Homogeneous Turbulent Shear Flow Research Articles

A compressible turbulence model for the dissipation rate

In this work, the ability of a Reynolds stress model to compute turbulent homogeneous shear flow with significant compressibility effects is discussed. Several studies of compressible turbulent flows carried out in the past years have shown that the pressure strain correlation is mainly responsible for the strong changes in the magnitude of the Reynolds stress anisotropies. Two recent compressible models of this term are considered in conjunction with the standard model of the dissipation rate of the turbulent kinetic energy to predict compressible homogeneous flow highly sheared are tested. It is found that deficiencies appear in the calculations even if the pressure strain model is improved by compressibility corrections. Consistent with earlier studies, this deficiency is attributed to the use of the incompressible model for turbulent dissipation. However, a compressibility correction of this equation model uncovers the main focus of the present study. This correction makes the standard coefficients of this equation depend on the turbulent gradient Mach and Mach numbers. The proposed model is tested for low and strong compressibility cases from the DNS results of Sarkar. A comparison of the proposed model predictions with the DNS results shows good qualitative agreement. Therefore, compressibility correction for the incompressible model of the turbulent dissipation rate is found to be an important issue for the compressible homogeneous turbulent shear flow.

Higher-order realizable algebraic Reynolds stress modeling based on the square root tensor

In this study, realizable algebraic Reynolds stress modeling based on the square root tensor [Phys. Rev. E \textbf{92}, 053010 (2015)] is further developed for extending its applicability to more complex flows. In conventional methods, it was difficult to construct an algebraic Reynolds stress model satisfying the realizability conditions when the model involves higher-order nonlinear terms on the mean velocity gradient. Such higher-order nonlinear terms are required to predict turbulent flows with three-dimensional mean velocity. The present modeling based on the square root tensor enables us to make the model always satisfy the realizability conditions, even when it involves higher-order nonlinearity. To construct a realizable algebraic Reynolds stress model applicable to turbulent flows with three-dimensional mean velocity, a quartic-nonlinear eddy-viscosity model is proposed. The performance of the model is numerically verified in a turbulent channel flow, a homogeneous turbulent shear flow, and an axially rotating turbulent pipe flow. The present model gives a good result in each turbulent flow. Note that the mean swirl flow in an axially rotating turbulent pipe flow is reproduced because the present model involves cubic nonlinearity. Such a higher-order realizable algebraic Reynolds stress model, involving quartic nonlinearity on the mean velocity, is expected to be useful in numerically stable predictions of turbulent flows with three-dimensional mean velocity.

Droplets in homogeneous shear turbulence

We simulate the flow of two immiscible and incompressible fluids separated by an interface in a homogeneous turbulent shear flow at a shear Reynolds number equal to 15 200. The viscosity and density of the two fluids are equal, and various surface tensions and initial droplet diameters are considered in the present study. We show that the two-phase flow reaches a statistically stationary turbulent state sustained by a non-zero mean turbulent production rate due to the presence of the mean shear. Compared to single-phase flow, we find that the resulting steady-state conditions exhibit reduced Taylor-microscale Reynolds numbers owing to the presence of the dispersed phase, which acts as a sink of turbulent kinetic energy for the carrier fluid. At steady state, the mean power of surface tension is zero and the turbulent production rate is in balance with the turbulent dissipation rate, with their values being larger than in the reference single-phase case. The interface modifies the energy spectrum by introducing energy at small scales, with the difference from the single-phase case reducing as the Weber number increases. This is caused by both the number of droplets in the domain and the total surface area increasing monotonically with the Weber number. This reflects also in the droplet size distribution, which changes with the Weber number, with the peak of the distribution moving to smaller sizes as the Weber number increases. We show that the Hinze estimate for the maximum droplet size, obtained considering break-up in homogeneous isotropic turbulence, provides an excellent estimate notwithstanding the action of significant coalescence and the presence of a mean shear.

