The effects of temperature-dependent viscosity and the instabilities in convection rolls of a layer of fluid-saturated porous medium

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Abstract
Convection of two-dimensional rolls in an infinite horizontal layer of fluid-saturated porous medium heated from below is studied numerically. Several important finite-amplitude states are isolated, and their bifurcation properties are shown. Effects of the temperature-dependent viscosity are included. The stability of these states is investigated with respect to the class of disturbances that have a ½π phase shift relative to the basic state. In particular, the oscillatory mechanism and the mean-flow generating mechanism through the variable viscosity are discussed.