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1
Tuckerman, Laurette S., Matthew Chantry, and Dwight Barkley. "Patterns in Wall-Bounded Shear Flows." Annual Review of Fluid Mechanics 52, no. 1 (January 5, 2020): 343–67. http://dx.doi.org/10.1146/annurev-fluid-010719-060221.
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Experiments and numerical simulations have shown that turbulence in transitional wall-bounded shear flows frequently takes the form of long oblique bands if the domains are sufficiently large to accommodate them. These turbulent bands have been observed in plane Couette flow, plane Poiseuille flow, counter-rotating Taylor–Couette flow, torsional Couette flow, and annular pipe flow. At their upper Reynolds number threshold, laminar regions carve out gaps in otherwise uniform turbulence, ultimately forming regular turbulent–laminar patterns with a large spatial wavelength. At the lower threshold, isolated turbulent bands sparsely populate otherwise laminar domains, and complete laminarization takes place via their disappearance. We review results for plane Couette flow, plane Poiseuille flow, and free-slip Waleffe flow, focusing on thresholds, wavelengths, and mean flows, with many of the results coming from numerical simulations in tilted rectangular domains that form the minimal flow unit for the turbulent–laminar bands.
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Duguet, Yohann. "Intermittency in Transitional Shear Flows." Entropy 23, no. 3 (February 26, 2021): 280. http://dx.doi.org/10.3390/e23030280.
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LESCHZINER, M. A., G. M. FISHPOOL, and S. LARDEAU. "TURBULENT SHEAR FLOW: A PARADIGMATIC MULTISCALE PHENOMENON." Journal of Multiscale Modelling 01, no. 02 (April 2009): 197–222. http://dx.doi.org/10.1142/s1756973709000104.
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The paper provides a broad discussion of multiscale and structural features of sheared turbulent flows. Basic phenomenological aspects of turbulence are first introduced, largely in descriptive terms with particular emphasis placed on the range of scales encountered in turbulent flows and in the identification of characteristic scale ranges. There follows a discussion of essential aspects of computational modeling and simulation of turbulence. Finally, the results of simulations for two groups of flows are discussed. These combine shear, separation, and periodicity, the last feature provoked by either a natural instability or by unsteady external forcing. The particular choice of examples is intended to illustrate the capabilities of such simulations to resolve the multiscale nature of complex turbulent flows, as well as the challenges encountered.
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Libby, P. A. "Turbulent shear flows 5." International Journal of Heat and Fluid Flow 9, no. 3 (September 1988): 348. http://dx.doi.org/10.1016/0142-727x(88)90053-7.
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Liu, Zhiyu, S. A. Thorpe, and W. D. Smyth. "Instability and hydraulics of turbulent stratified shear flows." Journal of Fluid Mechanics 695 (February 20, 2012): 235–56. http://dx.doi.org/10.1017/jfm.2012.13.
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AbstractThe Taylor–Goldstein (T–G) equation is extended to include the effects of small-scale turbulence represented by non-uniform vertical and horizontal eddy viscosity and diffusion coefficients. The vertical coefficients of viscosity and diffusion, ${A}_{V} $ and ${K}_{V} $, respectively, are assumed to be equal and are expressed in terms of the buoyancy frequency of the flow, $N$, and the dissipation rate of turbulent kinetic energy per unit mass, $\varepsilon $, quantities that can be measured in the sea. The horizontal eddy coefficients, ${A}_{H} $ and ${K}_{H} $, are taken to be proportional to the dimensionally correct form, ${\varepsilon }^{1/ 3} {l}^{4/ 3} $, found appropriate in the description of horizontal dispersion of a field of passive markers of scale $l$. The extended T–G equation is applied to examine the stability and greatest growth rates in a turbulent shear flow in stratified waters near a sill, that at the entrance to the Clyde Sea in the west of Scotland. Here the main effect of turbulence is a tendency towards stabilizing the flow; the greatest growth rates of small unstable disturbances decrease, and in some cases flows that are unstable in the absence of turbulence are stabilized when its effects are included. It is conjectured that stabilization of a flow by turbulence may lead to a repeating cycle in which a flow with low levels of turbulence becomes unstable, increasing the turbulent dissipation rate and so stabilizing the flow. The collapse of turbulence then leads to a condition in which the flow may again become unstable, the cycle repeating. Two parameters are used to describe the ‘marginality’ of the observed flows. One is based on the proximity of the minimum flow Richardson number to the critical Richardson number, the other on the change in dissipation rate required to stabilize or destabilize an observed flow. The latter is related to the change needed in the flow Reynolds number to achieve zero growth rate. The unstable flows, typical of the Clyde Sea site, are relatively further from neutral stability in Reynolds number than in Richardson number. The effects of turbulence on the hydraulic state of the flow are assessed by examining the speed and propagation direction of long waves in the Clyde Sea. Results are compared to those obtained using the T–G equation without turbulent viscosity or diffusivity. Turbulence may change the state of a flow from subcritical to supercritical.
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Nagano, Y., and M. Hishida. "Improved Form of the k-ε Model for Wall Turbulent Shear Flows." Journal of Fluids Engineering 109, no. 2 (June 1, 1987): 156–60. http://dx.doi.org/10.1115/1.3242636.
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An improved k-ε turbulence model for predicting wall turbulence is presented. The model was developed in conjunction with an accurate calculation of near-wall and low-Reynolds-number flows to meet the requirements of the Evaluation Committee report of the 1980–1981 Stanford Conference on Complex Turbulent Flows. The proposed model was tested by application to turbulent pipe and channel flows, a flat plate boundary layer, a relaminarizing flow, and a diffuser flow. In all cases, the predicted values of turbulent quantities agreed almost completely with measurements, which many previously proposed models failed to predict correctly, over a wide range of the Reynolds number.
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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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Neuhaus, Lars, Daniel Ribnitzky, Michael Hölling, Matthias Wächter, Kerstin Avila, Martin Kühn, and Joachim Peinke. "Model wind turbine performance in turbulent–non-turbulent boundary layer flow." Journal of Physics: Conference Series 2767, no. 4 (June 1, 2024): 042018. http://dx.doi.org/10.1088/1742-6596/2767/4/042018.
