Dynamical eigenfunction decomposition of turbulent channel flow

The results of an analysis of low-Reynolds-number turbulent channel flow based on the Karhunen-Loéve(K-L) expansion are presented. The turbulent flow field is generated by a direct numerical simulation of the Navier-Stokes equations at a Reynolds number Re,= 80 (based on the wall shear velocity and channel half-width). The K-L procedure is then applied to determine the eigenvalues and eigenfunctions for this flow. The random coefficients of the K-L expansion are subsequently found by projecting the numerical flow field onto these eigenfunctions. The resulting expansion captures 90% of the turbulent energy with significantly fewer modes than the original trigonometric expansion. The eigenfunctions, which appear either as rolls or shearing motions, posses viscous boundary layers at the walls and are much richer in harmonics than the original basis functions. Chaotic temporal behaviour is observed in all modes and increases for higher-order eigenfunctions. The structure and dynamical behaviour of the eigenmodes are discussed as well as their use in the representation of the turbulent flow.     

Analysis of Streamwise Velocity Fluctuations in Turbulent Pipe Flow with the Use of an Ultrasonic Doppler Flowmeter

Data collected from several studies of experimental and numerical nature in wall-bounded turbulent flows and in particular in internal flows (channel and pipe flows, Mochizuki and Nieuwstadt [1]) at different Reynolds numbers R ⁺(Ru _*/ν), indicate that: (i) the peak of the rms-value (normalized by u _*) of the streamwise velocity fluctuations (σ _u ⁺|_peak) is essentially independent of the Reynolds number, (ii) the position of the rms peak value (y ⁺|_peak) is weakly dependent of the Reynolds number, (iii) the skewness of the streamwise velocity fluctuations (S _u ) is close to zero at the position in which the variance has its peak. A series of measurements of streamwise velocity fluctuations has been performed in turbulent pipe flow with the use of an Ultrasonic Doppler Velocimeter and our results support those reported in [1]. This revised version was published online in July 2006 with corrections to the Cover Date.     

Numerical analysis of the rotating viscous flow approaching a solid sphere

A numerical simulation is performed to investigate the flow induced by a sphere moving along the axis of a rotating cylindrical container filled with the viscous fluid. Three‐dimensional incompressible Navier–Stokes equations are solved using a finite element method. The objective of this study is to examine the feature of waves generated by the Coriolis force at moderate Rossby numbers and that to what extent the Taylor–Proudman theorem is valid for the viscous rotating flow at small Rossby number and large Reynolds number. Calculations have been undertaken at the Rossby numbers (R_o) of 1 and 0.02 and the Reynolds numbers (R_e) of 200 and 500. When R_o=O(1), inertia waves are exhibited in the rotating flow past a sphere. The effects of the Reynolds number and the ratio of the radius of the sphere and that of the rotating cylinder on the flow structure are examined. When R_o ? 1, as predicted by the Taylor–Proudman theorem for inviscid flow, the so‐called ‘Taylor column’ is also generated in the viscous fluid flow after an evolutionary course of vortical flow structures. The initial evolution and final formation of the ‘Taylor column’ are exhibited. According to the present calculation, it has been verified that major theoretical statement about the rotating flow of the inviscid fluid may still approximately predict the rotating flow structure of the viscous fluid in a certain regime of the Reynolds number. Copyright © 2004 John Wiley & Sons, Ltd.     

