Optimal Control of Buoyant Flows with Temperature-Dependent Viscosity

This paper shows the effects of a boundary control on pattern formation in a Rayleigh-Benard problem with temperature-dependent viscosity. In particular, a rectangular domain infinite in one of the horizontal dimensions is considered. The conductive state bifurcates to a stationary pattern for the constant viscosity case. And the boundary control hinders instability up to the point where it is inhibited for the value of the control at which the gradient disappears. For the variable viscosity case, the conductive state bifurcates to a different stationary pattern, and the critical threshold is lower. The boundary control changes the critical wave number and favors instability up to the point where it is inhibited for the value of the control at which the gradient disappears.