Tertiary patterns in inclined layer convection

Abstract

Convection in an inclined layer generates various types of spatio-temporal patterns due to interaction of buoyancy and shear. At small angles of incline, the secondary instability of the uniform base state occurs in the form of buoyancy dominated longitudinal rolls. Above a critical angle of incline marking a co-dimension 2 point, shear driven transverse roll instabilities take over as the secondary instabilities. Computing the location of the co-dimension 2 point for varying thermal driving and inclination angle and determining all secondary bifurcations together with the resulting tertiary states allows to characterize the nonlinear phase diagram of inclined layer convection system. The semi-analytically computed phase diagram quantitatively matches experimental observations by Daniels et al. Close to the co-dimension 2 point, a subcritical secondary bifurcation leading to bistability is identified. In the bistable region, heteroclinic cycles generate bursting behavior.