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Abstract With increasing distance from the coast and greater hub heights, wind turbines expand into unknown, hardly researched environmental conditions. As height increases, laminar flow conditions become more likely. With the simultaneous increase in rotor diameter, very different flow conditions, from laminar to turbulent, occur over the rotor area. It is crucial to understand the effects of these different flow conditions on wind turbines. We approach this through wind tunnel experiments, presenting a setup with two different active grids. This setup enables the generation of four different flows – homogeneous, shear, turbulent–non-turbulent, and turbulent–non-turbulent shear flow – each with four different turbulence levels. The turbulent–non-turbulent flows exhibit a turbulence intensity gradient between the quasi-laminar flow at the upper and turbulent flow at the lower rotor half, establishing a turbulent–non-turbulent interface between the two rotor halves. In a second step, we investigate the Model Wind Turbine Oldenburg with a rotor diameter of 1.8 m (MoWiTO 1.8) under these conditions and analyze their effects on power output and blade loads. While the power fluctuations depend directly on the turbulence intensity, an additional turbulence intensity gradient shows no significant effect. A stronger effect can be observed for the blade root bending moments, the fluctuations of which increase with shear and also in turbulent–non-turbulent flow.
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Sarkar, S. "Compressibility Effects on Turbulence Growth in High-Speed Shear Flows." Applied Mechanics Reviews 47, no. 6S (June 1, 1994): S179—S183. http://dx.doi.org/10.1115/1.3124401.
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Compressibility effects on the evolution of turbulence are obtained from direct numerical simulation of homogeneous shear flow. It is found that when the gradient Mach number - a parameter based on the mean shear rate, integral length scale and speed of sound - increases, the growth of turbulent kinetic energy is inhibited. The reduced ‘efficiency’ of production is shown to lead to the inhibited growth of turbulent kinetic energy. Implications for inhomogeneous shear flows are discussed.
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DOU, HUA-SHU, and BOO CHEONG KHOO. "CRITERIA OF TURBULENT TRANSITION IN PARALLEL FLOWS." Modern Physics Letters B 24, no. 13 (May 30, 2010): 1437–40. http://dx.doi.org/10.1142/s0217984910023815.
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Based on the energy gradient method, criteria for turbulent transition are proposed for pressure driven flow and shear driven flow, respectively. For pressure driven flow, the necessary and sufficient condition for turbulent transition is the presence of the velocity inflection point in the averaged flow. For shear driven flow, the necessary and sufficient condition for turbulent transition is the existence of zero velocity gradient in the averaged flow profile. It is shown that turbulent transition can be effected via a singularity of the energy gradient function which may be associated with the chaotic attractor in dynamic system. The role of disturbance in the transition is also clarified in causing the energy gradient function to approach the singularity. Finally, it is interesting that turbulence can be controlled by modulating the distribution of the energy gradient function.
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MIYAMOTO, HITOSHI, and TOHRU KANDA. ""MULTIRESOLUTIONAL-PROPER ORTHOGONAL" HYBRID ANALYSIS ON TURBULENT STRUCTURES IN OPEN-CHANNEL COMPLEX GEOMETRY FLOWS." International Journal of Wavelets, Multiresolution and Information Processing 04, no. 02 (June 2006): 297–310. http://dx.doi.org/10.1142/s0219691306001270.
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We propose a hybrid expansion that consists of a multiresolution approximation (MRA) and a proper orthogonal decomposition (POD) to analyze turbulent flow structures in open-channel flows with complex geometries. The open-channel cavity flows are examined here and their velocity vectors are measured by using particle image velocimetry (PIV). In the first step of the hybrid expansion, the velocity time-series are classified into three distinct components using the MRA, i.e. pseudo-mean velocity, organized turbulence in a mixing shear layer, and incoherent turbulence. In the next step, these velocity components are decomposed by applying the POD. The principal components of the pseudo-mean velocity and the organized turbulence disclose the predominant flow characteristics, such as spatial structures of recirculating flows in the cavity and organized turbulent motions along the mixing shear layer, hysteretic behavior in modal time-series, and so forth. The results strongly support that the present hybrid analysis is effective for detecting spatiotemporal hierarchical structures in turbulent flows with complex geometries.
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Mostafa, A. A. "Turbulent Diffusion of Heavy-Particles in Turbulent Jets." Journal of Fluids Engineering 114, no. 4 (December 1, 1992): 667–71. http://dx.doi.org/10.1115/1.2910083.
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The turbulent dispersion of heavy suspended particles in turbulent shear flows is analyzed when crossing trajectory effects are important. A semiempirical expression for particle diffusion coefficient is developed via a comparison with experimental data of two-phase turbulent jet flows. This expression gives the particle momentum diffusion coefficient in terms of the gas diffusion coefficient, mean relatively velocity, and root mean square of the fluctuating fluid velocity. The proposed expression is used in a two-phase flow mathematical model to predict different particle-laden jet flows. The good agreement between the predictions and data suggests that the developed expression for particle diffusion coefficient is reasonably accurate in predicting particle dispersion in turbulent free shear flows.
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Khapko, T., P. Schlatter, Y. Duguet, and D. S. Henningson. "Turbulence collapse in a suction boundary layer." Journal of Fluid Mechanics 795 (April 14, 2016): 356–79. http://dx.doi.org/10.1017/jfm.2016.205.
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Turbulence in the asymptotic suction boundary layer is investigated numerically at the verge of laminarisation using direct numerical simulation. Following an adiabatic protocol, the Reynolds number $Re$ is decreased in small steps starting from a fully turbulent state until laminarisation is observed. Computations in a large numerical domain allow in principle for the possible coexistence of laminar and turbulent regions. However, contrary to other subcritical shear flows, no laminar–turbulent coexistence is observed, even near the onset of sustained turbulence. High-resolution computations suggest a critical Reynolds number $Re_{g}\approx 270$, below which turbulence collapses, based on observation times of $O(10^{5})$ inertial time units. During the laminarisation process, the turbulent flow fragments into a series of transient streamwise-elongated structures, whose interfaces do not display the characteristic obliqueness of classical laminar–turbulent patterns. The law of the wall, i.e. logarithmic scaling of the velocity profile, is retained down to $Re_{g}$, suggesting a large-scale wall-normal transport absent in internal shear flows close to the onset. In order to test the effect of these large-scale structures on the near-wall region, an artificial volume force is added to damp spanwise and wall-normal fluctuations above $y^{+}=100$, in viscous units. Once the largest eddies have been suppressed by the forcing, and thus turbulence is confined to the near-wall region, oblique laminar–turbulent interfaces do emerge as in other wall-bounded flows, however only transiently. These results suggest that oblique stripes at the onset are a prevalent feature of internal shear flows, but will not occur in canonical boundary layers, including the spatially growing ones.