Numerical prediction of turbulent boundary layer noise from a sharp-edged flat plate

An efficient hybrid uncorrelated wall plane waves–boundary element method (UWPW-BEM) technique is proposed to predict the flow-induced noise from a structure in low Mach number turbulent flow. Reynolds-averaged Navier-Stokes equations are used to estimate the turbulent boundary layer parameters such as convective velocity, boundary layer thickness, and wall shear stress over the surface of the structure. The spectrum of the wall pressure fluctuations is evaluated from the turbulent boundary layer parameters and by using semi-empirical models from literature. The wall pressure field underneath the turbulent boundary layer is synthesized by realizations of uncorrelated wall plane waves (UWPW). An acoustic BEM solver is then employed to compute the acoustic pressure scattered by the structure from the synthesized wall pressure field. Finally, the acoustic response of the structure in turbulent flow is obtained as an ensemble average of the acoustic pressures due to all realizations of uncorrelated plane waves. To demonstrate the hybrid UWPW-BEM approach, the self-noise generated by a flat plate in turbulent flow with Reynolds number based on chord Re_c = 4.9 × 10⁵ is predicted. The results are compared with those obtained from a large eddy simulation (LES)-BEM technique as well as with experimental data from literature.     

Direct numerical simulation of turbulent heat transfer in annuli: Effect of heat flux ratio

Fully developed turbulent flow and heat transfer in a concentric annular duct is investigated for the first time by using a direct numerical simulation (DNS) with isoflux conditions imposed at both walls. The Reynolds number based on the half-width between inner and outer walls, δ=(r₂-r₁)/2, and the laminar maximum velocity is Re_δ=3500. A Prandtl number Pr=0.71 and a radius ratio r^*=0.1 were retained. The main objective of this work is to examine the effect of the heat flux density ratio, q^*=q₁/q₂, on different thermal statistics (mean temperature profiles, root mean square (rms) of temperature fluctuations, turbulent heat fluxes, heat transfer, etc.). To validate the present DNS calculations, predictions of the flow and thermal fields with q^*=1 are compared to results recently reported in the archival literature. A good agreement with available DNS data is shown. The effect of heat flux ratio q^* on turbulent thermal statistics in annular duct with arbitrarily prescribed heat flux is discussed then. This investigation highlights that heat flux ratio has a marked influence on the thermal field. When q^* varies from 0 to 0.01, the rms of temperature fluctuations and the turbulent heat fluxes are more intense near the outer wall while changes in q^* from 1 to 100, lead to opposite trends.     

Propagating structures in wall-bounded turbulent flows

The Karhunen—Loève procedure is used to analyze two turbulent channel flow simulations. In both instances this reveals the presence of propagating plane wave structures in the turbulent flows. These waves appear to play an essential role in the local production of turbulence via bursting or sweeping events. The envelope of the propagating modes propagates with a speed which is equal to the mean velocity at the locus of maximal average Reynolds stress. Despite marked differences between the two flows similar results are obtained from each simulation. This is suggestive of the existence of universal or near universal features in the turbulent boundary layer. An analogy with critical layer mechanisms of transitional flows is discussed.Dedicated to Professor J.L. Lumley on the occasion of his 60th birthday.We gratefully acknowledge support provided by DARPA-URI under Contract Number N00014-86-K0754. The use of the Pittsburgh Supercomputing Center is also acknowledged.     

Direct Numerical Simulation of Transitional Turbulent Flow in a Closed Rotor-Stator Cavity

The transitional turbulent regime in confined flow between a rotating and a stationary disc is studied using direct numerical simulation. Besides its fundamental importance as a three-dimensional prototype flow, such flows frequently arise in many industrial devices, especially in turbomachinary applications. The present contribution extends the DNS simulation into the turbulent flow regime, to a rotational Reynolds number Re =3 × 10⁵. An annular rotor-stator cavity of radial extension ΔR and height H, is considered with L = 4.72(L = ΔR/H) and Rm = 2.33 (Rm = (R ₁+ R ₀)/ΔR). The direct numerical simulation is performed by integrating the time-dependent Navier–Stokes equations until a statistically steady state is reached. A three-dimensional spectral method is used with the aim of providing both very accurate instantaneous fields and reliable statistical data. The instantaneous quantities are analysed in order to enhance our knowledge of the physics of turbulent rotating flows. Also, the results have been averaged so as to provide target turbulence data for any subsequent modelling attempts at reproducing the flow. This revised version was published online in July 2006 with corrections to the Cover Date.     

