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International audience; The denoising of Lagrangian trajectories based on regularized B-spline is investigated. The aim is to find systematic criteria for optimization of algorithms used in 4D-PTV in order to optimize the quality of 4D-PTV measurements of turbulent flows as well as high-order of turbulence statistics. We introduce and adapt to this context two innovative tuning strategies which are commonly used in the Tikhonov regularization of inverse problems based on -curve shape and Normalized Cumulative Periodogram (NCP). The corresponding strategies are tested on synthetic Lagrangian trajectories computed from Direct Numerical Simulation with additional white Gaussian noise. Error-based quantities like Signal-to-Noise Ratio as well as statistical Lagrangian quantities are investigated to compare the different strategies. We then apply the algorithm to experimental data from a 4D-PTV Lagrangian measurements in a turbulent Von Kármán flow. We show the ability of those strategies to optimize the quality of the signal compared to conventional methods. Moreover, the strategies are more adaptable to real experimental noise.

International audience; We study the three-dimensional structure of turbulent velocity fields around extreme events of local energy transfer in the dissipative range. Velocity fields are measured by tomographic particle velocimetry at the centre of a von Kármán flow with resolution reaching the Kolmogorov scale. The characterization is performed through both direct observation and an analysis of the velocity gradient tensor invariants at the extremes. The conditional average of local energy transfer on the second and third invariants seems to be the largest in the sheet zone, but the most extreme events of local energy transfer mostly correspond to the vortex stretching topology. The direct observation of the velocity fields allows for identification of three different structures: the screw and roll vortices, and the U-turn. They may correspond to a single structure seen at different times or in different frames of reference. The extreme events of local energy transfer come along with large velocity and vorticity norms, and the structure of the vorticity field around these events agrees with previous observations of numerical works at similar Reynolds numbers.

Dynamical behavior of the turbulent channel flow separation induced by a wall-mounted two-dimensional bump is studied, with an emphasis on unsteadiness characteristics of vortical motions evolving in the separated flow. The present investigations are based on an experimental approach and Direct Numerical Simulation ( Dns ). The main interests are devoted to give further insight on mean flow properties, characteristic scales and physical mechanisms of low-frequencies unsteadiness. The study also aims to clarify the Reynolds number effects. Results are presented for turbulent flows at moderate Reynolds-number R e τ ranging from 125 to 730 where R e τ is based on friction velocity and channel half-height. A large database of time-resolved two-dimensional Piv measurements is used to obtain the velocity distributions in a region covering the entire shear layer and the flow surrounding the bump. An examination of both high resolved velocity and wall-shear stress measurements showed that for moderate Reynolds numbers, a separated region exists until a critical value. Under this conditions, a thin region of reverse flow is formed above the bump and a large-scale vortical activity is clearly observed and analyzed. Three distinct self-sustained oscillations are identified in the separated zone. The investigation showed that the flow exhibits the shear-layer instability and vortex-shedding type instability of the bubble. A low-frequency self-sustained oscillation associated with a flapping phenomenon is also identified. The experimental results are further emphasized using post-processed data from Direct Numerical Simulations, such as flow statistics and Dynamic Mode Decomposition. Physical mechanisms associated with observed self-sustained oscillations are then suggested and results are discussed in the light of instabilities observed in a laminar regime for the same flow configuration.

This paper investigates the universality of the Eulerian velocity structure functions using velocity fields obtained from the stereoscopic particle image velocimetry (SPIV) technique in experiments and direct numerical simulations (DNS) of the Navier-Stokes equations. It shows that the numerical and experimental velocity structure functions up to order 9 follow a log-universality (Castaing et al. Phys. D Nonlinear Phenom. 1993), this leads to a collapse on a universal curve, when units including a logarithmic dependence on the Reynolds number are used. This paper then investigates the meaning and consequences of such log-universality, and shows that it is connected with the properties of a &ldquo, multifractal free energy&rdquo, based on an analogy between multifractal and thermodynamics. It shows that in such a framework, the existence of a fluctuating dissipation scale is associated with a phase transition describing the relaminarisation of rough velocity fields with different H&ouml, lder exponents. Such a phase transition has been already observed using the Lagrangian velocity structure functions, but was so far believed to be out of reach for the Eulerian data.

