Stability of an Advective Flow in a Horizontal Fluid Layer Heat-Insulated from Below with Rigid Boundaries

Abstract—

In this paper, we study the stability of an advective flow in a flat horizontal layer of an incompressible fluid with rigid boundaries. A linear temperature distribution is set on the upper boundary of the layer while the lower boundary is thermally insulated. The plane-parallel flow due to the action of horizontal convection is described analytically as an exact solution of the Navier–Stokes equations in the Boussinesq approximation. In the linear theory, the stability of an advective flow to normal perturbations is studied at various values of the Prandtl number. The most dangerous modes are determined, and neutral curves are plotted. In the nonlinear formulation of the problem, the structure of finite-amplitude perturbations in the supercritical region near the minima of the neutral curves is studied.