On the Weissenberg effect of turbulence

Within the framework of the Navier–Stokes equations, the Weissenberg effect of turbulence is investigated. We begin with our investigation on the elastic effect of homogeneous turbulent shear flow. First, in the sense of Truesdell (Physics of Fluids, 1964) on the natural time of materials, we derive the natural time of turbulence, and use it together with the natural viscosity of turbulence derived in the article of Huang et al. (Journal of Turbulence, 2003) to define the natural Weissenberg number of turbulence as a measure of the elastic effect of homogeneous turbulence. Second, we define a primary Weissenberg number of turbulence, which in laminar flow reduces to the Weissenberg number widely applied in rheology to characterize the elasticity of visco-elastic fluids. Our analysis based on the experimental results of Tavoularis and Karnik (Journal of Fluid Mechanics, 1989) indicates that the larger is the Weissenberg number of turbulence, the more elastic becomes the turbulent flow concerned. Furthermore, we put forth a general Weissenberg number of turbulence, which includes the primary Weissenberg number of turbulence as a special case, to measure the overall elastic effects of turbulence. Besides, it is shown that the general Weissenberg number can also be used to characterize the elastic effects of non-Newtonian fluids in laminar flow.

A Statistical Dynamic Model for the Turbulent Transport of Kinetic Energy in Shear Layers

Dynamic statistical equations for the turbulent fluxes of scalars and momentum in incompressible flows are derived after time wise integration of the equation for the oscillating transported property, decomposing the turbulent fluxes in terms representing distinct features of the main and fluctuating flow that influence the respective turbulent transport. These expressions provide a means for discussing the gradient diffusion hypothesis for the turbulent transport, for reconsidering the mixed length model in entirely continuous terms, and for seeking possible alternatives or corrections. Applying this methodology to the turbulent transport flux of kinetic energy, two dominating terms are found: one identified with a kinetic energy gradient model for shear layers; the other related to the main velocity gradient. Accordingly, a composed, Statistical Dynamic model is proposed for the turbulent transport of kinetic energy in shear layers, adding a velocity derivative term to Daly and Harlow’s generalized gradient model. This velocity derivative term is calibrated in a nearly homogeneous turbulent shear flow, and the resulting Statistical Dynamic model is proved superior to Daly and Harlow’s and other gradient models in channel and boundary layer flows.

Fractally Fourier decimated homogeneous turbulent shear flow in noninteger dimensions.

Time evolution of the fully resolved incompressible homogeneous turbulent shear flow in noninteger Fourier dimensions is numerically investigated. The Fourier dimension of the flow field is extended from the integer value 3 to the noninteger values by projecting the Navier-Stokes equation on the fractal set of the active Fourier modes with dimensions 2.7≤d≤3.0. The results of this study revealed that the dynamics of both large and small scale structures are nontrivially influenced by changing the Fourier dimension d. While both turbulent production and dissipation are significantly hampered as d decreases, the evolution of their ratio is almost independent of the Fourier dimension. The mechanism of the energy distribution among different spatial directions is also impeded by decreasing d. Due to this deficient energy distribution, turbulent field shows a higher level of the large-scale anisotropy in lower Fourier dimensions. In addition, the persistence of the vortex stretching mechanism and the forward spectral energy transfer, which are three-dimensional turbulence characteristics, are examined at changing d, from the standard case d=3.0 to the strongly decimated flow field for d=2.7. As the Fourier dimension decreases, these forward energy transfer mechanisms are strongly suppressed, which in turn reduces both the small-scale intermittency and the deviation from Gaussianity. Besides the energy exchange intensity, the variations of d considerably modify the relative weights of local to nonlocal triadic interactions. It is found that the contribution of the nonlocal triads to the total turbulent kinetic energy exchange increases as the Fourier dimension increases.

