function for the TTI but departs significantly for the TNI due to the intermittency in the flow. In terms of particle concentration, the entrainment is most efficient for the TTI with gravity. The results are related to droplet entrainment in clouds.
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Neuhaus, Lars, Matthias Wächter, and Joachim Peinke. "The fractal turbulent–non-turbulent interface in the atmosphere." Wind Energy Science 9, no. 2 (February 22, 2024): 439–52. http://dx.doi.org/10.5194/wes-9-439-2024.
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Abstract. With their constant increase in size, wind turbines are reaching unprecedented heights. Therefore, at these heights, they are influenced by wind conditions that have not yet been studied in detail. With increasing height, a transition to laminar conditions becomes more and more likely. In this paper, the presence of the turbulent–non-turbulent interface (TNTI) in the atmosphere is investigated. Three different on- and offshore locations are investigated. Our fractal scaling analysis leads to typical values known from ideal laboratory and numerical studies. The height distribution of the probability of the TNTI is determined and shows a frequent occurrence at the height of the rotor of future multi-megawatt turbines. The indicated universality of the fractality of the TNTI allows the use of simplified models in laboratory and numerical investigations.
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Yu, Jia-Long, and Xi-Yun Lu. "Topological evolution near the turbulent/non-turbulent interface in turbulent mixing layer." Journal of Turbulence 20, no. 5 (May 4, 2019): 300–321. http://dx.doi.org/10.1080/14685248.2019.1640368.
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Steiner, Helfried, and Christian Walchshofer. "Small-scale mixing at the turbulent/non-turbulent interface in turbulent jets." PAMM 11, no. 1 (December 2011): 601–2. http://dx.doi.org/10.1002/pamm.201110290.
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FERNANDO, H. J. S., and J. C. R. HUNT. "Turbulence, waves and mixing at shear-free density interfaces. Part 1. A theoretical model." Journal of Fluid Mechanics 347 (September 25, 1997): 197–234. http://dx.doi.org/10.1017/s0022112097006514.
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This paper presents a theoretical model of turbulence and mixing at a shear-free stable density interface. In one case (single-sided stirring) the interface separates a layer of fluid of density ρ in turbulent motion, with r.m.s. velocity uH and lengthscale LH, from a non-turbulent layer with density ρ+Δρ, while in the second case (double-sided stirring) the lower layer is also in turbulent motion. In both cases, the external Richardson number Ri=ΔbLH/ u2H (where Δb is the buoyancy jump across the interface) is assumed to be large. Based on the hypotheses that the effect of the interface on the turbulence is as if it were suddenly imposed (which is equivalent to generating irrotational motions) and that linear waves are generated in the interface, the techniques of rapid distortion theory are used to analyse the linear aspects of the distortion of turbulence and of the interfacial motions. New physical concepts are introduced to account for the nonlinear aspects.To describe the spectra and variations of the r.m.s. fluctuations of velocity and displacements, a statistically steady linear model is used for frequencies above a critical frequency ωr/μc, where ωr(=Δb/2uH) is the maximum resonant frequency and μc<1. As in other nonlinear systems, observations below this critical frequency show the existence of long waves on the interface that can grow, break and cause mixing between the two fluid layers. A nonlinear model is constructed based on the fact that these breaking waves have steep slopes (which determines the form of the displacement spectrum) and on the physical argument that the energy of the vertical motions of these dissipative nonlinear waves should be comparable to that of the forced linear waves, which leads to an approximately constant value for the parameter μc. The model predictions of the vertical r.m.s. interfacial velocity, the interfacial wave amplitude and the velocity spectra agree closely with new and published experimental results.An exact unsteady inviscid linear analysis is used to derive the growth rate of the full spectrum, which asymptotically leads to the growth of resonant waves and to the energy transfer from the turbulent region to the wave motion of the stratified layer. Mean energy flux into the stratified layer, averaged over a typical wave cycle, is used to estimate the boundary entrainment velocity for the single-sided stirring case and the flux entrainment velocity for the double-sided stirring case, by making the assumption that the ratio of buoyancy flux to dissipation rate in forced stratified layers is constant with Ri and has the same value as in other stratified turbulent flows. The calculations are in good agreement with laboratory measurements conducted in mixing boxes and in wind tunnels. The contribution of Kelvin–Helmholtz instabilities induced by the velocity of turbulent eddies parallel to the interface is estimated to be insignificant compared to that of internal waves excited by turbulence.
