Linear Inviscid Damping for Couette Flow in Stratified Fluid
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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.
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- 1.Bateman, H.: Higher Transcendental Functions. McGraw-Hill Book Company, Inc., New York (1953)Google Scholar
- 11.Eliassen, A., Høiland, E., Riis, E.: Two-Dimensional Perturbation of a Flow with Constant Shear of a Stratified Fluid, Publ. No. 1, pp. 1-30. Institute for Weather, Climate Research, Oslo (1953)Google Scholar
- 15.Høiland, E.: On the dynamic effect of variation in density on two-dimensional perturpation of floaw with constnat shear. Grof. Publ. XVIII, 3–12 (1953)Google Scholar
- 18.Orr, W.M.F.: Stability and instability of steady motions of a perfect liquid. Proc. Ir. Acad. Sect. A Math Astron. Phys. Sci. 27, 9–66 (1907)Google Scholar
- 22.Wei, D., Zhang, Z., Zhao, W.: Linear Inviscid damping for a class of monotone shear flow in Sobolev spaces. Commun. Pure. Appl. Math. (2016). doi: 10.1002/cpa.21672