A study of large-scale motions from a new direct numerical simulation database of the turbulent boundary layer up to Re{\theta} ~ 2500 is presented. The statistics of large-scale streamwise structures have been investigated using two-dimensional and three-dimensional extraction procedures. The large-scale structures are abstracted using a robust skeletonization method usually applied to other research domains to simplify complex 3D objects. Different structure parameters such as the length, shape or angle are investigated. The features of the detected structures are compared to their mean counterparts extracted from two-point correlations. Structures as large as 10 boundary layer thickness are observed. The streamwise length of these structures follows a -2 power law distribution, similar to the experimental findings at higher Reynolds numbers., Comment: 32 pages, 16 figures

The modified Townsend-Perry attached eddy model of Vassilicos et al (2015) combines the outer peak/plateau behaviour of rms streamwise turbulence velocity profiles and the Townsend-Perry log-decay of these profiles at higher distances from the wall. This model was validated by these authors for high Reynolds number tur- bulent pipe flow data and is shown here to describe equally well and with about the same parameter values turbulent boundary layer flow data from four different facilities and a wide range of Reynolds numbers. The model has predictive value as, when extrapolated to the extremely high Reynolds numbers of the SLTEST data obtained at the Great Salt Lake Desert atmospheric test facility, it matches these data quite well., Comment: 12 pages, 3 figures

The spatio-temporal pressure–velocity correlation in a turbulent boundary layer is investigated so as to understand the link between pressure fluctuations and turbulent coherent structures. A new experimental set-up is developed to measure the pressure fluctuations at the wall and in the field and, simultaneously, the velocity field by stereoscopic particle image velocimetry. The present measurement area covers the whole boundary layer thickness, and the spatial resolution of the measurement is good enough to assess the representative length scales of the flow. The Reynolds number effect is quantified from the data at $\mathit{Re}_{{\it\theta}}=7300$, 10 000, 18 000. The spatio-temporal three-dimensional structures of the pressure–velocity correlations, $\boldsymbol{R}_{pu}$, $\boldsymbol{R}_{pv}$ and $\boldsymbol{R}_{pw}$, are evaluated. The wall pressure fluctuations are closely coupled with coherent structures which occupy a large region of the boundary layer in the wall-normal and spanwise directions and up to $10{\it\delta}/U_{e}$ in time, where ${\it\delta}$ and $U_{e}$ denote the boundary layer thickness and the free stream velocity. Reynolds number effects are mainly observed on the size and intensity of the pressure–velocity correlations. Conditioning the correlations on the pressure signal sign shows different types of flow phenomena linked to the positive and negative pressure events. For the wall pressure, positive pressure fluctuations appear to be correlated with the leading edge of a large sweeping motion of splatting type followed by a large ejection. The negative pressure fluctuations are linked to a localized ejection upstream, followed by a large sweeping motion downstream. For the pressure fluctuations in the field, in addition to the structures observed with the wall pressure, the pressure–velocity correlations exhibit a significant correlation in a region very extended in time. Such long structures appear to be independent of the one observed at the wall and to grow significantly in time with the Reynolds number when scaling with external variables. When conditioned by the pressure sign, clear ejection and sweeping motions are observed with associated streamwise vortical structures at a scale of the order of $0.2{\it\delta}$. These structures can be linked to the large-scale motion and very-large-scale motion previously observed by different authors and seem to organize in a scheme analogous to the near-wall cycle, but at a much larger scale.

This study reports on experimentally observed rare near-wall reverse flow events in a fully developed turbulent flat plate boundary layer at zero pressure gradient with Reynolds numbers between Re θ ≈ 2500 and Re θ ≈ 8000 ( Re τ ≈ 800 – 2400 ). The reverse flow events are captured using high magnification particle image velocimetry sequences with record lengths varying from 50 000 to 126 000 samples. Time resolved particle image sequences allow singular reverse flow events to be followed over several time steps whereas long records of nearly statistically independent samples provide a variety of single snapshots at a higher spatial resolution. The probability of occurrence lies in the order of 0.012–0.018% which matches predictions from direct numerical simulations (DNS). The typical size of the reverse flow bubble is about 30 wall units in length and 5 wall units in height which agrees well with similar observations made in existing DNS data.