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Variano, Evan A., and Edwin A. Cowen. "Turbulent transport of a high-Schmidt-number scalar near an air–water interface." Journal of Fluid Mechanics 731 (August 14, 2013): 259–87. http://dx.doi.org/10.1017/jfm.2013.273.
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AbstractWe measure solute transport near a turbulent air–water interface at which there is zero mean shear. The interface is stirred by high-Reynolds-number homogeneous isotropic turbulence generated far below the surface, and solute transport into the water is driven by an imposed concentration gradient. The air–water interface is held at a constant concentration much higher than that in the bulk of the water by maintaining pure${\mathrm{CO} }_{2} $gas above a water tank that has been initially purged of dissolved${\mathrm{CO} }_{2} $. We measure velocity and concentration fluctuations below the air–water interface, from the viscous sublayer to the middle of the ‘source region’ where the effects of the surface are first felt. Our laboratory measurement technique uses quantitative imaging to collect simultaneous concentration and velocity fields, which are measured at a resolution that reveals the dynamics in the turbulent inertial subrange. Two-point statistics reveal the spatial structure of velocity and concentration fluctuations, and are examined as a function of depth beneath the air–water interface. There is a clear dominance of large scales at all depths for all quantities, but the relative importance of scales changes markedly with proximity to the interface. Quadrant analysis of the turbulent scalar flux shows a four-way balance of flux components far from the interface, which near the interface evolves into a two-way balance between motions that are raising and lowering parcels of low-concentration fluid.
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Gu, Li, Hang Yuan, Qiu Lan Li, Zi Nan Jiao, and Lan Lan Wang. "Comparison of Turbulent Intensity Component of the Stratified Flow in the Braided River with Different Upstream Flowrates." Applied Mechanics and Materials 448-453 (October 2013): 554–58. http://dx.doi.org/10.4028/www.scientific.net/amm.448-453.554.
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The physical model experiment was carried out to study the effect of velocity ratio of two layers on the turbulence intensity of stratified flow in the typical braided rivers with two symmetrical anabranches. Two velocity ratios were selected, and the distributions of depth-averaged turbulent intensity component in the left anabranch were analyzed. When velocity ratio became smaller, the turbulent intensity increased and peak turbulent intensity zone transferred from the left area of centerline to the right area of centerline at the section before the bend apex of the anabranch. In the outlet section of the anabranch, turbulent intensity increased at the inner bank. The distributions of lateral-averaged turbulence intensity components in the vertical sections of left anabranch were also analyzed. Turbulence intensity component in the interface of hot and cold water was both high in two velocity ratios. As water flowed downstream, the difference of turbulent intensity component in the vertical direction decreased obviously.
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Tavares, H. S., L. Biferale, M. Sbragaglia, and A. A. Mailybaev. "Validation and application of the lattice Boltzmann algorithm for a turbulent immiscible Rayleigh–Taylor system." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 379, no. 2208 (August 30, 2021): 20200396. http://dx.doi.org/10.1098/rsta.2020.0396.
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We develop a multicomponent lattice Boltzmann (LB) model for the two-dimensional Rayleigh–Taylor turbulence with a Shan–Chen pseudopotential implemented on GPUs. In the immiscible case, this method is able to accurately overcome the inherent numerical complexity caused by the complicated structure of the interface that appears in the fully developed turbulent regime. The accuracy of the LB model is tested both for early and late stages of instability. For the developed turbulent motion, we analyse the balance between different terms describing variations of the kinetic and potential energies. Then we analyse the role of the interface in the energy balance and also the effects of the vorticity induced by the interface in the energy dissipation. Statistical properties are compared for miscible and immiscible flows. Our results can also be considered as a first validation step to extend the application of LB model to three-dimensional immiscible Rayleigh-Taylor turbulence. This article is part of the theme issue ‘Progress in mesoscale methods for fluid dynamics simulation’.
