Linear Inviscid Damping for Couette Flow in Stratified Fluid
arXiv:1610.08924 · doi:10.1007/s00021-017-0328-3
Abstract
We study the inviscid damping of Couette flow with an exponentially stratified density. The optimal decay rates of the velocity field and the density are obtained for general perturbations with minimal regularity. For Boussinesq approximation model, the decay rates we get are consistent with the previous results in the literature. We also study the decay rates for the full Euler equations of stratified fluids, which were not studied before. For both models, the decay rates depend on the Richardson number in a very similar way. Besides, we also study the dispersive decay due to the exponential stratification when there is no shear.
References in corpus (3)
- Inviscid dynamical structures near Couette flow
- Linear inviscid damping for monotone shear flows in a finite periodic channel, boundary effects, blow-up and critical Sobolev regularity
- Sharp decay estimates for an anisotropic linear semigroup and applications to the SQG and inviscid Boussinesq systems