Stability of Advective Flow in a Rotating Horizontal Incompressible Fluid Layer Heat-Insulated from Below with Rigid Boundaries at Low Prandtl Number

The stability of advective flow in a rotating plane horizontal incompressible fluid layer with rigid boundaries is investigated. The linear temperature distribution is specified on the upper boundary of the layer and the lower boundary is heat-insulated. Advective flow developed due to horizontal convection is described analytically in the form of a new exact solution of the Navier-Stokes equations in the Boussinesq approximation. The stability of advective flow with respect to normal perturbations is investigated at a low Prandtl number over a wide range of the Taylor number within the framework of the linear theory. The most dangerous modes are determined and the neutral curves are constructed. The effect of rotation on the structure of finite-amplitude perturbations in the supercritical domain in the neighborhood of minima of neutral curves is studied within the framework of the nonlinear formulation of the problem.