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Humphrey, Joseph A. C. "Turbulent shear flows 4 — selected papers from the fourth international symposium on turbulent shear flows." International Journal of Heat and Fluid Flow 8, no. 1 (March 1987): 76–78. http://dx.doi.org/10.1016/0142-727x(87)90056-7.
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DIMOTAKIS, PAUL E. "The mixing transition in turbulent flows." Journal of Fluid Mechanics 409 (April 25, 2000): 69–98. http://dx.doi.org/10.1017/s0022112099007946.
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Data on turbulent mixing and other turbulent-flow phenomena suggest that a (mixing) transition, originally documented to occur in shear layers, also occurs in jets, as well as in other flows and may be regarded as a universal phenomenon of turbulence. The resulting fully-developed turbulent flow requires an outer-scale Reynolds number of Re = Uδ/v [gsim ] 1–2 × 104, or a Taylor Reynolds number of ReT = u′ λT/v [gsim ] 100–140, to be sustained. A proposal based on the relative magnitude of dimensional spatial scales is offered to explain this behaviour.
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Chantry, Matthew, and Tobias M. Schneider. "Studying edge geometry in transiently turbulent shear flows." Journal of Fluid Mechanics 747 (April 23, 2014): 506–17. http://dx.doi.org/10.1017/jfm.2014.150.
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AbstractIn linearly stable shear flows at moderate Reynolds number, turbulence spontaneously decays despite the existence of a codimension-one manifold, termed the edge, which separates decaying perturbations from those triggering turbulence. We statistically analyse the decay in plane Couette flow, quantify the breaking of self-sustaining feedback loops and demonstrate the existence of a whole continuum of possible decay paths. Drawing parallels with low-dimensional models and monitoring the location of the edge relative to decaying trajectories, we provide evidence that the edge of chaos does not separate state space globally. It is instead wrapped around the turbulence generating structures and not an independent dynamical structure but part of the chaotic saddle. Thereby, decaying trajectories need not cross the edge, but circumnavigate it while unwrapping from the turbulent saddle.
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Schumann, U., and T. Gerz. "Turbulent Mixing in Stably Stratified Shear Flows." Journal of Applied Meteorology 34, no. 1 (January 1, 1995): 33–48. http://dx.doi.org/10.1175/1520-0450-34.1.33.
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Abstract Vertical mixing of momentum and heat is investigated in turbulent stratified shear flows. It is assumed that the flow has uniform shear and stratification with homogeneous turbulence and that an equilibrium is reached between kinetic and potential energy without gravity wave oscillations. A simple model is derived to estimate vertical diffusivities for Richardson numbers in between 0 and about 1. The model is based on the budgets of kinetic and potential energy and assumes a linear relationship between dissipation, shear, and vertical velocity variance for closure. Scalar fluctuations are related to shear or buoyancy frequency depending on the Richardson number. The turbulent Prandtl number and the growth rate of kinetic energy are specified as functions of this number. Model coefficients are determined mainly from laboratory measurements. Data from large-eddy simulations are used to determine the "stationary" Richardson number with balanced shear production, dissipation, and buoyancy terms. The results of the model are compared with data from laboratory experiments in air or saltwater, with measurements in the atmospheric boundary layer and in the stable troposphere, and with results from the numerical simulations. The model interpolates the observations within the scatter of the data. Theanalysis shows intrinsic relationships between several mixing parameters.
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So, Ronald M. C. "An Analytically Derived Shear Stress and Kinetic Energy Equation for One-Equation Modelling of Complex Turbulent Flows." Symmetry 13, no. 4 (March 31, 2021): 576. http://dx.doi.org/10.3390/sym13040576.
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The Reynolds stress equations for two-dimensional and axisymmetric turbulent shear flows are simplified by invoking local equilibrium and boundary layer approximations in the near-wall region. These equations are made determinate by appropriately modelling the pressure–velocity correlation and dissipation rate terms and solved analytically to give a relation between the turbulent shear stress τ/ρ and the kinetic energy of turbulence (k=q2/2). This is derived without external body force present. The result is identical to that proposed by Nevzgljadov in A Phenomenological Theory of Turbulence, who formulated it through phenomenological arguments based on atmospheric boundary layer measurements. The analytical approach is extended to treat turbulent flows with external body forces. A general relation τ/ρ=a11−AFRiFq2/2 is obtained for these flows, where FRiF is a function of the gradient Richardson number RiF, and a1 is found to depend on turbulence models and their assumed constants. One set of constants yields a1= 0.378, while another gives a1= 0.328. With no body force, F ≡ 1 and the relation reduces to the Nevzgljadov equation with a1 determined to be either 0.378 or 0.328, depending on model constants set assumed. The present study suggests that 0.328 is in line with Nevzgljadov’s proposal. Thus, the present approach provides a theoretical base to evaluate the turbulent shear stress for flows with external body forces. The result is used to reduce the k–ε model to a one-equation model that solves the k-equation, the shear stress and kinetic energy equation, and an ε evaluated by assuming isotropic eddy viscosity behavior.
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de Kat, Roeland, and Bharathram Ganapathisubramani. "Frequency–wavenumber mapping in turbulent shear flows." Journal of Fluid Mechanics 783 (October 15, 2015): 166–90. http://dx.doi.org/10.1017/jfm.2015.558.
