Hydrodynamic stability in the presence of a stochastic forcing: A case study in convection

Abstract

We investigate the stability of statistically stationary conductive states for Rayleigh–Bénard convection that arise due to a bulk stochastic internal heating. Our results indicate that stochastic forcing at small magnitude has little to no effect, while strong stochastic forcing has a destabilizing effect. The methodology put forth in this article, which combines rigorous analysis with careful computation, provides an approach to hydrodynamic stability which is applicable to a variety of systems subject to a large scale stochastic forcing.