Mixing in shear flows

Christian Zillinger proposera un double-exposé le matin sur le format habituel du séminaire d'Analyse.

Pour les personnes qui le souhaitent, la discussion continuera l'après-midi avec les exposés de Roberta Bianchini et Noé Lahaye.

Programme

10:15-11:00 C. Zillinger: Mixing and dissipation in transport problems

Putting ink in water or stirring milk into coffee are everyday examples of mixing. In this talks I give an introduction on how "mixing" can be defined and described quantitatively and how it can interact with diffusion. How should one stir to most quickly or efficiently arrive at a thorough mixture?

 

11:30-12:15 C. Zillinger: Mixing and resonances in the Boussinesq equations

The Boussinesq equations are a common model of a heat conducting fluid. In this talk we discuss how mixing and dissipation interact to yield good linear stability properties and can even suppress buoyancy instabilities. Yet, this not reflected in the behavior of the nonlinear problem, which is much more unstable. We discuss how to overcome this mismatch and how to capture nonlinear resonances by using "traveling waves".

 

14:45-15:30 N. Lahaye: Mixing in the stratified (and rotating) ocean

This talk will address the problem of mixing in stratified fluids from a physical perspective. Specifically, I will discuss its importance for ocean circulation. Secondly, I will propose a case study involving internal waves (propagating perturbations of currents and densities that are ubiquitous in geophysical flows) and examine how this type of flow can lead to mixing via the usual destabilisation mechanisms in stratified fluids (convective and Kelvin-Helmholtz instability).

 

16:00-17:00 R. Bianchini: (In-)stability of the Boussinesq equations around a shear flow

I will be presenting a result on the asymptotic stability (nonlinear inviscid damping) of the 2D Boussinesq equations, specifically concerning the fully inviscid and non-diffusive scenario around the Couette flow. Interestingly, the proof will demonstrate an algebraic instability in both vorticity and density gradients, a phenomenon previously identified by Hartman in 1975.