Claude Cambon

Spectral approach to non-isotropic turbulence subjected to rotation

The non-isotropic effects of solid-body rotation on homogeneous turbulence are investigated in this paper. A spectral formalism using eigenmodes introduces the spectral Coriolis effects more easily and leads to simpler expressions for the integral quadratic terms which come mostly from classical two-point closures. The analysis is then applied to a specific eddy damped quasi-normal Markovian model, which includes the inertial waves regime in the evaluation of triple correlations. This procedure allows for a departure from isotropy by external rotation effects. When started with rigorously isotropic initial data, the various trends observed on the Reynolds stresses and the integral lengthscales remain in accordance with the results from direct simulations; moreover they reflect a very specific spectral angular distribution. Such an angular dependence allows a drain of spectral energy from the parallel to the normal wave vectors (with respect to the rotation axis), and thus appears consistent with a trend toward two-dimensionality.

Energy Transfer in Rotating Turbulence

The influence of rotation on the spectral energy transfer of homogeneous turbulence is investigated in this paper. Given the fact that linear dynamics, e.g. the inertial waves regime found in an RDT (rapid distortion theory) analysis, cannot aect a homogeneous isotropic turbulent flow, the study of nonlinear dynamics is of prime importance in the case of rotating flows. Previous theoretical (including both weakly nonlinear and EDQNM theories), experimental and DNS (direct numerical simulation) results are collected here and compared in order to give a self-consistent picture of the nonlinear eects of rotation on turbulence. The inhibition of the energy cascade, which is linked to a reduction of the dissipation rate, is shown to be related to a damping of the energy transfer due to rotation. A model for this eect is quantied by a model equation for the derivative-skewness factor, which only involves a micro-Rossby number Ro ! =! 0 =(2) { ratio of r.m.s. vorticity and background vorticity { as the relevant rotation parameter, in accordance with DNS and EDQNM results. In addition, anisotropy is shown also to develop through nonlinear interactions modied by rotation, in an intermediate range of Rossby numbers (Ro L 1), which is characterized by a macro-Rossby number Ro L based on an integral lengthscale L and the micro-Rossby number previously dened. This anisotropy is mainly an angular drain of spectral energy which tends to concentrate energy in the wave-plane normal to the rotation axis, which is exactly both the slow and the two-dimensional manifold. In addition, a polarization of the energy distribution in this slow two-dimensional manifold enhances horizontal (normal to the rotation axis) velocity components, and underlies the anisotropic structure of the integral lengthscales. Finally a generalized EDQNM (eddy damped quasi-normal Markovian) model is used to predict the underlying spectral transfer structure and all the subsequent developments of classic anisotropy indicators in physical space. The results from the model are compared to recent LES results and are shown to agree well. While the EDQNM2 model was developed to simulate ‘strong’ turbulence, it is shown that it has a strong formal analogy with recent weakly nonlinear approaches to wave turbulence.

Detailed investigation of energy transfers in homogeneous stratified turbulence

This paper investigates some irreversible mechanisms occurring in homogeneous stably stratified turbulent flows. In terms of the eigenmodes of the linear regime, the velocity‐temperature field is decomposed into a vortex and two wavy components. Using an eddy‐damped quasinormal Markovian (EDQNM) closure with the axisymmetry hypothesis, an analysis of the anisotropic energy transfers between the vortex kinetic energy, the wave kinetic and potential energy is made. Within the light of triadic exchanges, and by analogy of the resonance condition for three linearly interacting gravity waves, the closure model allows one to compute the detailed transfers for eight types of interactions. Results of the calculations include time evolution plots, for the isotropic closure model as well as two different types of the anisotropic closure. The pure vortical interactions are shown to be responsible for the irreversible anisotropic structure created by stable stratification, and this structure prevents the inverse casc...

Stability analysis and large-eddy simulation of rotating turbulence with organized eddies

Rotation strongly affects the stability of turbulent flows in the presence of large eddies. In this paper, we examine the applicability of the classic Bradshaw-Richardson criterion to flows more general than a simple combination of rotation and pure shear. Two approaches are used. Firstly the linearized theory is applied to a class of rotating two-dimensional flows having arbitrary rates of strain and vorticity and streamfunctions that are quadratic. This class includes simple shear and elliptic flows as special cases. Secondly, we describe a large-eddy simulation of initially quasi-homogeneous three-dimensional turbulence superimposed on a periodic array of two-dimensional Taylor-Green vortices in a rotating frame. The results of both approaches indicate that, for a large structure of vorticity W and subject to rotation Q, maximum destabilization is obtained for zero tilting vorriciry (4 W + 2Q = 0) whereas stability occurs for zero absolute vorticity ( W + 2l2 = 0). These results are consistent with the Bradshaw-Richardson criterion; however the numerical results show that in other cases the Bradshaw-Richardson number

Turbulence amplification by a shock wave and rapid distortion theory

Amplification of turbulent kinetic energy in an axial compression is examined in the frame of homogeneous rapid distortion theory (RDT) by using the Craya–Herring formalism. By separating the turbulent field into solenoidal and dilatational modes (Helmholtz decomposition), one can show the dilatational mode is mediated by the parameter Δm0=D0/a0k0, which corresponds to the initial ratio between the acoustic time scale (a0k0)−1 and the compression time scale D0−1, with D0 the compression rate. It is shown here that amplification of total kinetic energy is then limited by two analytical solutions obtained for Δm0=0 (purely solenoidal‐acoustical regime) and for Δm0≫1 (‘‘pressure released’’ regime), respectively. The results of the theory are first compared to results of direct numerical simulations (DNS) on homogeneous axial compression. The applicability of this homogeneous approach to the shock wave turbulence interaction, is then discussed. Considering a shock‐induced compression at given Mach number, it ...

Wave turbulence in rapidly rotating flows

An asymptotic quasi-normal Markovian (AQNM) model is developed in the limit of small Rossby number

Toward a new Reynolds stress model for rotating turbulent flows

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An analysis of rotating shear flow using linear theory and DNS and LES results

and high Reynolds number, i.e. for rapidly rotating turbulent flow. Based on the ‘slow’ amplitudes of inertial waves, the kinetic equations are close to those that would be derived from Eulerian wave-turbulence theory. However, for their derivation we start from an EDQNM statistical closure model in which the velocity field is expanded in terms of the eigenmodes of the linear wave regime. Unlike most wave-turbulence studies, our model accounts for the detailed anisotropy as the angular dependence in Fourier space. Nonlinear equations at small Rossby number are derived for the set

ON THE THREE-DIMENSIONAL INSTABILITIES OF PLANE FLOWS SUBJECTED TO CORIOLIS FORCE

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Nonlinear formation of structures in rotating stratified turbulence

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