Turbulent kinetic energy production and flow structures in compressible homogeneous shear flow

The production of turbulent kinetic energy (TKE) and flow structures in compressible homogeneous turbulent shear flow (HTSF) are investigated by using direct numerical simulation. A theoretical analysis suggests that the vertical turbulent transport process should be responsible for the production of TKE in HTSF. It is manifested based on a conditional average method that the pure TKE production becomes increasingly larger in strain regions than in vortex regions of the flow. The velocity-derivative correlation in the shear plane is employed to identify the streaky structures in HTSF, which also tend to occur predominantly in strain regions of turbulence. Localized analyses of conditional averages reveal that the streaky structures in compressible HTSF are closely related to the negative productions of TKE. A comparative study implies that flow compressibility has a considerable effect on the spatial distributions and patterns of the strain- and vortex-dominated fields, which in turn cause the discrepancies in distribution of the TKE production and streaky structures between incompressible and compressible HTSFs.

Simulation of homogeneous turbulent shear flows at higher Reynolds numbers: numerical challenges and a remedy

In a recent study, Isaza and Collins [J. Fluid Mech., 637 (2009), pp. 213–239] found the asymptotic state of homogeneous turbulent shear flows (HTSFs) to be sensitively dependent on the initial shear parameter (), and yet be almost independent of the initial Reynolds number (R λ≡qλ/ν). The stringent resolution criteria they employed, however, restricted their studies to relatively low Reynolds numbers. In this paper, we present higher resolution direct numerical simulations of HTSFs over a wider range of Reynolds numbers, aided in part by an improved parallelisation scheme that utilises two-dimensional domain decomposition. We maximise the time-window for our simulations by determining appropriate settings for the initial energy spectrum, viscosity and domain configuration, thereby ensuring that we attain the highest possible asymptotic Reynolds number at the chosen grid resolution. In the course of our study, we find that the pseudo-spectral method suffers from Gibbs oscillations while resolving the thin vortical structures that tend to form in HTSFs. The nonlinear growth of these oscillations leads to spurious energy buildup in the high-wavenumber region of the spectrum, and contaminates the flow field. Consequently, the growth of the integral length scale is found to be numerically stunted, well before the intended final Reynolds number is attained. The issue is rectified by the application of exponential-type spectral filters, which stabilise the simulations and extend the runtime window, permitting attainment of larger asymptotic Reynolds numbers. Various large-scale flow statistics are then studied, and their dependence on the initial value of the shear parameter and Reynolds number corroborates the findings of Isaza and Collins.

On clustering of aerosol particles in homogeneous turbulent shear flows

The objective of this paper is to present a model for predicting clustering of aerosol particles in uniformly sheared turbulent flows laden with small heavy particles. The background of the model for predicting clustering is based on a kinetic equation for the two-point probability density function of the relative velocity distribution of two particles. The effect of clustering of particles in homogeneous turbulent shear flows is demonstrated and compared with known results of direct numerical simulations. It is shown that the universality of the clustering process can take place if the characteristic cluster size is smaller than the shear scale.

An Extension of the SSG Model on Compressible Turbulent Flow

This work focuses on the performance and validation of some recent Reynolds stress models in compressible homogeneous shear flow. The SSG model developed by Speziale Sarkar and Gatski has shown a great success in simulating a variety of incompressible complex turbulent flows. On the other hand, it has not predicted correctly the compressible turbulence at high speed shear flow. Thus, a compressibility correction for this model is the major aim of this study. In the present work, two recent compressible models for the pressure strain-strain correlation have been used to modify the linear term of the SSG model. These modifications make the linear term dependent on a turbulent Mach number. In addition, compressibility correction model for the slow part of the pressure strain is proposed. The obtained results are compared with DNS results of Sarkar. The results show that important parameters characteristic of compressibility in homogeneous turbulent shear flow are well captured by the extended SSG model.