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Kadasch, Eckhard, Matthias Sühring, Tobias Gronemeier, and Siegfried Raasch. "Mesoscale nesting interface of the PALM model system 6.0." Geoscientific Model Development 14, no. 9 (September 3, 2021): 5435–65. http://dx.doi.org/10.5194/gmd-14-5435-2021.
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Abstract. In this paper, we present a newly developed mesoscale nesting interface for the PALM model system 6.0, which enables PALM to simulate the atmospheric boundary layer under spatially heterogeneous and non-stationary synoptic conditions. The implemented nesting interface, which is currently tailored to the mesoscale model COSMO, consists of two major parts: (i) the preprocessor INIFOR (initialization and forcing), which provides initial and time-dependent boundary conditions from mesoscale model output, and (ii) PALM's internal routines for reading the provided forcing data and superimposing synthetic turbulence to accelerate the transition to a fully developed turbulent atmospheric boundary layer. We describe in detail the conversion between the sets of prognostic variables, transformations between model coordinate systems, as well as data interpolation onto PALM's grid, which are carried out by INIFOR. Furthermore, we describe PALM's internal usage of the provided forcing data, which, besides the temporal interpolation of boundary conditions and removal of any residual divergence, includes the generation of stability-dependent synthetic turbulence at the inflow boundaries in order to accelerate the transition from the turbulence-free mesoscale solution to a resolved turbulent flow. We demonstrate and evaluate the nesting interface by means of a semi-idealized benchmark case. We carried out a large-eddy simulation (LES) of an evolving convective boundary layer on a clear-sky spring day. Besides verifying that changes in the inflow conditions enter into and successively propagate through the PALM domain, we focus our analysis on the effectiveness of the synthetic turbulence generation. By analysing various turbulence statistics, we show that the inflow in the present case is fully adjusted after having propagated for about two to three eddy-turnover times downstream, which corresponds well to other state-of-the-art methods for turbulence generation. Furthermore, we observe that numerical artefacts in the form of grid-scale convective structures in the mesoscale model enter the PALM domain, biasing the location of the turbulent up- and downdrafts in the LES. With these findings presented, we aim to verify the mesoscale nesting approach implemented in PALM, point out specific shortcomings, and build a baseline for future improvements and developments.
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Otsuka, Junichi, and Yasunori Watanabe. "LABORATORY OBSERVATIONS OF DISSOLVED CARBON DIOXIDE TRANSPORT UNDER REGULAR BREAKING WAVES." Coastal Engineering Proceedings, no. 36 (December 30, 2018): 77. http://dx.doi.org/10.9753/icce.v36.waves.77.
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Air bubbles and strong turbulence that form in water from breaking waves play important roles in gas transfer across the air-sea interface (Melville, 1996). The entrained bubbles increase the total area of air-water interface per unit volume and enhance local gas dissolution into water. The dissolved gases mix in the water mass diffuse by the strong turbulence. These gas transfer-enhancing factors have been parameterized by only wind speed in models of gas transfer velocity in the deep ocean. Bulk parameters based on wind speed cannot be used for a surf zone, where waves break due to shoaling. In a surf zone, the cross-shore distributions of entrained bubbles and the turbulent intensity vary as waves propagate. The physical process of gas transfer under the complex air-water turbulent flows in breaking waves has not been clarified. Thus, breaking-wave factors that enhance gas transfer in a surf zone cannot be parameterized. In this study, we observed the transport process of dissolved carbon dioxide (DCO2) under air-water turbulent flows in a laboratory surf zone using image measurement systems.
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da Silva, Carlos B., Ricardo J. N. dos Reis, and José C. F. Pereira. "The intense vorticity structures near the turbulent/non-turbulent interface in a jet." Journal of Fluid Mechanics 685 (September 5, 2011): 165–90. http://dx.doi.org/10.1017/jfm.2011.296.