Direct numerical simulation of the turbulent energy balance and the shear stresses in power-law fluid flows in pipes

The results of direct numerical simulation of turbulent flows of non-Newtonian pseudoplastic fluids in a straight pipe are presented. The data on the distributions of the turbulent stress tensor components and the shear stress and turbulent kinetic energy balances are obtained for steady turbulent flows at the Reynolds numbers of 10⁴ and 2×10⁴. As distinct from Newtonian fluid flows, the viscous shear stresses turn out to be significant even far from the wall. In power-law fluid flows the mechanism of the energy transport from axial to transverse component fluctuations is suppressed. It is shown that with decrease in the fluid index the turbulent transfer of the momentum and the velocity fluctuations between the wall layer and the flow core reduces, while the turbulent energy flux toward the wall increases. The earlier-proposed models for the average viscosity and the non-Newtonian one-point correlations are in good agreement with the data of direct numerical simulation.     

Compound wall treatment with low‐Re turbulence model

A generalized treatment for the wall boundary conditions relating to turbulent flows is developed that blends the integration to a solid wall with wall functions. The blending function ensures a smooth transition between the viscous and turbulent regions. An improved low Reynolds number k?ε model is coupled with the proposed compound wall treatment to determine the turbulence field. The eddy viscosity formulation maintains the positivity of normal Reynolds stresses and Schwarz' inequality for turbulent shear stresses. The model coefficients/functions preserve the anisotropic characteristics of turbulence. Computations with fine and coarse meshes of a few flow cases yield appreciably good agreement with the direct numerical simulation and experimental data. The method is recommended for computing the complex flows where computational grids cannot satisfy a priori the prerequisites of viscous/turbulence regions. Copyright © 2011 John Wiley & Sons, Ltd.     

High‐order discontinuous Galerkin spectral element methods for transitional and turbulent flow simulations

In this paper, we investigate the accuracy and efficiency of discontinuous Galerkin spectral method simulations of under‐resolved transitional and turbulent flows at moderate Reynolds numbers, where the accurate prediction of closely coupled laminar regions, transition and developed turbulence presents a great challenge to large eddy simulation modelling. We take full advantage of the low numerical errors and associated superior scale resolving capabilities of high‐order spectral methods by using high‐order ansatz functions up to 12th order. We employ polynomial de‐aliasing techniques to prevent instabilities arising from inexact quadrature of nonlinearities. Without the need for any additional filtering, explicit or implicit modelling, or artificial dissipation, our high‐order schemes capture the turbulent flow at the considered Reynolds number range very well. Three classical large eddy simulation benchmark problems are considered: a circular cylinder flow at Re_D=3900, a confined periodic hill flow at Re_h=2800 and the transitional flow over a SD7003 airfoil at Re_c=60,000. For all computations, the total number of degrees of freedom used for the discontinuous Galerkin spectral method simulations is chosen to be equal or considerably less than the reported data in literature. In all three cases, we achieve an equal or better match to direct numerical simulation results, compared with other schemes of lower order with explicitly or implicitly added subgrid scale models. Copyright © 2014 John Wiley & Sons, Ltd.     

Direct Numerical Simulation of Turbulent Pipe Flow at Moderately High Reynolds Numbers