On the basis of (i) particle image velocimetry data of a turbulent boundary layer with large field of view and good spatial resolution and (ii) a mathematical relation between the energy spectrum and specifically modeled flow structures, we show that the scalings of the streamwise energy spectrum E_{11}(k_{x}) in a wave-number range directly affected by the wall are determined by wall-attached eddies but are not given by the Townsend-Perry attached eddy model's prediction of these spectra, at least at the Reynolds numbers Re_{τ} considered here which are between 10^{3} and 10^{4}. Instead, we find E_{11}(k_{x})∼k_{x}^{-1-p} where p varies smoothly with distance to the wall from negative values in the buffer layer to positive values in the inertial layer. The exponent p characterizes the turbulence levels inside wall-attached streaky structures conditional on the length of these structures. A particular consequence is that the skin friction velocity is not sufficient to scale E_{11}(k_{x}) for wave numbers directly affected by the wall.

An experiment conducted in the framework of the EUHIT project and designed to characterize large scale structures in an adverse pressure gradient boundary layer flow is presented. Up to 16 sCMOS cameras were used in order to perform large scale turbulent boundary layer PIV measurements with a large field of view and appropriate spatial resolution. To access the span-wise / wall-normal signature of the structures as well, stereoscopic PIV measurements in span-wise/wall-normal planes were performed at specific stream-wise locations. To complement these large field of view measurements, long-range micro-PIV, time resolved near wall velocity profiles and film-based measurements were performed in order to determine the wall-shear stress and its fluctuations at some specific locations along the model., 50 pages

Three-dimensional pressure–velocity correlations in a turbulent boundary layer have been investigated to understand the relationship between the pressure fluctuations and the coherent structures. Simultaneous measurements of the fluctuating pressure and velocity fields have been performed by the point pressure measurement technique and stereo PIV. The space–time three-dimensional structures of the pressure–velocity correlations, \(R_{pu}\), \(R_{pv}\) and \(R_{pw}\), are evaluated. The wall pressure fluctuations are closely coupled with large-scale coherent structures, i.e., large-scale sweep and ejection. For the pressure fluctuations in the field, the pressure–velocity correlations \(R_{pu}\) and \(R_{pw}\) exhibit a meaningful correlation in a region very extended in time in addition to the structures observed with the wall pressure. The Reynolds number effect is quantified from the data at \(Re_\theta \) \(=\) 7 300, 10 000, and 18 000, it is mostly evidenced on the size and intensity of the correlations. Such 3D structures of the pressure–velocity correlations can be consistent with the evidence of large-scale and very-large-scale motions reported in the literature.

LES results are presented for the flow over different bump profiles installed on the bottom wall of a channel. Three bump geometries are considered in order to investigate the effects of adverse pressure gradients and changes in curvature on the mean flow and Reynolds stresses. The first bump geometry corresponds to a profile for which DNS results are available at a Reynolds number \(Re_{\tau } =\) 617 based on the channel inlet friction velocity. The other two geometries are generated by modifying the rear portion of the initial profile to produce a longer APG region and promote smoother curvature changes as compared to the original profile. LES computations are performed at the same Reynolds numbers than previous DNS, which is also used to validate LES results in the original bump. Finally, RANS results are also presented for the three bump profiles. RANS computations are performed using a two-equation eddy-viscosity Shear Stress Transport (SST) model and one Reynolds stresses transport model.

The study of turbulent flows calls for measurements with high resolution both in space and in time. We propose a new approach to reconstruct High-Temporal-High-Spatial resolution velocity fields by combining two sources of information that are well-resolved either in space or in time, the Low-Temporal-High-Spatial (LTHS) and the High-Temporal-Low-Spatial (HTLS) resolution measurements. In the framework of co-conception between sensing and data post-processing, this work extensively investigates a Bayesian reconstruction approach using a simulated database. A Bayesian fusion model is developed to solve the inverse problem of data reconstruction. The model uses a Maximum A Posteriori estimate, which yields the most probable field knowing the measurements. The DNS of a wall-bounded turbulent flow at moderate Reynolds number is used to validate and assess the performances of the present approach. Low resolution measurements are subsampled in time and space from the fully resolved data. Reconstructed velocities are compared to the reference DNS to estimate the reconstruction errors. The model is compared to other conventional methods such as Linear Stochastic Estimation and cubic spline interpolation. Results show the superior accuracy of the proposed method in all configurations. Further investigations of model performances on various range of scales demonstrate its robustness. Numerical experiments also permit to estimate the expected maximum information level corresponding to limitations of experimental instruments., Comment: 15 pages, 6 figures

