Secondary instabilities of convection in a shallow cavity

Abstract

Analysis of secondary instabilities of natural convection in a shallow cavity heated from a side has been carried out. For mercury with Prandtl number equal to 0.027 analysis of the primary instabilities by linear theory shows that an instability sets in as transverse cells at Grashof number equal to 9157.6. Instability resulting in oscillatory longitudinal rolls is also possible, their critical Grashof number being equal to 10608.4. The secondary instabilities of the equilibrium states of transverse cells for mercury have been determined. The results show roughly that stable transverse cells with wavelength shorter than the critical become unstable by subharmonic resonance, but the instability for longer cells sets in by a combination resonance. The instability as longitudinal oscillatory rolls reappears at larger values of Grashof number, although slightly delayed by the presence of the transverse cells.