Waves, turbulence and invariants in geophysical flows
This work focuses on waves and turbulence in geophysical fluid dynamics. We present different approaches to describe the emergence of macroscopic properties in these systems, regardless of the detail of the underlying flow dynamics. We show in particular that the emergence of robust properties at large scale can be related to invariants of the flow model and to the existence or the breaking of specific symmetries. Firstly, statistical physics arguments make it possible to quantify the combined effect of turbulence and dynamical invariants. It is thus possible to construct phase diagrams, which are useful for describing some aspects of self-organization of geostrophic eddies, or for interpreting the efficiency of turbulent mixing in stratified fluids. Secondly, methods from non-linear physics make it possible to understand the interactions between waves and mean flows in stratified fluids. Thirdly, tools from topology developed initially in condensed matter physics make it possible to understand the emergence of unidirectional edge states when certain discrete symmetries are broken. In particular, we show the topological origin of equatorial Kelvin waves, by calculating a Chern invariant associated with Poincaré waves in the rotating shallow water model.
Section CNU n°28 - Milieux denses et matériaux