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
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.