Cell-pattern sensitivity to box configuration in a saturated porous medium

Abstract

Steady small-amplitude thermal convection in a fluid-saturated. infinitely extended porous layer is investigated theoretically in the wavenumber range 1/√2−1. It was shown that the point of multiple bifurcation Ra0 = (3/√2 + 2)π2, α0 = 2−0.25 leads to secondary bifurcation when the wavenumber decreases.As a result a new branch of a stable, complicated, three-dimensional flow in the square cell was discovered for α close to α0. This branch joins two adjacent branches of three-dimensional flows emanating from the trivial solution and causes their stability transition at the branching points.