On the onset of advective flow in a stratified medium induced by weak symmetry breaking of horizontal translations

Abstract

In this paper, we analytically study the mechanism of the onset of the liquid/gas flow in a non-isothermal stratified medium. The flow is induced by small spatial inhomogeneities of the exchange coefficients. In a statically stable stratified medium heated strictly from above, as is known, there is heat diffusion directed from top to bottom. We consider the system, which is slightly non-invariant with respect to translations along with horizontal directions. It may occur, for example, due to the dependence of the thermal conductivity coefficient on horizontal coordinates. In this case, we show that it could result in the rise of horizontal inhomogeneity in the distributions of buoyancy and hydrostatic pressure and, consequently, in the onset of the horizontal advection. We consider harmonic variations of the thermal conductivity of small amplitude. By applying a linear approximation to a set of governing equations, we derive explicit analytical expressions for temperature perturbations and velocity components. Finally, we investigate the possibility of an intense response of the system on slight initial symmetry breaking in a definite range of parameter values.