Mathematical Study of Rotating Fluids with Resonant Surface Stress Anne-laure Dalibard and Laure Saint-raymond
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چکیده
We are interested here in describing the linear response of a highly rotating fluid to some surface stress tensor, which admits fast time oscillations and may be resonant with the Coriolis force. In addition to the usual Ekman layer, we exhibit another much larger boundary layer, and we prove that for large times, the effect of the surface stress may no longer be localized in the vicinity of the surface. From a mathematical point of view, the main novelty here is to introduce some systematic approach for the study of boundary effects. The goal of this paper is to understand the influence of a surface stress depending on time on the evolution of an incompressible and homogeneous rotating fluid. More precisely, we are interested in the effects of a resonant forcing, i.e. of a stress oscillating with the same period as the rotation of the fluid. In the non-resonant case, the works by Desjardins and Grenier [5] then by Masmoudi [16] show that the wind forcing creates essentially some boundary layer in the vicinity of the surface, which contributes to the mean motion by a source term, known as the Ekman pumping. For a precise description of the method leading to such convergence results, we refer to the book [4] by Chemin, Desjardins, Gallagher and Grenier. Here the situation is much more complicated since the resonant part of the forcing will be proved to generate another boundary layer with a different typical size, and may overall destabilize the whole fluid with the apparition of a vertical profile. We give here a precise description of these (linear) effects of the Coriolis force in presence of resonant wind.
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تاریخ انتشار 2008