# Fluid Mechanics and Acoustics Laboratory - UMR 5509

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

## Our partners

Andrea Maffioli - KTH, Stockholm

## Vertical spectra of stratified turbulence at large horizontal scales

Vendredi 7 juillet 2017 - 11h - ECL - bât H10 salle B11

The vertical structure of stably stratified turbulence consists in a series of layers in the velocity and density fields, resulting in decorrelation of these fields over short vertical distances. This physical picture results in vertical energy spectra that are very steep, possessing the well-known form $E_h(k_v) = \alpha N^2 k_v^{-3}$, where $N$ is the Brunt-Väisälä frequency, $k_v$ is the vertical wavenumber and $\alpha$ is a constant. This vertical spectrum has been measured in the ocean and in the atmosphere. However, it has not been convincingly reproduced in an experiment or a numerical simulation of stratified turbulence to date. In this work I propose a scale decomposition of the velocity field into large scales and small scales by using a spectral filter. This also allows the vertical spectrum to be decomposed into a large-scale vertical spectrum and a small-scale vertical spectrum. The large-scale vertical spectrum isolates the anisotropic dynamics of stratified turbulence while the small-scale vertical spectrum isolates the approximately isotropic dynamics. The scale decomposition is applied to high-resolution Direct Numerical Simulations (DNS) of strongly stratified turbulence with forcing. It is found that the large-scale vertical spectra obtained from the DNS are in very good agreement with the above form, approximately over the wavenumber range predicted by theory. This is the first time that this vertical spectrum has been observed in a controlled experiment or simulation. This result is important because it shows there is a range of scales in stratified turbulence that are in buoyancy-inertial balance.

Presentation Slides