# 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

Soutenance de thèse ECL

## Henri Lam

Mardi 14 décembre 2021, 14h00, amphi 203, bât. W1

### Interaction of waves and eddies in rotating or stably stratified flows

Composition du jury
Directeurs de thèse :
F. S. Godeferd, Directeur de Recherche, CNRS
A. Delache, Maitre de conférences, Université de Saint-Etienne

Rapporteurs :
C. P. Caulfield, Professeur, University of Cambridge
M. K. Verma, Professeur, IIT Kanpur

Examinateurs :
A. Naso, Chargée de recherche, CNRS
S. Galtier, Professeur, Ecole polytechnique

Invités :
B. Favier, Chargé de recherche, CNRS
R. Marino, Chargé de recherche, CNRS
A. Maffioli, Maitre de conférences, École centrale de Lyon

### Résumé

Geophysical flow as the oceans and atmosphere are subject to eddies structure and waves, such as inertial waves due to rotation and gravity waves due to stratification. Their dynamics can influence a large number of weather phenomena as the Jet stream, or the Quasi-biennial Oscillation which in turn modify the weather and climate on Earth. Hence, a better understanding of the waves and eddies phenomena and interaction can lead to a better comprehension of the physical phenomena occurring on Earth.
To do this, I propose a new separation technique of waves and eddies in stratified turbulence and rotating turbulence from 3D field resulting of DNS. This separation is based on the dispersion relation of waves. This dispersion relation is obtained by simulating the Green’s function and take into account the sweeping effect due to large structures that have an inhomogeneous velocity in time and space like the vertically sheared horizontal flow in stratified turbulence (resp. the geostrophic mode in rotating turbulence). It allows us to study independently waves and eddies but also how waves and eddies interact with one another. I establish the evolution equations for the waves part, eddies parts and large structure separately by taking all interactions. Different regimes are studied from results of DNS with a low Froude number $\textit{Fr} \ll 1$ in stratified turbulence (resp. Rossby number $\textit{Ro}\ll 1$ in rotating turbulence) but with a varying buoyancy Reynolds number $\textit{Re}_b$ (resp. Inertial Reynolds number $\textit{Re}_I$). We observe that the distribution of energy between waves and eddies follow the $\textit{Fr}$ (resp. $\textit{Ro}$) number. By applying the separation technique, I observe a large transfer of energy from waves to eddies. Moreover, I also observe in the rotating case that it is mostly waves/waves and waves/eddies interactions that transfer energy to the geostrophic mode. A few inverse cascades are observed for particular types of transfers. The dissipation and mixing due to waves and eddies against the different parameters are calculated. Finally, 2D velocity fields are decomposed into their wave and eddy parts.

Sankey diagram representing the different terms of the balance of energy and flux for $Ro=0.06$ and $Re_I=28$. Red color is for waves, blue is for eddies and green for the GM.

## Agenda

• ### Mardi 14 décembre 2021 14:00-15:00 -

Soutenance de thèse Henri Lam