Fabien S. Godeferd

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...

Wave turbulence in rapidly rotating flows

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

Direct numerical simulations of turbulence with confinement and rotation

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Statistical modelling and direct numerical simulations of decaying stably stratified turbulence. Part 2. Large-scale and small-scale anisotropy

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

Nonlinear formation of structures in rotating stratified turbulence

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Turbulent diffusion in rapidly rotating flows with and without stable stratification

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Statistical modelling and direct numerical simulations of decaying stably stratified turbulence. Part 1. Flow energetics

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Zonal approach to centrifugal, elliptic and hyperbolic instabilities in Stuart vortices with external rotation

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Refined vorticity statistics of decaying rotating three-dimensional turbulence

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