The dynamical behavior of the flow separation induced by a wall-mounted two-dimensional bump is studied. The present investigation is based on an experimental approach that aims to provide further insight into the separate flow dynamic in such configuration. The main interest is devoted to the separation Reynolds number dependency. A general feature of separated flows dynamics is also addressed by statistical and structural information derived from the present experimental approach. Results are presented for turbulent water inflow for a moderate Reynolds-number range from 165 to 605 based on friction velocity and channel half-height (so-called Karman number). The ratio of the bump height h and the channel full height H is 0.335. The unsteady separation process and the associate instability mechanism are very sensitive to small perturbations. So, in order to preserve the flow physics, all of the experimental techniques employed in the present study are non-intrusive. An examination of the high resolved velocity fields showed that for a moderate Karman number, a separate area exists. Under this condition, a thin region of reverse flow was formed above the bump and a large-scale vortical activity, characterized by low-frequencies, are clearly observed. The reported results do not only yield the expected turbulent separation bubble dependencies. They also show that the well known coexisting instabilities process, which find their origin in laminar flow regime, persist for higher Karman numbers.Copyright © 2014 by ASME

The work presents comparative results between wall friction and pressure coefficient predictions from Large Eddy Simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) computations in channel flows with an adverse pressure gradient created by a 2-D bump. LES results are obtained using the semi-spectral code, MFLOPS3D, developed at Laboratoire de Mecanique de Lille, while RANS solutions are computed using a commercial code based on 2nd-order finite volume discretization with typical two-equation turbulence models and one seven-equation Reynolds stress transport model. Reynolds numbers range from Reτ = 617 to 2000, based on the friction velocity at the channel inlet. It is found that LES produces very consistent results when compared to DNS or other highly resolved LES. Two-equation and seven-equation RANS models are found to correctly predict friction coefficients in zero and favorable pressure gradient regions, but they fail in regions of adverse pressure gradients. The Reynolds stress transport model shows a better performance when compared to two-equation eddy-viscosity models, particularly in the higher Reynolds number cases. However, none of the RANS models is able to capture the full physics of turbulence related with adverse pressure gradients. The limitations of RANS models are observed both in separated and attached flow conditions at the rear portion of the bump. Such limitations seem to be related to the fact that these models do not correctly describe the evolution of the turbulent kinetic energy close to the walls in adverse pressure gradient regions.

We develop a new numerical method which treats resolved and sub-grid scales as two different fluid components evolving according to their own dynamical equations. These two fluids are nonlinearly interacting and can be transformed one into another when their scale becomes comparable to the grid size. Equations describing the two-fluid dynamics were rigorously derived from Euler equations [B. Dubrulle, S. Nazarenko, Physica D 110 (1997) 123‐138] and they do not involve any adjustable parameters. The main assumption of such a derivation is that the large-scale vortices are so strong that they advect the sub-grid scales as a passive scalar, and the interactions of small scales with small and intermediate scales can be neglected. As a test for our numerical method, we performed numerical simulations of 2D turbulence with a spectral gap, and we found a good agreement with analytical results obtained for this case by Nazarenko and Laval [Non-local 2D turbulence and passive scalars in Batchelor’s regime, J. Fluid Mech., in press]. We used the two-fluid method to study three typical problems in 2D dynamics of incompressible fluids: decaying turbulence, vortex merger and forced turbulence. The two-fluid simulations performed on at 128 2 and 256 2 resolution were compared with pseudo-spectral simulations using hyperviscosity performed at the same and at much higher resolution. This comparison shows that performance of the two-fluid method is much better than one of the pseudo-spectral method at the same resolution and comparable computational cost. The most significant improvement is observed in modeling of the small-scale component, so that effective inertial interval increases by about two decades compared to the high-resolution pseudo-spectral method. Using the two-fluid method, we demonstrated that the k 3 tail always exists for the energy spectrum, although its amplitude is slowly decreasing in decaying turbulence. © 2000 Elsevier Science B.V. All rights reserved.