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AbstractThe characteristics of the intense vorticity structures (IVSs) near the turbulent/non-turbulent (T/NT) interface separating the turbulent and the irrotational flow regions are analysed using a direct numerical simulation (DNS) of a turbulent plane jet. The T/NT interface is defined by the radius of the large vorticity structures (LVSs) bordering the jet edge, while the IVSs arise only at a depth of about $5\eta $ from the T/NT interface, where $\eta $ is the Kolmogorov micro-scale. Deep inside the jet shear layer the characteristics of the IVSs are similar to the IVSs found in many other flows: the mean radius, tangential velocity and circulation Reynolds number are $R/ \eta \approx 4. 6$, ${u}_{0} / {u}^{\ensuremath{\prime} } \approx 0. 8$, and ${\mathit{Re}}_{\Gamma } / { \mathit{Re}}_{\lambda }^{1/ 2} \approx 28$, where ${u}_{0} $, and ${\mathit{Re}}_{\lambda } $ are the root mean square of the velocity fluctuations and the Reynolds number based on the Taylor micro-scale, respectively. Moreover, as in forced isotropic turbulence the IVSs inside the jet are well described by the Burgers vortex model, where the vortex core radius is stable due to a balance between the competing effects of axial vorticity production and viscous diffusion. Statistics conditioned on the distance from the T/NT interface are used to analyse the effect of the T/NT interface on the geometry and dynamics of the IVSs and show that the mean radius $R$, tangential velocity ${u}_{0} $ and circulation $\Gamma $ of the IVSs increase as the T/NT interface is approached, while the vorticity norm $\vert \omega \vert $ stays approximately constant. Specifically $R$, ${u}_{0} $ and $\Gamma $ exhibit maxima at a distance of roughly one Taylor micro-scale from the T/NT interface, before decreasing as the T/NT is approached. Analysis of the dynamics of the IVS shows that this is caused by a sharp decrease in the axial stretching rate acting on the axis of the IVSs near the jet edge. Unlike the IVSs deep inside the shear layer, there is a small predominance of vortex diffusion over stretching for the IVSs near the T/NT interface implying that the core of these structures is not stable i.e. it will tend to grow in time. Nevertheless the Burgers vortex model can still be considered to be a good representation for the IVSs near the jet edge, although it is not as accurate as for the IVSs deep inside the jet shear layer, since the observed magnitude of this imbalance is relatively small.
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Nokes, R. I. "On the entrainment rate across a density interface." Journal of Fluid Mechanics 188 (March 1988): 185–204. http://dx.doi.org/10.1017/s0022112088000692.
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Mixed-layer deepening due to grid-generated turbulence is studied experimentally with the aim of explaining the contradictory results of previous studies. Entrainment rates are calculated at fixed distances from the grid in order to avoid the necessity of using an empirical expression for the decay of the turbulent velocity scale. It is shown that an incorrect form of this decay law can cause large errors in the predicted Richardson number dependence of the entrainment rate. For this study this dependence can be expressed as a power law of the form E = KRi−1,2. The spread of the results imply that an error of at least ± 10% is realistic in the determination of the exponent.The turbulent velocity decay law is also deduced from the data, and it is found that the decay cannot be represented by a simple power law. Indeed two distinct flow regions, with differing decay rates, are present.
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Bhowmick, Taraprasad, and Michele Iovieno. "Direct Numerical Simulation of a Warm Cloud Top Model Interface: Impact of the Transient Mixing on Different Droplet Population." Fluids 4, no. 3 (August 1, 2019): 144. http://dx.doi.org/10.3390/fluids4030144.
