Stability of Advective Flow in a Horizontal Incompressible Fluid Layer in the Presence of the Navier Slip Condition

Abstract

Abstract—The exact solution of the Navier–Stokes equations in the Boussinesq approximation that describes plane-parallel advective flow in the plane incompressible fluid layer with horizontal boundaries on which the Navier slip condition and the linear temperature distribution are specified is given. The behavior of the velocity and temperature with increase in the slip parameter is considered. The stability of advective flow with respect to plane and spiral perturbations is investigated within the framework of the linear theory. Finite-amplitude perturbations in the supercritical domain in the neighborhood of minima of neutral curves are studied within the framework of the nonlinear formulation of the problem.