Influence of initial mean helicity on homogeneous turbulent shear flow

Helicity statistics are studied in homogeneous turbulent shear flow. Initial mean helicity is imposed on an isotropic turbulence field using a decomposition of the flow into complex-valued helical waves. The initial decay of the turbulent kinetic energy is weakened in the presence of strong mean helicity, consistent with an analytic analysis of the spectral tensor of velocity correlations. While exponential growth of the mean turbulent kinetic energy is obtained, the mean helicity decays. Probability distribution functions (PDFs) of helicity are skewed and show that the imposed mean helicity prevails throughout the simulations. A wavelet-based scale-dependent analysis shows a trend to two dimensionalization for large scales of motion and a preference for helical motion at small scales. The magnitude of the skewness of the PDFs decreases for smaller scales. Joint PDFs indicate a strong correlation of the signs of both, helicity and superhelicity, for all cases. This correlation supports the conjecture that superhelicity dissipates helicity.

A Three-Equation Variant of the SST k-ω Model Sensitized to Rotation and Curvature Effects

A new variant of the SST k-ω model sensitized to system rotation and streamline curvature is presented. The new model is based on a direct simplification of the Reynolds stress model under weak equilibrium assumptions [York et al., 2009, “A Simple and Robust Linear Eddy-Viscosity Formulation for Curved and Rotating Flows,” International Journal for Numerical Methods in Heat and Fluid Flow, 19(6), pp. 745–776]. An additional transport equation for a transverse turbulent velocity scale is added to enhance stability and incorporate history effects. The added scalar transport equation introduces the physical effects of curvature and rotation on turbulence structure via a modified rotation rate vector. The modified rotation rate is based on the material rotation rate of the mean strain-rate based coordinate system proposed by Wallin and Johansson (2002, “Modeling Streamline Curvature Effects in Explicit Algebraic Reynolds Stress Turbulence Models,” International Journal of Heat and Fluid Flow, 23, pp. 721–730). The eddy viscosity is redefined based on the new turbulent velocity scale, similar to previously documented k-ɛ- υ2 model formulations (Durbin, 1991, “Near-Wall Turbulence Closure Modeling without Damping Functions,” Theoretical and Computational Fluid Dynamics, 3, pp. 1–13). The new model is calibrated based on rotating homogeneous turbulent shear flow and is assessed on a number of generic test cases involving rotation and/or curvature effects. Results are compared to both the standard SST k-ω model and a recently proposed curvature-corrected version (Smirnov and Menter, 2009, “Sensitization of the SST Turbulence Model to Rotation and Curvature by Applying the Spalart-Shur Correction Term,” ASME Journal of Turbomachinery, 131, pp. 1–8). For the test cases presented here, the new model provides reasonable engineering accuracy without compromising stability and efficiency, and with only a small increase in computational cost.

Effect of the shear parameter on velocity-gradient statistics in homogeneous turbulent shear flow

The effect of the shear parameter on the small-scale velocity statistics in an homogeneous turbulent shear flow is investigated using direct numerical simulations (DNSs) of the incompressible Navier–Stokes equations on a 5123 grid. We use a novel pseudo-spectral algorithm that allows us to set the initial value of the shear parameter in the range 3–30 without the shortcomings of previous numerical approaches. We find that the tails of the probability distribution function of components of the vorticity vector and rate-of-strain tensor are progressively distorted with increasing shear parameter. Furthermore, we show that the shear parameter has a direct effect on the structure of the vorticity field, which manifests through changes in its alignment with the eigenvectors of the rate-of-strain tensor. We also find that increasing the shear parameter causes the main contribution to enstrophy production to shift from the nonlinear terms to the rapid terms (terms that are proportional to the mean shear) due to the aforementioned changes in the alignment. We attempt to explain these trends using viscous rapid distortion theory; however, while the theory does capture some effects of the shear parameter, it fails to predict the correct dependence on Reynolds number. Comparisons with recent experiments are also shown. The trends predicted by the DNS and the experiments are in good agreement. Moreover, the prefactors in the Reynolds number scaling laws for the skewness and flatness of the longitudinal velocity derivative are shown to have a statistically significant dependence on the shear parameter.