We use numerical simulations to prove that the dynamics of the small-scale vorticity in twodimensional incompressible fluids is nearly passive and that the feedback of the small scales onto the large-scale dynamics is important only for the part of the large-scale range which is adjacent or close to the small-scale range. The dynamics of high Reynolds number turbulent flows usually couples a broad range of scales, from the energy injection scale to the dissipative scale. This range is too wide to be fully resolved by direct numerical simulations of the Navier-Stokes equations. This motivated a number of attempts to describe separately the behavior of the “energy containing” scales (corresponding to either the large scales or the scales of the mean motions) via modeling of the action of the “dissipative” small or random scales of motions. In most cases, the modeling is empirical and based on hand waving or dimensional arguments about the small-scale dynamics. There are a few attempts to derive a model from asymptotic expansions based on the NavierStokes equations. Traditionally, these models are based on two different expansion parameters, based on the ratio of the typical length and time t of the small scale motions, and the typical length L and time scale T of the energy containing large-scale motions. This results in two parameters: e L and h tT . For example, the

The work presents comparative results between wall friction coe cient predictions from Large Eddy Simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) computations in channel ows with an adverse pressure gradient created by a two-dimensional bump. LES results are obtained using the semi-spectral code, MFLOPS3D, developed at Laboratoire de M ecanique de Lille (LML), while RANS solutions are computed using a commercial code based on 2nd-order nite volume discretization with typical two-equation turbulence models and one seven-equation Reynolds stresses transport model. Computations are performed in two bump pro les installed in a channel. Reynolds numbers range from Re = 617 to 950 based on the friction velocity at the channel inlet. It is found that LES produces very consistent results when compared to DNS or other highly resolved LES. On the other hand, RANS models are found to predict an incorrect evolution of the friction coe cient in regions of adverse pressure gradient, even if separation or re-attachment locations are correctly predicted. This limitation of RANS models is observed both in separated and attached ow situations and it seems to be related to the fact that these models do not correctly describe the evolution of the turbulent kinetic energy close to the walls in adverse pressure gradient regions.

International audience; A direct numerical simulation (DNS) of a turbulent channel flow with a lower curved wall is performed at Reynolds number $Re_\tau \simeq 617$ at inlet. This adverse-pressure gradient turbulent flow is characterized by strong peaks of turbulent kinetic energy at both walls, as a consequence of the breakdown of more organized flow structures. To elucidate the underlying instability scenario, low-speed streak structures are extracted from the turbulent flow field and base flows formed with conditional streak averages, superimposing the mean streamwise velocity profile, are used for linear stability analyzes. The size and shape of the counter-rotating streamwise vortices associated with the instability modes are shown to be reminiscent of the coherent vortices emerging from the streak skeletons in the direct numerical simulation. The distance of the streak's centre from the wall is used as a criterion for the conditional averages and the corresponding streak base flows are characterised by more or less pronounced contours of inflection points in the averaging windows normal to the wall. It is shown, that the strength of instability of the streak base flows can be inferred from a simplified one-dimensional stability analysis, using local inflectional profiles at different spanwise locations.

International audience; We use proper orthogonal decomposition (POD) to estimate the flow in the near-wall region based on information from the outer buffer layer. Our goal is to assess how the flow structures in the inner wall region are connected to those further away from the wall, and to investigate the nature of the coupling between the inner and the outer region in the POD framework. Reconstructions are carried out for numerical simulations of a plane channel flow at two different Reynolds numbers. We show that elongated structures with a spanwise wavelength smaller than a critical value tend to be concentrated in the inner layer. The critical wavelength is shown to scale with the inner layer height, and interactions between the inner and the outer layer appear to take place predominantly over a self-similar, height-dependent, range of wavenumbers, in agreement with Townsend's attached eddy hypothesis. The reconstructed field appears to capture an adequate energy content and to remain correlated with the real field even close to the wall, which reflects the persistence of energetic structures over the extent of the buffer layer.