Fully resolved direct numerical simulations (DNSs) have been performed with a high-order spectral element method to study the flow of an incompressible viscous fluid in a smooth circular pipe of radius R and axial length 25R in the turbulent flow regime at four different friction Reynolds numbers Re _τ ?=?180, 360, 550 and $1\text{,}000$ . The new set of data is put into perspective with other simulation data sets, obtained in pipe, channel and boundary layer geometry. In particular, differences between different pipe DNS are highlighted. It turns out that the pressure is the variable which differs the most between pipes, channels and boundary layers, leading to significantly different mean and pressure fluctuations, potentially linked to a stronger wake region. In the buffer layer, the variation with Reynolds number of the inner peak of axial velocity fluctuation intensity is similar between channel and boundary layer flows, but lower for the pipe, while the inner peak of the pressure fluctuations show negligible differences between pipe and channel flows but is clearly lower than that for the boundary layer, which is the same behaviour as for the fluctuating wall shear stress. Finally, turbulent kinetic energy budgets are almost indistinguishable between the canonical flows close to the wall (up to y ^?+??≈?100), while substantial differences are observed in production and dissipation in the outer layer. A clear Reynolds number dependency is documented for the three flow configurations.     

Scalar transport from a point source in flows over wavy walls

Simultaneous measurements of the velocity and concentration field in fully developed turbulent flows over a wavy wall are described. The concentration field originates from a low-momentum plume of a passive tracer. PLIF and digital particle image velocimetry are used to make spatially resolved measurements of the structure of the scalar distribution and the velocity. The measurements are performed at three different Reynolds numbers of Re _b = 5,600, Re _b = 11,200 and Re _b = 22,400, respectively, based on the bulk velocity u _b and the total channel height 2h. The velocity field and the scalar field are investigated in a water channel with an aspect ratio of 12:1, where the bottom wall of the test section consists of a train of sinusoidal waves. The wavy wall is characterized by the amplitude to wavelength ratio α = 0.05 and the ratio β between the wave amplitude and the half channel height where β = 0.1. The scalar is released from a point source at the wave crest. For the concentration measurements, Rhodamine B is used as tracer dye. At low to moderate Reynolds number, the flow field is characterized through a recirculation zone which develops after the wave crest. The recirculation zone induces high intensities of the fluctuations of the streamwise velocity and wall-normal velocity. Furthermore, large-scale structures are apparent in the flow field. In previous investigations it has been shown that these large-scale structures meander laterally in flows over wavy bottom walls. The investigations show a strong effect of the wavy bottom wall on the scalar mixing. In the vicinity of the source, the scalar is transported by packets of fluid with a high scalar concentration. As they move downstream, these packets disintegrate into filament-like structures which are subject to strong gradients between the filaments and the surrounding fluid. The lateral scale of the turbulent plume is smaller than the lateral scale of the large-scale structures in the flow field and the plume dispersion is dominated by the structures in the flow field. Due to the lateral meandering of the large-scale structures of the flow field, also the scalar plume meanders laterally. Compared to turbulent plumes in plane channel flows, the wavy bottom wall enhances the mixing effect of the turbulent flow and the spreading rate of the scalar plume is increased.     

Instability of small-amplitude convective flows in a rotating layer with free boundaries

The stability of steady convective flows in a horizontal layer with free boundaries, heated from below and rotating about a vertical axis, is studied in the Boussinesq approximation (Rayleigh-Bénard convection). The flows considered are convective rolls or square cells that are sums of two perpendicular rolls with equal wave numbers k. It is assumed that the Rayleigh number is almost critical in order for convective flows with a wave number k: R = R _c (k) + ε² to arise, the amplitude of the supercritical states being of the order of ε. It is shown that the flows are always unstable relative to perturbations that are the sum of one long-and two short-wave modes corresponding to linear rolls turned through small angles in opposite directions.     

