Transport, Fluids and Mixing

Long-time behaviour in the 2D Euler-Boussinesq equations near a stably stratified Couette flow

speaker: Michele Dolce (Imperial College London)

abstract: Fluids in the ocean are often inhomogeneous, incompressible and, in relevant physical regimes, can be described by the 2D Euler-Boussinesq system. Equilibrium states are then commonly observed to be stably stratified, namely the density increases with depth. We are interested in considering the case when also a background shear flow is present. In the talk, I will describe quantitative results for small perturbations around a stably stratified Couette flow. We show that the density variation and velocity decay in L2 with a rate O(t-(12)), namely they undergo inviscid damping. On the other hand, the vorticity and density gradient grow as O(t(12)), a phenomenon that we call shear-buoyancy instability. This is first precisely quantified at the linear level. For the nonlinear problem, the result holds on the optimal time-scale on which a perturbative regime can be considered. Namely, given an initial perturbation of size O(ε), thanks to the linear instability, it becomes of size O(1) on a time-scale of order O(ε-2). This is joint work with J. Bedrossian, R. Bianchini and M. Coti Zelati.

timetable:
Wed 26 Jan, 14:00 - 14:30,
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