Multimode stretched spiral vortex and nonequilibrium energy spectrum in homogeneous shear flow turbulence

The stretched spiral vortex [T. S. Lundgren, “Strained spiral vortex model for turbulent structures,” Phys. Fluids 25, 2193 (1982)] is identified in turbulence in homogeneous shear flow and the spectral properties of this flow are studied using direct-numerical simulation data. The effects of mean shear on the genesis, growth, and annihilation processes of the spiral vortex are elucidated, and the role of the spiral vortex in the generation of turbulence is shown. As in homogeneous isotropic turbulence [K. Horiuti and T. Fujisawa, “The multi mode stretched spiral vortex in homogeneous isotropic turbulence,” J. Fluid Mech. 595, 341 (2008)], multimodes of the spiral vortex are extracted. Two symmetric modes of configurations with regard to the vorticity alignment along the vortex tube in the core region and dual vortex sheets spiraling around the tube are often educed. One of the two symmetric modes is created by a conventional rolling-up of a single spanwise shear layer. Another one is created by the convergence of the recirculating flow or streamwise roll [F. Waleffe, “Homotopy of exact coherent structures in plane shear flows,” Phys. Fluids 15, 1517 (2003)] caused by the upward and downward motions associated with the streaks. The vortex tube is formed by axial straining and lowering of pressure in the recirculating region. The spanwise shear layers are entrained by the tube and they form spiral turns. The latter symmetric mode tends to be transformed into the former mode with lapse of time due to the action of the pressure Hessian term. The power law in the inertial subrange energy spectrum is studied. The base steady spectrum fits the equilibrium Kolmogorov −5/3 spectrum, to which a nonequilibrium component induced by the fluctuation of the dissipation rate ε is added. This component is extracted using the conditional sampling on ε, and it is shown that it fits the −7/3 power in accordance with the statistical theory. The correlation between these spectra and the appearance and diminution of the streaks and the two modes of the spiral vortex is discussed. The temporal variations of the spectrum are divided into two regimes, Phases 1 and 2. Large energy contained in the low-wavenumber range in Phase 1 is cascaded to the small scales in Phase 2. This energy transfer is accomplished by the reversal in the sign of −7/3 power component.

Study on Langevin model parameters of velocity in turbulent shear flows

This paper deals with the stochastic equation used to predict the fluctuating velocity of a fluid particle in a nonhomogeneous turbulent flow, in the frame of probability density function (PDF) approaches. It is shown that a Langevin-type equation is appropriate provided its parameters (drift and diffusion matrices) are suitably specified. By following the approach proposed in the literature for homogeneous turbulent shear flows, these parameters have been identified using data from direct numerical simulations (DNS) of both channel and pipe flows. Using statistics extracted from the computation of the channel flow, it is shown that the drift matrix of the stochastic differential equation can reasonably be assumed to be diagonal but not spherical. This behavior of the drift coefficients is confirmed by the available results for a turbulent pipe flow at low Reynolds number. Concerning the diffusion matrix, it is found that this matrix is anisotropic for low Reynolds number flows, a property which has been observed earlier for a homogeneous turbulent shear flow. The pertinence of the present estimation of the drift and diffusion tensors is assessed through different kinds of tests including the incorporation of these parameters in a purely Lagrangian, or stand-alone, PDF computation.

