Statistical saturation of buoyant flow induced by a fluctuating acceleration

We study buoyancy-driven convection in a laterally heated, two-dimensional cavity under a fluctuating acceleration field, to model flow conditions in a microgravity environment. In the limit of a large aspect ratio cavity (the length in the direction perpendicular to the temperature gradient is much larger than in the parallel direction), an analytic solution can be found in which the flow reaches a statistical steady state of zero average vorticity and mean squared vorticity that scales as the stochastic Rayleigh number squared. We also present the results of a full numerical solution of the Navier-Stokes equation for a fluid driven by a fluctuating acceleration field in a square cavity and confirm the scaling of the flow obtained in the asymptotic analysis.