Nonlinear convection regimes in superposed fluid and porous layers under vertical vibrations: Negative porosity gradients

Abstract

We study numerically a nonlinear problem on the excitation of average convection in a fluid layer heated from below and partially filled with a porous medium in the gravity field. The porous medium is non-uniform in the vertical direction, and its permeability and porosity grow with depth at a negative porosity gradient. The layer oscillates vertically with high frequency and small amplitude. It is shown that in the absence of vibrations harmonic velocity oscillations can occur in the layer. In this case, the heat flux performs small-amplitude oscillations, to it is assumed to be quasi-stationary. With increasing supercriticality, the velocity oscillations become irregular and are accompanied by heat flux fluctuations with high enough amplitude. Changes in the heat flux are caused by the instability of long-wave convective rolls that penetrate pores. Additional vortices having a shorter wavelength and interacting with long-wave rolls are observed within a high porosity region near the hot lower boundary of the layer. This region constitutes the major part of the total temperature difference at the solid boundaries of the layer. Vibrations of a high enough intensity suppress the supercritical velocity and heat flux oscillations, thus preventing additional vortex formation.