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Spatial turbulence spectra for high-Reynolds-number shear flows are usually obtained by mapping experimental frequency spectra into wavenumber space using Taylor’s hypothesis, but this is known to be less than ideal. In this paper, we propose a cross-spectral approach that allows us to determine the entire wavenumber–frequency spectrum using two-point measurements. The method uses cross-spectral phase differences between two points – equivalent to wave velocities – to reconstruct the wavenumber–frequency plane, which can then be integrated to obtain the spatial spectrum. We verify the technique on a particle image velocimetry (PIV) data set of a turbulent boundary layer. To show the potential influence of the different mappings, the transfer functions that we obtained from our PIV data are applied to hot-wire data at approximately the same Reynolds number. Comparison of the newly proposed technique with the classic approach based on Taylor’s hypothesis shows that – as expected – Taylor’s hypothesis holds for larger wavenumbers (small spatial scales), but there are significant differences for smaller wavenumbers (large spatial scales). In the range of Reynolds number examined in this study, double-peaked spectra in the outer region of a turbulent wall flow are thought to be the result of using Taylor’s hypothesis. This is consistent with previous studies that focused on examining the limitations of Taylor’s hypothesis (del Álamo & Jiménez, J. Fluid Mech., vol. 640, 2009, pp. 5–26). The newly proposed mapping method provides a data-driven approach to map frequency spectra into wavenumber spectra from two-point measurements and will allow the experimental exploration of spatial spectra in high-Reynolds-number turbulent shear flows.
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Rohr, J. J., E. C. Itsweire, K. N. Helland, and C. W. Van Atta. "An investigation of the growth of turbulence in a uniform-mean-shear flow." Journal of Fluid Mechanics 187 (February 1988): 1–33. http://dx.doi.org/10.1017/s002211208800031x.
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A uniform-mean-gradient shear flow was produced using a ten-layer closed-loop water channel, providing long enough dimensionless flow development times (τ = (x/Ū) (∂ Ū/∂z)) for the turbulence to grow. The rate of growth of the turbulence compares well with similar measurements in wind-tunnel-generated uniform shear flows for which the mean shears and centreline velocities are larger by an order of magnitude. Preliminary investigations were undertaken to study the growth of the turbulent intensity as functions of the mean shear, centreline velocity, and initial disturbance lengthscales. Initial disturbance lengthscales were varied by using grids of different mesh sizes.Turbulent intensities were found to increase nearly linearly with τ. Differences in grid mesh size produce different offsets in the turbulent intensity level, with a larger grid mesh producing a higher positive offset. This offset persists throughout the growth of the turbulent intensity. These observations provide valuable insight in interpreting previous wind-tunnel measurements, in particular the high-shear experiments of Karnik & Tavoularis (1983). Comparison with the theoretical predictions of Tavoularis (1985) allows for an improved universal characterization of evolving turbulence in a uniform mean shear.
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Patiño, Francisco, Léa Voivenel, Michael Gauding, Luminita Danaila, and Émilien Varea. "On The Determination Of Conditional Statistics Along Gradient Trajectories At The Turbulent/Non-Turbulent Interface Of Jet Flows." Proceedings of the International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics 21 (July 8, 2024): 1–15. http://dx.doi.org/10.55037/lxlaser.21st.179.
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Conditional sampling and averaging are valuable techniques for discerning and quantifying notable regions within turbulent flows. These methods have been particularly prevalent in experimental and numerical investigations of turbulent shear flows. Conditional statistics effectively analyze the dynamics and characteristics of turbulent flows, offering insights into transitional behaviors and distinct features within these regimes. This approach is instrumental in studying turbulent shear flows, such as jets or mixing layers, where a well-defined zone separates the turbulent core from the non-turbulent surrounding fluid. This zone, known as the Turbulent/Non-Turbulent Interface (TNTI), plays a crucial role in various phenomenological changes, including the transfer of mass, momentum, and scalar fluxes. While statistics in jet flows are often reported along the radial direction for a given downstream position, this method can obscure the underlying physical processes. Scalar dissipation rate, transport, or turbulent kinetic energy involve velocity or concentration gradients at the flow interface. To date, the impact of sampling direction on conditional statistics within jet flows has not yet been thoroughly discussed. This study focuses on determining gradient trajectories at the interface of turbulent flows. Gradient trajectories have been used to explore structures in turbulent flows, proving effective in analyzing homogeneous shear turbulence. This study introduces a methodology for sampling conditional data by computing gradient trajectories intersecting the TNTI. The primary objective is to verify whether sampling statistics along the gradient of scalar concentration provide a more detailed understanding of the processes occurring near the TNTI. The methodology involves computing a field of gradient trajectories from concentration fields obtained through Planar Laser-Induced Fluorescence (PLIF) in a N2/N2 jet with Re = 2900. Conditional statistics at the TNTI of a jet flow along the gradient trajectory for a given downstream position are calculated and reported. The paper aims to compare conditional statistics along gradient trajectories with those obtained along radial and normal directions at the TNTI. It is expected that gradient trajectory statistics align more closely with normal direction statistics near the interface and diverge as it gets into the jet or coflow fluid.
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Glazunov, A. V., E. V. Mortikov, K. V. Barskov, E. V. Kadancev, and S. S. Zilitinkevich. "The layered structure of stably stratified turbulent shear flows." Известия Российской академии наук. Физика атмосферы и океана 55, no. 4 (September 17, 2019): 13–26. http://dx.doi.org/10.31857/s0002-351555413-26.
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The data of numerical simulation of stably stratified turbulent Couette flows are analyzed for various values of the Richardson number. Two different methods were used: Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES). It is shown that the flow contains large organized structures, along with chaotic turbulence, regardless of the simulation method. These structures appear as inclined layers in the temperature field with weakly stable stratification, separated by very thin layers with large temperature gradients. The existence of such layered structures in nature is indirectly confirmed by the analysis of field measurement data on the meteorological mast, where temperature gradient distribution histograms are found to be far from the normal distribution and similar to temperature gradient probability distributions obtained by numerical models data. The simulations indicate an increase of the turbulent Prandtl number with increasing of the gradient Richardson number. It is highly likely that the identified structures serve as effective barriers for vertical turbulent heat flux, without the blocking of momentum transfer. We proposed the hypothesis, that it is precisely these structures that serve as the physical mechanism for maintaining turbulence under supercritically stable stratification.