International audience; Streaks play a major role in the process of turbulent generation. Numerous studies have been performed to characterize them, most of which used only single point measurements and only a few characteristics were studied. To investigate the streaks in more detail, a stereoscopic particle image velocimetry (SPIV) experiment was conducted to record 2D3C velocity fields in ten planes parallel to the wall from y + = 14.5 to y + = 48 at Reynolds number Re θ = 7,800 in a fully developed turbulent boundary layer along a flat plate. This study develops a method based on pattern recognition to detect streaks from velocity fields obtained by SPIV and characteristizes them in depth. The results are in good agreement with the previous studies and expand significantly the information about the characteristics of the streaks

A direct numerical simulation (DNS) of a channel flow with one curved surface was performed at moderate Reynolds number (Re_tau = 395 at the inlet). The adverse pressure gradient was obtained by a wall curvature through a mathematical mapping from physical coordinates to Cartesian ones. The code, using spectral spanwise and normal discretization, combines the advantage of a good accuracy with a fast integration procedure compared to standard numerical procedures for complex geometries. The turbulent flow slightly separates on the profile at the lower curved wall and is at the onset of separation at the opposite flat wall. The thin separation bubble is characterized with a reversal flow fraction. Intense vortices are generated near the separation line on the lower wall but also at the upper wall. Turbulent normal stresses and kinetic energy budget are investigated along the channel., Comment: 23 pages, submitted to Journal of Turbulence

We report successive bifurcations in direct numerical simulations (DNSs) of a Taylor–Green flow, in both a hydro- and a magneto-hydrodynamic case. Hydrodynamic bifurcations occur in between different metastable states with different dynamo action, and are triggered by the numerical noise. The various states encountered range from stationary to chaotic or turbulent through possible oscillatory states. The corresponding sequence of bifurcations is reminiscent of the sequence obtained in the von Karman (VK) flow, at aspect ratio Γ=2 (Nore et al 2003 J. Fluid Mech. 477 51). We then use kinematic simulations to compute the dynamo thresholds of the different metastable states. A more detailed study of the turbulent state reveals the existence of two windows of dynamo action. Stochastic numerical simulations are then used to mimic the influence of turbulence on the dynamo threshold of the turbulent state. We show that the dynamo threshold is increased (respectively decreased) by the presence of large scale (resp. small scale) turbulent velocity fluctuations. Finally, DNSs of the magneto-hydrodynamic equations are used to explore the linear and nonlinear stage of the dynamo instability. In the linear stage, we show that the magnetic field favours the bifurcation from the basic state directly towards the turbulent or chaotic stable state. The magnetic field can also temporarily stabilize a metastable state, resulting in cycles of dynamo action, with different Lyapunov exponents. The critical magnetic Reynolds number for dynamo action is found to increase strongly with the Reynolds number. Finally, we provide a preliminary study of the saturation regime above the dynamo threshold. At large magnetic Prandtl number, we have observed two main types of saturations, in agreement with an analytical prediction of Leprovost and Dubrulle (2005 Eur. Phys. J. B 44 395): (i) intermittent dynamo, with vanishing most probable value of the magnetic energy; (ii) dynamo with non vanishing mean value of the magnetic energy. We describe a sequence of bifurcation of the dynamo at low Reynolds number and at increasing magnetic Prandtl number, where the dynamo switches from stationary mode to chaotic modes in a complex manner, involving intermittency in a way reminiscent to what is observed in dynamical systems with low number of degrees of freedom.

We present the results of a numerical investigation of the turbulent kinematic dynamo problem in a high Prandtl number regime. The scales of the magnetic turbulence we consider are far smaller than the Kolmogorov dissipative scale, so that the magnetic wavepackets evolve in a nearly smooth velocity field. Firstly, we use a stochastic Euler-Maruyama method to simulate the Kraichnan-Kazantsev model (KKM) in which the strain matrix is taken to be independent of coordinate and Gaussian white in time. We test the theoretical predictions for the growth of rates of the magnetic energy and higher order moments (Kazantsev 1968; Chertkov et al. 1999; Kulsrud & Anderson 1992), the shape of the energy spectrum (Schekochihin et al. 2002a; Kazantsev 1968; Nazarenko et al. 2003; Kulsrud & Anderson 1992) and the behavior of the polarization and spectral flatness, new measures introduced in Nazarenko et al. (2003). In general, the results appear to be in good agreement with the theory, with the exception that the predicted decay of the polarization in time is not reproduced well in the stochastic numerics. Secondly, in order to study the sensitivity of the KKM predictions to the choice of strain statistics, we perform additional simulations for the case of a Gaussian strain with a finite correlation time and also for a strain taken from a DNS data set. These experiments are based on non-stochastic schemes, using a timestep that is much smaller than the correlation time of the strain. We find that the KKM is generally insensitive to the choice of strain statistics and most KKM results, including the decay of the polarization, are reproduced well. The only exception appears to be the flatness whose spectrum is not reproduced in accordance with the KKM predictions in these simulations.