Polymer-laden homogeneous shear-driven turbulent flow: a model for polymer drag reduction

Drag reduction (DR) under a turbulent boundary layer implies the suppression of turbulent momentum flux to the wall, a large-eddy phenomenon. Our hypothesis is that the essential mechanisms by which dilute concentrations of long-chain polymer molecules reduce momentum flux involve only the interactions among turbulent velocity fluctuations, polymer molecules and mean shear. Experiments indicate that these interactions dominate in a polymer-active ‘elastic layer’ outside the viscous sublayer and below a Newtonian inertial layer in a polymer-laden turbulent boundary layer. We investigate our hypothesis by modelling the suppression of momentum flux with direct numerical simulation (DNS) of homogeneous turbulent shear flow (HTSF) and the finite extensible nonlinear elastic with Peterlin approximation (FENE-P) model for polymer stress. The polymer conformation tensor equation was solved using a new hyperbolic algorithm with no artificial diffusion. We report here on the equilibrium state with fixed mean shear rateS, where progressive increases in non-dimensional polymer relaxation timeWeS(shear Weissenberg number) or concentration parameter 1 − β produced progressive reductions in Reynolds shear stress, turbulence kinetic energy and turbulence dissipation rate, concurrent with increasing polymer stress and elastic potential energy. The changes in statistical variables underlying polymer DR with 1 − β,WeS, %DRand polymer-induced changes to spectra are similar to experiments in channel and pipe flows and show that the experimentally measured increase in normalized streamwise velocity variance is an indirect consequence of DR that is true only at lower DR. Comparison of polymer stretch and elastic potential energy budgets with channel flow DNS showed qualitative correspondence when distance from the wall was correlated toWeS. AsWeSincreased, the homogeneous shear flow displayed low-DR, high-DR and maximum-DR (MDR) regimes, similar to experiments, with each regime displaying distinctly different polymer–turbulence physics. The suppression of turbulent momentum flux arises from the suppression of vertical velocity fluctuations primarily by polymer-induced suppression of slow pressure–strain rate correlations. In the high-Weissenberg-number MDR-like limit, the polymer nearly completely blocks Newtonian inter-component energy transfer to vertical velocity fluctuations and turbulence is maintained by the polymer contribution to pressure–strain rate. Our analysis from HTSF with the FENE-P representation of polymer stress and its comparisons with experimental and DNS studies of wall-bounded polymer–turbulence supports our central hypothesis that the essential mechanisms underlying polymer DR lie directly in the suppression of momentum flux by polymer–turbulence interactions in the presence of mean shear and indirectly in the presence of the wall as the shear-generating mechanism.

Experimental and numerical investigations of flow structure and momentum transport in a turbulent buoyancy-driven flow inside a tilted tube

Buoyancy-driven turbulent mixing of fluids of slightly different densities [At=Δρ/(2⟨ρ⟩)=1.15×10−2] in a long circular tube tilted at an angle θ=15° from the vertical is studied at the local scale, both experimentally from particle image velocimetry and laser induced fluorescence measurements in the vertical diametrical plane and numerically throughout the tube using direct numerical simulation. In a given cross section of the tube, the axial mean velocity and the mean concentration both vary linearly with the crosswise distance z from the tube axis in the central 70% of the diameter. A small crosswise velocity component is detected in the measurement plane and is found to result from a four-cell mean secondary flow associated with a nonzero streamwise component of the vorticity. In the central region of the tube cross section, the intensities of the three turbulent velocity fluctuations are found to be strongly different, that of the streamwise fluctuation being more than twice larger than that of the spanwise fluctuation which itself is about 50% larger than that of the crosswise fluctuation. This marked anisotropy indicates that the turbulent structure is close to that observed in homogeneous turbulent shear flows. Still in the central region, the turbulent shear stress dominates over the viscous stress and reaches a maximum on the tube axis. Its crosswise variation is approximately accounted for by a mixing length whose value is about one-tenth of the tube diameter. The momentum exchange in the core of the cross section takes place between its lower and higher density parts and there is no net momentum exchange between the core and the near-wall regions. A sizable part of this transfer is due both to the mean secondary flow and to the spanwise turbulent shear stress. Near-wall regions located beyond the location of the extrema of the axial velocity (|z|≳0.36 d) are dominated by viscous stresses which transfer momentum toward (from) the wall near the top (bottom) of the tube.