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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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Gerz, T., U. Schumann, and S. E. Elghobashi. "Direct numerical simulation of stratified homogeneous turbulent shear flows." Journal of Fluid Mechanics 200 (March 1989): 563–94. http://dx.doi.org/10.1017/s0022112089000765.
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The exact time-dependent three-dimensional Navier-Stokes and temperature equations are integrated numerically to simulate stably stratified homogeneous turbulent shear flows at moderate Reynolds numbers whose horizontal mean velocity and mean temperature have uniform vertical gradients. The method uses shear-periodic boundary conditions and a combination of finite-difference and pseudospectral approximations. The gradient Richardson number Ri is varied between 0 and 1. The simulations start from isotropic Gaussian fields for velocity and temperature both having the same variances.The simulations represent approximately the conditions of the experiment by Komori et al. (1983) who studied stably stratified flows in a water channel (molecular Prandtl number Pr = 5). In these flows internal gravity waves build up, superposed by hot cells leading to a persistent counter-gradient heat-flux (CGHF) in the vertical direction, i.e. heat is transported from lower-temperature to higher-temperature regions. Further, simulations with Pr = 0.7 for air have been carried out in order to investigate the influence of the molecular Prandtl number. In these cases, no persistent CGHF occurred. This confirms our general conclusion that the counter-gradient heat flux develops for strongly stable flows (Ri ≈ 0.5–1.0) at sufficiently large Prandtl numbers (Pr = 5). The flux is carried by hot ascending, as well as cold descending turbulent cells which form at places where the highest positive and negative temperature fluctuations initially existed. Buoyancy forces suppress vertical motions so that the cells degenerate to two-dimensional fossil turbulence. The counter-gradient heat flux acts to enforce a quasi-static equilibrium between potential and kinetic energy.Previously derived turbulence closure models for the pressure-strain and pressure-temperature gradients in the equations for the Reynolds stress and turbulent heat flux are tested for moderate-Reynolds-number flows with strongly stable stratification (Ri = 1). These models overestimate the turbulent interactions and underestimate the buoyancy contributions. The dissipative timescale ratio for stably stratified turbulence is a strong function of the Richardson number and is inversely proportional to the molecular Prandtl number of the fluid.
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Chowdhury, M. Nasimul, Abdul A. Khan, and Oscar Castro-Orgaz. "A Numerical Approach to Analyzing Shallow Flows over Rough Surfaces." Fluids 9, no. 9 (September 1, 2024): 204. http://dx.doi.org/10.3390/fluids9090204.
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The hydraulic characteristics (such as velocity profiles, near-bed velocity profile, bed shear stress, and resistance coefficients) of shallow flows over rough surfaces were investigated using numerical simulations. A novel method is presented to simulate shallow flows over rough surfaces in a two-dimensional (2D) numerical domain, where the physical numerical domain represents bed topography. Results reveal that the model can accurately predict spatially averaged velocity profiles, turbulence characteristics, shear stresses, and uniform flow depths. The analysis identified two distinct flow regions based on mean and turbulent flow profiles. Results show that the turbulent shear stress profiles provide a more accurate estimation of the bed shear stresses. Resistance coefficients (friction factor or Manning’s roughness coefficient) vary with Froude number and submergence ratio (depth divided by roughness height).
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Wallace, J. M., and F. Hussain. "Coherent Structures in Turbulent Shear Flows." Applied Mechanics Reviews 43, no. 5S (May 1, 1990): S203—S209. http://dx.doi.org/10.1115/1.3120807.
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What is firmly known about the kinematic properties and dynamic importance of coherent structures in bounded and unbounded turbulent shear flows is briefly summarized. The nature of instabilities giving rise to these structures is discussed. Unanswered questions requiring further research are posed.
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Lesieur, M. "Numerical simulations of turbulent shear flows." Applied Scientific Research 51, no. 1-2 (June 1993): 345–51. http://dx.doi.org/10.1007/bf01082559.
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Lu, Q. Q., J. R. Fontaine, and G. Aubertin. "Particle Dispersion in Shear Turbulent Flows." Aerosol Science and Technology 18, no. 1 (January 1993): 85–99. http://dx.doi.org/10.1080/02786829308959586.
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Jacob, Boris, Luca Biferale, Gaetano Iuso, and Carlo Massimo Casciola. "Anisotropic fluctuations in turbulent shear flows." Physics of Fluids 16, no. 11 (November 2004): 4135–42. http://dx.doi.org/10.1063/1.1789546.
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Schumacher, J., K. R. Sreenivasan, and P. K. Yeung. "Derivative moments in turbulent shear flows." Physics of Fluids 15, no. 1 (January 2003): 84–90. http://dx.doi.org/10.1063/1.1524627.
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Yoder, D. A., J. R. DeBonis, and N. J. Georgiadis. "Modeling of turbulent free shear flows." Computers & Fluids 117 (August 2015): 212–32. http://dx.doi.org/10.1016/j.compfluid.2015.05.009.
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Hunt, J. C. R., S. Leibovich, and K. J. Richards. "Turbulent shear flows over low hills." Quarterly Journal of the Royal Meteorological Society 114, no. 484 (October 1988): 1435–70. http://dx.doi.org/10.1002/qj.49711448405.
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Liang, Jun-Hong, Xiaoliang Wan, Kenneth A. Rose, Peter P. Sullivan, and James C. McWilliams. "Horizontal Dispersion of Buoyant Materials in the Ocean Surface Boundary Layer." Journal of Physical Oceanography 48, no. 9 (September 2018): 2103–25. http://dx.doi.org/10.1175/jpo-d-18-0020.1.