Influence of wavy surfaces on coherent structures in a turbulent flow

We describe how outer flow turbulence phenomena depend on the interaction with the wall. We investigate coherent structures in turbulent flows over different wavy surfaces and specify the influence of the different surface geometries on the coherent structures. The most important contribution to the turbulent momentum transport is attributed to these structures, therefore this flow configuration is of large engineering interest. In order to achieve a homogeneous and inhomogeneous reference flow situation two different types of surface geometries are considered: (1) three sinusoidal bottom wall profiles with different amplitude-to-wavelength ratios of α = 2a/Λ = 0.2 (Λ = 30 mm), α = 0.2 (Λ = 15 mm), and α = 0.1 (Λ = 30 mm); and (2) a profile consisting of two superimposed sinusoidal waves with α = 0.1 (Λ = 30 mm). Measurements are carried out in a wide water channel facility (aspect ratio 12:1). Digital particle image velocimetry (PIV) is performed to examine the spatial variation of the streamwise, spanwise and wall-normal velocity components in three measurement planes. Measurements are performed at a Reynolds number of 11,200, defined with the half channel height h and the bulk velocity U _B. We apply the method of snapshots and perform a proper orthogonal decomposition (POD) of the streamwise, spanwise, and wall-normal velocity components to extract the most dominant flow structures. The structure of the most dominant eigenmode is related to counter-rotating, streamwise-oriented vortices. A qualitative comparison of the eigenfunctions for different sinusoidal wall profiles shows similar structures and comparable characteristic spanwise scales Λ _z = 1.5 H in the spanwise direction for each mode. The scale is observed to be slightly smaller for α = 0.2 (Λ = 15 mm) and slightly larger for α = 0.2 (Λ = 30 mm). This scaling for the flow over the basic wave geometries indicates that the size of the largest structures is neither directly linked to the solid wave amplitude, nor to the wavelength. The characteristic spanwise scale of the dominant eigenmode for the developed flow over the surface consisting of two superimposed waves reduces to 0.85 H. However, a scale in the order of 1.3 H is identified for the second mode. The eigenvalue spectra for the superimposed waves is much broader, more modes contribute to the energy-containing range. The turbulent flow with increased complexity of the bottom surface is characterized by an increased number of dominant large-scale structures with different spanwise scales.     

Simultaneous velocity and concentration field measurements of passive-scalar mixing in a confined rectangular jet

Simultaneous velocity and concentration fields in a confined liquid-phase rectangular jet with a Reynolds number based on the hydraulic diameter of 50,000 (or 10,000 based on the velocity difference between streams and the jet exit dimension) and a Schmidt number of 1,250 were obtained by means of a combined particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) system. Data were collected at the jet exit and six further downstream locations. The velocity and concentration field data were analyzed for flow statistics such as turbulent fluxes, turbulent viscosity and diffusivity, and turbulent Schmidt number (Sc _T ). The streamwise turbulent flux was found to be larger than the transverse turbulent flux, and the mean concentration gradient was not aligned with the turbulent flux vector. The average Sc _T was found to vary both in streamwise and in cross stream directions and had a mean value around 0.8, a value consistent with the literature. Spatial correlation fields of turbulent fluxes and concentration were then determined. The R _u′ϕ′ correlation was elliptical in shape with a major axis tilted downward with respect to the streamwise axis, whereas the R _v′ϕ′ correlation was an ellipse with a major axis aligned with the cross-stream direction. Negative regions of R _u′ϕ′ were observed in the outer streams, and these negatively correlated regions decayed with downstream distance and finally disappeared altogether. The R _ϕ′ϕ′ correlation field was found to be an ellipse with the major axis inclined at about 45° with respect to the streamwise direction. Linear stochastic estimation was used to interpret spatial correlation data and to determine conditional flow structures. It is believed that a vortex street formed near the splitter plate is responsible for the negatively correlated region observed in the R _u′ϕ′ spatial correlations of turbulent fluxes. A positive concentration fluctuation event was observed to correspond to a finger of nearly uniform concentration fluid reaching out into the outer stream, whereas a negative event corresponds to a pocket of nearly uniform fluid being entrained from the outer stream into the center jet region. Large-scale vortical structures were observed in the conditional velocity fields with an elliptical shape and a streamwise major axis. The growth of the structure size increased linearly initially but then grew more slowly as the flow transitioned toward channel flow. Support of this work was provided by the National Science Foundation through grants CTS-9985678 and CTS-0336435 and by the Dow Chemical Company. The author greatly acknowledge Charles Lipp at Dow Chemical and Ken Junk at Emerson Fisher for their valuable assistance in the design and construction of the flow system.     