On the asymptotic behaviour of large-scale turbulence in homogeneous shear flow

The asymptotic behaviour of large-scale velocity statistics in an homogeneous turbulent shear flow is investigated using direct numerical simulations (DNS) of the incompressible Navier–Stokes equations on a 5123 grid, and with viscous rapid distortion theory (RDT). We use a novel pseudo-spectral algorithm that allows us to set the initial value of the shear parameter in the range 3–30 without the shortcomings of previous numerical approaches. We find there is an explicit dependence of the early-time behaviour on the initial value of the shear parameter. Moreover, the long-time asymptotes of large-scale quantities such as the ratio of the turbulent kinetic energy production rate over dissipation rate, the Reynolds stress anisotropic tensor and the shear parameter itself depend sensitively on the initial value of the shear parameter over the range of Reynolds number we could achieve (26 ≤ Rλ ≤ 63) with the stringent resolution requirements that were satisfied. To gain further insight into the matter, we analyse the full viscous RDT. While inviscid RDT has received a great deal of attention, viscous RDT has not been fully analysed. Our motivation for considering viscous RDT is so that the energy dissipation rate enters the problem, enabling the shear parameter to be defined. We show asymptotic expansions for the short-time behaviour and numerically evaluate the integrals to determine the long-time prediction of viscous RDT. The results are in quantitative agreement with DNS for short times; however, at long times viscous RDT predicts the turbulent energy decays to zero. Through an analysis of the pressure–strain terms, we show that the nonlinear ‘slow’ terms are essential for rearranging turbulent energy from the streamwise direction to the mean shear direction, and this sustains the indefinite growth of the kinetic energy at long times. In effect, the nonlinear pressure–strain correlation maintains the three-dimensionality of the turbulence, countering the tendency of the mean shear to project the turbulence onto the two-dimensional plane of the mean-flow streamlines. We postulate that the predictions of viscous RDT at long times could be improved by introducing a model for the ‘slow’ pressure–strain term, along the lines of the Rotta model.

Comparing vortex methods and finite difference methods in a homogeneous turbulent shear flow

AbstractThe vortex method is applied to the calculation of a homogeneous shear turbulence, and compared with a finite difference code using identical calculation conditions. The core spreading method with spatial adaptation is selected as the viscous diffusion scheme of the vortex method. The shear rate is chosen so that it matches the maximum value observed in a fully developed channel flow. The isosurface, anisotropy tensors, and joint probability density functions reflect the ability of the present vortex method to quantitatively reproduce the anisotropic nature of strongly sheared turbulence, both instantaneously and statistically. Copyright © 2009 John Wiley & Sons, Ltd.

Experimental investigation of the large-scale velocity statistics in homogeneous turbulent shear flow

Motivated by the numerical results of Isaza and Collins [“On the asymptotic behaviour of large-scale turbulence in homogeneous shear flow,” J. Fluid Mech. (in press)], the sensitivity of the self-similar behavior of the large-scale velocity statistics in an homogeneous turbulent shear flow to the initial value of the shear parameter and Reynolds number is investigated in a wind tunnel. Using an active grid, the initial value of Reynolds number based on the Taylor microscale is varied over the range 100≤Rλ≤250. The shear is generated using screens of different solidities followed by a series of straightening channels [S. Garg and Z. Warhaft, Phys. Fluids 10, 662 (1998)], allowing us to vary the initial value of the shear parameter over the modest range 6≤S0*≤12. We find that the longtime behavior of the shear parameter depends on its initial value over the nondimensional time interval 5≤St≤25, but is less sensitive to the initial value of the Reynolds number. The ratio of the turbulent kinetic energy production over dissipation rate appears to show a similar dependence on the initial value of the shear parameter, but there is more significant scatter in the data. We find that the turbulent kinetic energy grows with downstream distance, in agreement with previous work, and that its growth rate too is a stronger function of the initial shear parameter than the initial Reynolds number. The experimental results for all of the large-scale velocity statistics are consistent with the earlier direct numerical simulation study.