?
Устойчивость адвективного течения во вращающемся горизонтальном теплоизолированном снизу слое несжимаемой жидкости с твердыми границами при малом числе Прандтля
The stability of advective flow in a flat rotating horizontal layer of incompressible fluid with solid boundaries is studied. A linear temperature distribution is set on the upper boundary of the layer, the lower boundary is thermally insulated. The advective flow due to horizontal convection is described analytically in the form of a new exact solution of the Navier-Stokes equations in the Boussinesq approximation. At a small value of the Prandtl number, the stability of the advective flow to normal perturbations for a wide range of the Taylor number is investigated in the framework of linear theory. The most dangerous modes are determined and neutral curves are constructed. In the framework of the nonlinear formulation of the problem, the influence of rotation on the structure of finite-amplitude perturbations in the supercritical region near the minima of neutral curves is studied.