Reynolds-number-dependence of the maximum in the streamwise velocity fluctuations in wall turbulence

A survey is made of the standard deviation of the streamwise velocity fluctuations in near-wall turbulence and in particular of the Reynolds-number-dependency of its peak value. The following canonical flow geometries are considered: an incompressible turbulent boundary layer under zero pressure gradient, a fully developed two-dimensional channel and a cylindrical pipe flow. Data were collected from 47 independent experimental and numerical studies, which cover a Reynolds number range of R _θ=U _∞ θ/v=300−20,920 for the boundary layer with θ the momentum thickness and R ⁺=u _*R/v=100-4,300 for the internal flows with R the pipe radius or the channel half-width. It is found that the peak value of the rms-value normalised by the friction velocity, u _*, is within statistical errors independent of the Reynolds number. The most probable value for this parameter was found to be 2.71±0.14 and 2.70±0.09 for the case of a boundary layer and an internal flow, respectively. The present survey also includes some data of the streamwise velocity fluctuations measured over a riblet surface. We find no significant difference in magnitude of the normalised peak value between the riblet and smooth surfaces and this property of the normalised peak value may for instance be exploited to estimate the wall shear stress from the streamwise velocity fluctuations. We also consider the skewness of the streamwise velocity fluctuations and find its value to be close to zero at the position where the variance has its peak value. This is explained with help of the equations of the third-order moment of velocity fluctuations. These results for the peak value of the rms of the streamwise velocity fluctuations and also the coincidence of this peak with the zero value of the third moment can be interpreted as confirmation of local equilibrium in the near-wall layer, which is the basis of inner-layer scaling. Furthermore, these results can be also used as a requirement which turbulence models for the second and triple velocity correlations should satisfy. The authors are indebted to Prof. P. Bradshaw for making available his list of references on this topic and for his remarks on “active” and “inactive” motions. We also gratefully acknowledge discussions with Prof. I. Castro regarding the value of σ _u ⁺ above rough walls.     

A two‐scale low‐Reynolds number turbulence model

In this study, a two‐scale low‐Reynolds number turbulence model is proposed. The Kolmogorov turbulence time scale, based on fluid kinematic viscosity and the dissipation rate of turbulent kinetic energy (ν, ε), is adopted to address the viscous effects and the rapid increasing of dissipation rate in the near‐wall region. As a wall is approached, the turbulence time scale transits smoothly from a turbulent kinetic energy based (k, ε) scale to a (ν, ε) scale. The damping functions of the low‐Reynolds number models can thus be simplified and the near‐wall turbulence characteristics, such as the ε distribution, are correctly reproduced. The proposed two‐scale low‐Reynolds number turbulence model is first examined in detail by predicting a two‐dimensional channel flow, and then it is applied to predict a backward‐facing step flow. Numerical results are compared with the direct numerical simulation (DNS) budgets, experimental data and the model results of Chien, and Lam and Bremhorst respectively. It is proved that the proposed two‐scale model indeed improves the predictions of the turbulent flows considered. Copyright © 2000 John Wiley & Sons, Ltd.     

