Stability of Supercritical Convection-Wave Number Selection Through Stability

Abstract

In this chapter we are going to study the stability of cellular convection in a layer of porous material filled with fluid and heated from below. This type of cellular convection could be described as Bénard convection in a DOB fluid. As in the Bénard problem R₁=0, R₂>0 and the bifurcation of conduction into convection is supercritical rather than two-sided. The analysis of Schlüter, Lortz and Busse (1965) for the stability of Bénard convection in an OB fluid applies to the DOB fluid. Their analysis shows that the common three-dimensional plan forms which are included in (76.6) are all unstable and only two-dimensional plan forms can be stable. This result is consistent with the stability picture for two-sided bifurcation into cellular convection which is shown in Fig. 77.1 (iii) in the limit p₁ → p₀, p₂→ p₀, ε_* → 0.