# Laboratoire de Mécanique des Fluides et d’Acoustique - UMR 5509

LMFA - UMR 5509
Laboratoire de Mécanique des Fluides et d’Acoustique
Lyon
France

## Nos partenaires

Alexandre Delache

## Isotropie rétablie en turbulence avec effet de stratification et de rotation : role de l’échelle d’Ozmidov et de Hopfinger

Jeudi 16 juin 2016 13h, UCBL Bât Omega

In oceanic, atmospheric or engineering flows, turbulence can be strongly affected by stratification and rotation. In contrast with isotropic turbulence, anisotropic structures emerge in stably stratified turbulence or in rotating turbulence :
quasi-horizontal structures appear to be organized in vertically sheared layers. These structures are a mix between internal wave and turbulence.
quasi-vertical structures appear as column of Taylor. These structures are a mix between inertial wave and turbulence.

Introducing the turbulent dissipation rate eps , two length scales can be obtained, namely the Ozmidov length scale [1] $L_o = \sqrt{\epsilon/N^3}$ and the Hopfinger length scale [2-3] $L_h = \sqrt{\epsilon/f^3}$. Lo and Lh compare the relative effects of inertia and of the buoyancy force or of the Coriolis force respectively, and thus quantify the rise of anisotropy in different scale ranges : at large scales (larger than Lo or Lh ) the anisotropy due to strong stratification or strong rotation is dominant, whereas at small scales (smaller than Lo or Lh ), universal 3D isotropic characteristics of turbulence appear to be restored.

To confirm directly the role of these two scales, we performed numerical simulations at high resolution (2048³ points) in freely decaying turbulence at four different stratification rates and six rotating rates. We confirm the role played by Lo and Lh by considering the angular energy spectra.

[1] R.V. Ozmidov, Izvestia Acad. Sci. USSR, Atmosphere and Ocean Physics, 1965,N 8
[2] Mory, M. & Hopfinger, Proceedings of a Workshop Held at INRIA, Sophia-Antipolis, Fance, December 10–14, 1984, Springer Berlin Heidelberg, E. Frisch, U. ; Keller, J. B. ; Papanicolaou, G. C. & Pironneau, O. (Eds.), 1985, 218-236
[3] O. Zeman,Phys. Fluids 6, 3221 (1994).