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ABSTRACTThe horizontal dispersion of materials with a constant rising speed under the exclusive influence of ocean surface boundary layer (OSBL) flows is investigated using both three-dimensional turbulence-resolving Lagrangian particle trajectories and the classical theory of dispersion in bounded shear currents generalized for buoyant materials. Dispersion in the OSBL is caused by the vertical shear of mean horizontal currents and by the turbulent velocity fluctuations. It reaches a diffusive regime when the equilibrium vertical material distribution is established. Diffusivity from the classical shear dispersion theory agrees reasonably well with that diagnosed using three-dimensional particle trajectories. For weakly buoyant materials that can be mixed into the boundary layer, shear dispersion dominates turbulent dispersion. For strongly buoyant materials that stay at the ocean surface, shear dispersion is negligible compared to turbulent dispersion. The effective horizontal diffusivity due to shear dispersion is controlled by multiple factors, including wind speed, wave conditions, vertical diffusivity, mixed layer depth, latitude, and buoyant rising speed. With all other meteorological and hydrographic conditions being equal, the effective horizontal diffusivity is larger in wind-driven Ekman flows than in wave-driven Ekman–Stokes flows for weakly buoyant materials and is smaller in Ekman flows than in Ekman–Stokes flows for strongly buoyant materials. The effective horizontal diffusivity is further reduced when enhanced mixing by breaking waves is included. Dispersion by OSBL flows is weaker than that by submesoscale currents at a scale larger than 100 m. The analytic framework will improve subgrid-scale modeling in realistic particle trajectory models using currents from operational ocean models.
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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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Mankbadi, Reda R., and Joseph T. C. Liu. "Near-wall response in turbulent shear flows subjected to imposed unsteadiness." Journal of Fluid Mechanics 238 (May 1992): 55–71. http://dx.doi.org/10.1017/s0022112092001630.
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Rapid-distortion theory is adapted to introduce a truly unsteady closure into a simple phenomenological turbulence model in order to describe the unsteady response of a turbulent wall layer exposed to a temporarily oscillating pressure gradient. The closure model is built by taking the ratio of turbulent shear stress to turbulent kinetic energy to be a function of the effective strain. The latter accounts for the history of the flow. The computed unsteady velocity fluctuations and modulated turbulent stresses compare favourably in the ‘non-quasi-steady’ frequency range, where quasi-steady assumptions would fail. This suggests that the concept of rapid distortion is especially appropriate for unsteady flows. This paper forms the basis for acoustical studies of the problem to be reported elsewhere.
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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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LÉVÊQUE, E., F. TOSCHI, L. SHAO, and J. P. BERTOGLIO. "Shear-improved Smagorinsky model for large-eddy simulation of wall-bounded turbulent flows." Journal of Fluid Mechanics 570 (January 3, 2007): 491–502. http://dx.doi.org/10.1017/s0022112006003429.
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A shear-improved Smagorinsky model is introduced based on results concerning mean-shear effects in wall-bounded turbulence. The Smagorinsky eddy-viscosity is modified asvT=(Csδ)2(|S|—|〈S〉|): the magnitude of the mean shear |〈S〉|is subtracted from the magnitude of the instantaneous resolved rate-of-strain tensor |S|;CSis the standard Smagorinsky constant and Δ denotes the grid spacing. This subgrid-scale model is tested in large-eddy simulations of plane-channel flows at Reynolds numbersReτ= 395 andReτ= 590. First comparisons with the dynamic Smagorinsky model and direct numerical simulations for mean velocity, turbulent kinetic energy and Reynolds stress profiles, are shown to be extremely satisfactory. The proposed model, in addition to being physically sound and consistent with the scale-by-scale energy budget of locally homogeneous shear turbulence, has a low computational cost and possesses a high potential for generalization to complex non-homogeneous turbulent flows.
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Gladskikh, Daria, Lev Ostrovsky, Yuliya Troitskaya, Irina Soustova, and Evgeny Mortikov. "Turbulent Transport in a Stratified Shear Flow." Journal of Marine Science and Engineering 11, no. 1 (January 6, 2023): 136. http://dx.doi.org/10.3390/jmse11010136.
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Within the framework of the theory of unsteady turbulent flows in a stratified fluid, a new parameterization of the turbulent Prandtl number is proposed. The parameterization is included in the k-ε-closure and used within the three-dimensional model of thermohydrodynamics of an enclosed water body where density distribution includes pycnocline. This allows us to describe turbulence in a stratified shear flow without the restrictions associated with the gradient Richardson number and justify the choice of closure constants. Numerical experiments, where the downward penetration of turbulence was considered, confirm the advantage of the developed approach in describing the effects neglected in the classical closures.
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LOMINADZE, J. G. "Hydrodynamic turbulence in unbounded shear flows." Laser and Particle Beams 18, no. 2 (April 2000): 183–87. http://dx.doi.org/10.1017/s0263034600182059.
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A new conception of subcritical transition to turbulence in unbounded smooth shear flows is discussed. According to this scenario, the transition to turbulence is caused by the interplay between the four basic phenomena: (a) linear “drift” of spatial Fourier harmonics (SFH) of disturbances in wave-number space (k-space); (b) transient growth of SFH; (c) viscous dissipation; (d) nonlinear process that closes a feedback loop of transition by angular redistribution of SFH in k-space; The key features of the concept are: transition to turbulence only by the finite amplitude vortex disturbances; anisotropy of the process in k-space; onset on chaos due to the dynamic (not stochastic) process. The evolution of 2D small-scale vortex disturbances in the parallel flows with uniform shear of velocity is analyzed in the framework of the weak turbulence approach. This numerical test analysis is carried out to prove the most problematic statement of the conception—existence of positive feedback caused by the nonlinear process (d). Numerical calculations also show the existence of a threshold: if amplitude of the initial disturbance exceeds the threshold value, the self maintenance of disturbances becomes realistic. The latter, in turn, is the characteristic feature of the flow transition to the turbulent state and its self maintenance.
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MEI, RENWEI, and KEVIN C. HU. "On the collision rate of small particles in turbulent flows." Journal of Fluid Mechanics 391 (July 25, 1999): 67–89. http://dx.doi.org/10.1017/s0022112099005212.