Numerical simulations are made for forced turbulence at a sequence of increasing values of Reynolds number, R, keeping fixed a strongly stable, volume-mean density stratification. At smaller values of R, the turbulent velocity is mainly horizontal, and the momentum balance is approximately cyclostrophic and hydrostatic. This is a regime dominated by so-called pancake vortices, with only a weak excitation of internal gravity waves and large values of the local Richardson number, Ri, everywhere. At higher values of R there are successive transitions to (a) overturning motions with local reversals in the density stratification and small or negative values of Ri; (b) growth of a horizontally uniform vertical shear flow component; and (c) growth of a large-scale vertical flow component. Throughout these transitions, pancake vortices continue to dominate the large-scale part of the turbulence, and the gravity wave component remains weak except at small scales., Comment: 8 pages, 5 figures (submitted to Phys. Rev. E)

A new dynamical turbulence model is validated by comparisons of its numerical simulations with fully resolved, Direct Numerical Simulations of the Navier-Stokes equations in 3D, isotropic, homogeneous conditions. In this model the small-scale velocities are computed using a Langevin, linear, inhomogeneous, stochastic equation that is derived from a quasi-linear approximation of the Navier-Stokes equations, in the spirit of Rapid Distortion Theory (RDT). The values of the turbulent viscosity involved in our Langevin model are compared with a theoretical prescription based on the Renormalization Group (RG) and the Distant Interaction Algorithms (DSTA) model. We show that the empirical turbulent viscosities derived from simulations of the Langevin model are in good quantitative agreement with the DSTA predictions. Finally, Langevin simulations are compared with Direct Numerical Simulation (DNS) and Large Eddy Simulations (LES) based on the EDQNM Eddy-Damped Quasi-Normal Markovian (EDQNM) closure. The Langevin RDT model is able to reproduce the correct spectrum shape, intermittency statistics, and coherent flow structures for both the resolved and the largest sub-grid scales. It also predicts the evolution of the resolved scales better than the alternative models.

We present a dynamic model of the subfiltered scales in plane parallel geometry using a generalized, stochastic rapid distortion theory ~RDT!. This new model provides expressions for the turbulent Reynolds subfilter-scale stresses via estimates of the subfilter velocities rather than velocity correlations. Subfilter-scale velocities are computed using an auxiliary equation which is derived from the Navier‐Stokes equations using a simple model of the subfilter energy transfers. It takes the shape of a RDT equation for the subfilter velocities, with a stochastic forcing. An analytical test of our model is provided by assuming delta-correlation in time for the supergrid energy transfers. It leads to expressions for the Reynolds stresses as a function of the mean flow gradient in the plane parallel geometry and can be used to derive mean equilibrium profiles both in the near-wall and core regions. In the near-wall region we derive a general expression for the velocity profile which is linear in the viscous layer and logarithmic outside. This expression involves two physical parameters: the von Karman constant and the size of the viscous layer ~which can be computed via a numerical implementation of our model!. Fits of experimental profiles using our general formula provides reasonable values of these parameters ( k50.4 to k50.45, the size of the viscous layer is about 15 wall units!. In the core region, we find that the shape of the profile depends on the geometry of the flow; it ranges from algebraic in channel flow, to exponential in the bulk of boundary layers, and linear in plane Couette flow. This classification is consistent with Oberlack’s system, which is based on symmetry arguments. Fits of boundary layer flows or channel flows at different Reynolds number over the whole flow region are performed using our results, and are found to be in very good agreement with available data. © 2001 American Institute of Physics. @DOI: 10.1063/1.1378038#