Statistical Saturation of Buoyant Flow Induced by a Fluctuating Acceleration

We study buoyancy driven convection in a laterally heated and two dimensional cavity under a uctuating acceleration eld, to model ow 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 ow reaches a statistical steady state of zero average vorticity and mean squared vorticity that scales as the stochastic Rayleigh number squared R 2 , with R = T d 2 p 2G 2 == p. is the coeecient of thermal expansion of the uid, T the temperature gradient across the cavity, d its length in the direction of the gradient, G 2 the intensity of the uctuations, their correlation time, the thermal diiusivity and the kinematic viscosity of the uid respectively. We also present the results of a full numerical solution of the Navier-Stokes equation for a uid driven by a uctuating acceleration eld in a square cavity, and connrm the scaling of the ow obtained in the asymptotic analysis.