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A theoretical framework is developed to predict the rate of geometric collision and the collision velocity of small size inertialess particles in general turbulent flows. The present approach evaluates the collision rate for small size, inertialess particles in a given instantaneous flow field based on the local eigenvalues of the rate-of-strain tensor. An ensemble average is then applied to the instantaneous collision rate to obtain the average collision rate. The collision rates predicted by Smoluchowski (1917) for laminar shear flow and by Saffman & Turner (1956) for isotropic turbulence are recovered. The collision velocities presently predicted in both laminar shear flow and isotropic turbulence agree well with the results from numerical simulations for particle collision in both flows. The present theory for evaluating the collision rate and the collision velocity is also applied to a rapidly sheared homogeneous turbulence to assess the effect of strong anisotropy on the collision rate. Using (ε/v)1/2, in which ε is the average turbulence energy dissipation rate and v is the fluid kinematic viscosity, as the characteristic turbulence shear rate to normalize the collision rate, the effect of the turbulence structure on the collision rate and collision velocity can be reliably described. The combined effects of the mean flow shear and the turbulence shear on the collision rate and collision velocity are elucidated.
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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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PRASTOWO, TJIPTO, ROSS W. GRIFFITHS, GRAHAM O. HUGHES, and ANDREW McC HOGG. "Mixing efficiency in controlled exchange flows." Journal of Fluid Mechanics 600 (March 26, 2008): 235–44. http://dx.doi.org/10.1017/s0022112008000554.
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Turbulence and mixing are generated by the shear between two counter-flowing layers in hydraulically controlled buoyancy-driven exchange flows through a constriction. From direct measurements of the density distribution and the amount of turbulent mixing in steady laboratory exchange flows we determine the overall efficiency of the mixing. For sufficiently large Reynolds numbers the mixing efficiency is 0.11(±0.01), independent of the aspect ratio and other details of constriction geometry, in good agreement with a scaling analysis. We conclude that the mixing in shear flows of this type has an overall efficiency significantly less than the maximum value widely proposed for stratified turbulence.
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KERSTEIN, ALAN R. "One-dimensional turbulence: model formulation and application to homogeneous turbulence, shear flows, and buoyant stratified flows." Journal of Fluid Mechanics 392 (August 10, 1999): 277–334. http://dx.doi.org/10.1017/s0022112099005376.
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A stochastic model, implemented as a Monte Carlo simulation, is used to compute statistical properties of velocity and scalar fields in stationary and decaying homogeneous turbulence, shear flow, and various buoyant stratified flows. Turbulent advection is represented by a random sequence of maps applied to a one-dimensional computational domain. Profiles of advected scalars and of one velocity component evolve on this domain. The rate expression governing the mapping sequence reflects turbulence production mechanisms. Viscous effects are implemented concurrently. Various flows of interest are simulated by applying appropriate initial and boundary conditions to the velocity profile. Simulated flow microstructure reproduces the −5/3 power-law scaling of the inertial-range energy spectrum and the dissipation-range spectral collapse based on the Kolmogorov microscale. Diverse behaviours of constant-density shear flows and buoyant stratified flows are reproduced, in some instances suggesting new interpretations of observed phenomena. Collectively, the results demonstrate that a variety of turbulent flow phenomena can be captured in a concise representation of the interplay of advection, molecular transport, and buoyant forcing.
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Lee, Moon Joo, John Kim, and Parviz Moin. "Structure of turbulence at high shear rate." Journal of Fluid Mechanics 216 (July 1990): 561–83. http://dx.doi.org/10.1017/s0022112090000532.
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The structure of homogeneous turbulence subject to high shear rate has been investigated by using three-dimensional, time-dependent numerical simulations of the Navier–Stokes equations. The instantaneous velocity fields reveal that a high shear rate produces structures in homogeneous turbulence similar to the ‘streaks’ that are present in the sublayer of wall-bounded turbulent shear flows. Statistical quantities such as the Reynolds stresses are compared with those in the sublayer of a turbulent channel flow at a comparable shear rate made dimensionless by turbulent kinetic energy and its dissipation rate. This study indicates that high shear rate alone is sufficient for generation of the streaky structures, and that the presence of a solid boundary is not necessary.Evolution of the statistical correlations is examined to determine the effect of high shear rate on the development of anisotropy in turbulence. It is shown that the streamwise fluctuating motions are enhanced so profoundly that a highly anisotropic turbulence state with a ‘one-component’ velocity field and ‘two-component’ vorticity field develops asymptotically as total shear increases. Because of high shear rate, rapid distortion theory predicts remarkably well the anisotropic behaviour of the structural quantities.
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Eckhardt, Bruno, Holger Faisst, Armin Schmiegel, and Tobias M. Schneider. "Dynamical systems and the transition to turbulence in linearly stable shear flows." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 366, no. 1868 (November 5, 2007): 1297–315. http://dx.doi.org/10.1098/rsta.2007.2132.
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Plane Couette flow and pressure-driven pipe flow are two examples of flows where turbulence sets in while the laminar profile is still linearly stable. Experiments and numerical studies have shown that the transition has features compatible with the formation of a strange saddle rather than an attractor. In particular, the transition depends sensitively on initial conditions and the turbulent state is not persistent but has an exponential distribution of lifetimes. Embedded within the turbulent dynamics are coherent structures, which transiently show up in the temporal evolution of the turbulent flow. Here we summarize the evidence for this transition scenario in these two flows, with an emphasis on lifetime studies in the case of plane Couette flow and on the coherent structures in pipe flow.
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SHIH, LUCINDA H., JEFFREY R. KOSEFF, JOEL H. FERZIGER, and CHRIS R. REHMANN. "Scaling and parameterization of stratified homogeneous turbulent shear flow." Journal of Fluid Mechanics 412 (June 10, 2000): 1–20. http://dx.doi.org/10.1017/s0022112000008405.
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Homogeneous sheared stratified turbulence was simulated using a DNS code. The initial turbulent Reynolds numbers (Re) were 22, 44, and 89, and the initial dimensionless shear rate (S*) varied from 2 to 16. We found (similarly to Rogers (1986) for unstratified flows) the final value of S* at high Re to be ∼ 11, independent of initial S*. The final S* varies at low Re, in agreement with Jacobitz et al. (1997). At low Re, the stationary Richardson number (Ris) depends on both Re and S*, but at higher Re, it varies only with Re. A scaling based on the turbulent kinetic energy equation which suggests this result employs instantaneous rather than initial values of flow parameters.At high Re the dissipation increases with applied shear, allowing a constant final S*. The increased dissipation occurs primarily at high wavenumbers due to the stretching of eddies by stronger shear. For the high-Re stationary flows, the turbulent Froude number (Frt) is a constant independent of S*. An Frt-based scaling predicts the final value of S* well over a range of Re. Therefore Frt is a more appropriate parameter for describing the state of developed stratified turbulence than the gradient Richardson number.