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Turbulent mixing through atmospheric cloud and clear air interface plays an important role in the life of a cloud. Entrainment and detrainment of clear air and cloudy volume result in mixing across the interface, which broadens the cloud droplet spectrum. In this study, we simulate the transient evolution of a turbulent cloud top interface with three initial mono-disperse cloud droplet population, using a pseudo-spectral Direct Numerical Simulation (DNS) along with Lagrangian droplet equations, including collision and coalescence. Transient evolution of in-cloud turbulent kinetic energy (TKE), density of water vapour and temperature is carried out as an initial value problem exhibiting transient decay. Mixing in between the clear air and cloudy volume produced turbulent fluctuations in the density of water vapour and temperature, resulting in supersaturation fluctuations. Small scale turbulence, local supersaturation conditions and gravitational forces have different weights on the droplet population depending on their sizes. Larger droplet populations, with initial 25 and 18 μ m radii, show significant growth by droplet-droplet collision and a higher rate of gravitational sedimentation. However, the smaller droplets, with an initial 6 μ m radius, did not show any collision but a large size distribution broadening due to differential condensation/evaporation induced by the mixing, without being influenced by gravity significantly.
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Ura, Masaru, and Nobuhiro Matsunaga. "ENTRAINMENT DUE TO MEAN FLOW IN TWO-LAYERED FLUID." Coastal Engineering Proceedings 1, no. 21 (January 29, 1988): 189. http://dx.doi.org/10.9753/icce.v21.189.
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The entrainment phenomena have been investigated across an interface between two-layered stratified flow induced by wind shear stress. The velocities of mean flow, turbulence and entrainment have been measured under three different conditions of water surface by using a wind-wave tank. When the entrainment velocity ue is expressed on the basis of the turbulent quantities at the interface, the turbulent entrainment coefficient E ( = ue/u) is given by E = A-(egl/u2)-3I1 ( A = 0.7). Here Eg, u and 1 are the effective buoyancy, the turbulence intensity and the integral lengthscale of turbulence at the interface, respectively. This result coincides with the relationship of entrainment due to oscillating grid turbulence, in which the mean flow does not exist. When, for the practical purpose, the estimation of ue is made by using the mean velocity Um and the depth h of mixed layer, Em ( - Ue/Um ) = Am•(egh/Um 2)"3/2 is derived from the transformation of E = A-(egl/u2)-3/2. There holds Am = A-Tf between Am and Tf, Tf being a turbulence factor given by (u/Um)4•(1/h)-3/2. It has been found that this relationship is also valid in various types of two-layered stratified flows as well as the wind-induced two-layered flows.
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Westerweel, Jerry, Alberto Petracci, René Delfos, and Julian C. R. Hunt. "Characteristics of the turbulent/non-turbulent interface of a non-isothermal jet." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, no. 1937 (February 28, 2011): 723–37. http://dx.doi.org/10.1098/rsta.2010.0308.
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The turbulent/non-turbulent interface of a jet is characterized by sharp jumps (‘discontinuities’) in the conditional flow statistics relative to the interface. Experiments were carried out to measure the conditional flow statistics for a non-isothermal jet, i.e. a cooled jet. These experiments are complementary to previous experiments on an isothermal Re =2000 jet, where, in the present experiments on a non-isothermal jet, the thermal diffusivity is intermediate to the diffusivity of momentum and the diffusivity of mass. The experimental method is a combined laser-induced fluorescence/particle image velocimetry method, where a temperature-sensitive fluorescent dye (rhodamine 6G) is used to measure the instantaneous temperature fluctuations. The results show that the cooled jet can be considered to behave like a self-similar jet without any significant buoyancy effects. The detection of the interface is based on the instantaneous temperature, and provides a reliable means to detect the interface. Conditional flow statistics reveal the superlayer jump in the conditional vorticity and in the temperature.
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Zhang, Xinxian, Tomoaki Watanabe, and Koji Nagata. "Passive scalar mixing near turbulent/non-turbulent interface in compressible turbulent boundary layers." Physica Scripta 94, no. 4 (January 30, 2019): 044002. http://dx.doi.org/10.1088/1402-4896/aafbdf.
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Yang, Jongmin, Min Yoon, and Hyung Jin Sung. "The turbulent/non-turbulent interface in an adverse pressure gradient turbulent boundary layer." International Journal of Heat and Fluid Flow 86 (December 2020): 108704. http://dx.doi.org/10.1016/j.ijheatfluidflow.2020.108704.
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