Titre/Title : Extreme events, mixing, and invariant manifolds in geophysical flows
Contact : Martin Obligado (équipe EDT)
Résumé/Abstract : Turbulent flows are characterized by a huge number of degrees of freedom, and display erratic behavior with extreme events and non-Gaussian statistics. However, under some conditions their dynamics can be captured by reduced systems with a few degrees of freedom. In this talk I will present some dimensional reductions that can be applied to stably stratified turbulence, a case of interest for atmospheric and oceanic flows. Such flows display strong and spatially localized vertical drafts, anisotropic mixing, and non-stationary large fluctuations in the velocity and the temperature, as well as in their gradients. Starting from the partial differential equations that describe the flow dynamics I will consider simple models that capture the competition between gravity waves on a fast time-scale, and non-linear steepening on a slower time-scale. One model, derived from empirical arguments, points to the existence in these flows of a resonant regime characterized by enhanced large-scale intermittency and linked to the emergence of specific structures in the velocity and temperature. This regime has a strong impact in the vertical mixing of Lagrangian tracers. A second model, derived more rigorously from the exact equations for the evolution of velocity and temperature gradients, indicates the system has a few invariant manifolds over which the dynamics of fluid elements becomes significantly slower. These manifolds are associated to regions of local stability and of local convection in the flow.