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Kantha, Lakshmi, and Hubert Luce. "Mixing Coefficient in Stably Stratified Flows." Journal of Physical Oceanography 48, no. 11 (November 2018): 2649–65. http://dx.doi.org/10.1175/jpo-d-18-0139.1.
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AbstractTurbulent mixing in the interior of the oceans is not as well understood as mixing in the oceanic boundary layers. Mixing in the generally stably stratified interior is primarily, although not exclusively, due to intermittent shear instabilities. Part of the energy extracted by the Reynolds stresses acting on the mean shear is expended in increasing the potential energy of the fluid column through a buoyancy flux, while most of it is dissipated. The mixing coefficient χm, the ratio of the buoyancy flux to the dissipation rate of turbulence kinetic energy ε, is an important parameter, since knowledge of χm enables turbulent diffusivities to be inferred. Theory indicates that χm must be a function of the gradient Richardson number. Yet, oceanic studies suggest that a value of around 0.2 for χm gives turbulent diffusivities that are in good agreement with those inferred from tracer studies. Studies by scientists working with atmospheric radars tend to reinforce these findings but are seldom referenced in oceanographic literature. The goal of this paper is to bring together oceanographic, atmospheric, and laboratory observations related to χm and to report on the values deduced from in situ data collected in the lower troposphere by unmanned aerial vehicles, equipped with turbulence sensors and flown in the vicinity of the Middle and Upper Atmosphere (MU) radar in Japan. These observations are consistent with past studies in the oceans, in that a value of around 0.16 for χm yields good agreement between ε derived from turbulent temperature fluctuations using this value and ε obtained directly from turbulence velocity fluctuations.
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STRANG, E. J., and H. J. S. FERNANDO. "Entrainment and mixing in stratified shear flows." Journal of Fluid Mechanics 428 (February 10, 2001): 349–86. http://dx.doi.org/10.1017/s0022112000002706.
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The results of a laboratory experiment designed to study turbulent entrainment at sheared density interfaces are described. A stratified shear layer, across which a velocity difference ΔU and buoyancy difference Δb is imposed, separates a lighter upper turbulent layer of depth D from a quiescent, deep lower layer which is either homogeneous (two-layer case) or linearly stratified with a buoyancy frequency N (linearly stratified case). In the parameter ranges investigated the flow is mainly determined by two parameters: the bulk Richardson number RiB = ΔbD/ΔU2 and the frequency ratio fN = ND=ΔU.When RiB > 1.5, there is a growing significance of buoyancy effects upon the entrainment process; it is observed that interfacial instabilities locally mix heavy and light fluid layers, and thus facilitate the less energetic mixed-layer turbulent eddies in scouring the interface and lifting partially mixed fluid. The nature of the instability is dependent on RiB, or a related parameter, the local gradient Richardson number Rig = N2L/ (∂u/∂z)2, where NL is the local buoyancy frequency, u is the local streamwise velocity and z is the vertical coordinate. The transition from the Kelvin–Helmholtz (K-H) instability dominated regime to a second shear instability, namely growing Hölmböe waves, occurs through a transitional regime 3.2 < RiB < 5.8. The K-H activity completely subsided beyond RiB ∼ 5 or Rig ∼ 1. The transition period 3.2 < RiB < 5 was characterized by the presence of both K-H billows and wave-like features, interacting with each other while breaking and causing intense mixing. The flux Richardson number Rif or the mixing efficiency peaked during this transition period, with a maximum of Rif ∼ 0.4 at RiB ∼ 5 or Rig ∼ 1. The interface at 5 < RiB < 5.8 was dominated by ‘asymmetric’ interfacial waves, which gradually transitioned to (symmetric) Hölmböe waves at RiB > 5:8.Laser-induced fluorescence measurements of both the interfacial buoyancy flux and the entrainment rate showed a large disparity (as large as 50%) between the two-layer and the linearly stratified cases in the range 1.5 < RiB < 5. In particular, the buoyancy flux (and the entrainment rate) was higher when internal waves were not permitted to propagate into the deep layer, in which case more energy was available for interfacial mixing. When the lower layer was linearly stratified, the internal waves appeared to be excited by an ‘interfacial swelling’ phenomenon, characterized by the recurrence of groups or packets of K-H billows, their degeneration into turbulence and subsequent mixing, interfacial thickening and scouring of the thickened interface by turbulent eddies.Estimation of the turbulent kinetic energy (TKE) budget in the interfacial zone for the two-layer case based on the parameter α, where α = (−B + ε)/P, indicated an approximate balance (α ∼ 1) between the shear production P, buoyancy flux B and the dissipation rate ε, except in the range RiB < 5 where K-H driven mixing was active.
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Cimarelli, A., A. Fregni, J. P. Mollicone, M. van Reeuwijk, and E. De Angelis. "Structure of turbulence in temporal planar jets." Physics of Fluids 34, no. 4 (April 2022): 045109. http://dx.doi.org/10.1063/5.0085091.
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A detailed analysis of the structure of turbulence in a temporal planar turbulent jet is reported. Instantaneous snapshots of the flow and three-dimensional spatial correlation functions are considered. It is found that the flow is characterized by large-scale spanwise vortices whose motion is felt in the entire flow field. Superimposed to this large-scale motion, a hierarchy of turbulent structures is present. The most coherent ones take the form of quasi-streamwise vortices and high and low streamwise velocity streaks. The topology of these interacting structures is analyzed by quantitatively addressing their shape and size in the different flow regions. Such information is recognized to be relevant for a structural description of the otherwise disorganized motion in turbulent free-shear flows and can be used for the assessment of models based on coherent structure assumptions. Finally, the resulting scenario provides a phenomenological description of the elementary processes at the basis of turbulence in free-shear flows.
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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.