Title: Hydrodynamic stability in the presence of a stochastic forcing:a case study in convection,
Abstract: We investigate the stability of a statistically stationary conductive state
for Rayleigh-Bénard convection between stress-free plates that arises due to
a bulk stochastic internal heating. This setup may be seen as a generalization
to a stochastic setting of the seminal 1916 study of Lord Rayleigh. Our results
indicate that stochastic forcing at small magnitude has a stabilizing effect,
while strong stochastic forcing has a destabilizing effect. The methodology put
forth in this article, which combines rigorous analysis with careful
computation, also provides an approach to hydrodynamic stability for a variety
of systems subject to a large scale stochastic forcing.