Wall modeling for implicit large-eddy simulation and immersed-interface methods

We propose and analyze a wall model based on the turbulent boundary layer equations (TBLE) for implicit large-eddy simulation (LES) of high Reynolds number wall-bounded flows in conjunction with a conservative immersed-interface method for mapping complex boundaries onto Cartesian meshes. Both implicit subgrid-scale model and immersed-interface treatment of boundaries offer high computational efficiency for complex flow configurations. The wall model operates directly on the Cartesian computational mesh without the need for a dual boundary-conforming mesh. The combination of wall model and implicit LES is investigated in detail for turbulent channel flow at friction Reynolds numbers from Re _τ  = 395 up to Re _τ =100,000 on very coarse meshes. The TBLE wall model with implicit LES gives results of better quality than current explicit LES based on eddy viscosity subgrid-scale models with similar wall models. A straightforward formulation of the wall model performs well at moderately large Reynolds numbers. A logarithmic-layer mismatch, observed only at very large Reynolds numbers, is removed by introducing a new structure-based damping function. The performance of the overall approach is assessed for two generic configurations with flow separation: the backward-facing step at Re _h = 5,000 and the periodic hill at Re _H = 10,595 and Re _H = 37,000 on very coarse meshes. The results confirm the observations made for the channel flow with respect to the good prediction quality and indicate that the combination of implicit LES, immersed-interface method, and TBLE-based wall modeling is a viable approach for simulating complex aerodynamic flows at high Reynolds numbers. They also reflect the limitations of TBLE-based wall models.     

Progress in subgrid-scale transport modelling for continuous hybrid non-zonal RANS/LES simulations

The partially integrated transport modelling (PITM) method can be viewed as a continuous approach for hybrid RANS/LES modelling allowing seamless coupling between the RANS and the LES regions. The subgrid turbulence quantities are thus calculated from spectral equations depending on the varying spectral cutoff location [Schiestel, R., Dejoan, A., 2005. Towards a new partially integrated transport model for coarse grid and unsteady turbulent flow simulations. Theoretical and Computational Fluid Dynamics 18, 443–468; Chaouat, B., Schiestel, R., 2005. A new partially integrated transport model for subgrid-scale stresses and dissipation rate for turbulent developing flows. Physics of Fluids, 17 (6)] The PITM method can be applied to almost all statistical models to derive its hybrid LES counterpart. In the present work, the PITM version based on the transport equations for the turbulent Reynolds stresses together with the dissipation transport rate equation is now developed in a general formulation based on a new accurate energy spectrum function E(κ) valid in both large and small eddy ranges that allows to calibrate more precisely the c_sgs2 function involved in the subgrid dissipation rate _sgs transport equation. The model is also proposed here in an extended form which remains valid in low Reynolds number turbulent flows. This is achieved by considering a characteristic turbulence length-scale based on the total turbulent energy and the total dissipation rate taking into account the subgrid and resolved parts of the dissipation rate. These improvements allow to consider a large range of flows including various free flows as well as bounded flows. The present model is first tested on the decay of homogeneous isotropic turbulence by referring to the well known experiment of Comte-Bellot and Corrsin. Then, initial perturbed spectra E(κ) with a peak or a defect of energy are considered for analysing the model capabilities in strong non-equilibrium flow situations. The second test case is the classical fully turbulent channel flow that allows to assess the performance of the model in non-homogeneous flows characterised by important anisotropy effects. Different simulations are performed on coarse and refined meshes for checking the grid independence of solutions as well as the consistency of the subgrid-scale model when the filter width is changed. A special attention is devoted to the sharing out of the energy between the subgrid-scales and the resolved scales. Both the mean velocity and the turbulent stress computations are compared with data from direct numerical simulations.     

Structuration de la convection mixte en milieu poreux confiné latéralement et chauffé par le bas : effets d''inertiePattern formation of mixed convection in a porous medium confined laterally and heated from below: effect of inertia

We consider the onset of convection in a porous medium heated from below and subjected to a horizontal mean flow. The effect of porous inertia is studied, and the transverse aspect ratio a of the medium is taken into accout. We find that the dominant modes are longitudinal rolls (L.R) if a is an integer or transverse traveling rolls (T.R) if a is below a_c with a_c<1. When a is not an integer with a>a_c, the setting on patterns are oscillatory three-dimensional structures (3D) for a>1 or T.R for a_c<a<1 provided that the Reynolds number remains below a critical value Re_K^*. We show that these structures are replaced by L.R if Re_K>Re_K^*. To cite this article: A. Delache et al., C. R. Mecanique 330 (2002) 885–891.