Cavity flow induced by a fluctuating acceleration field

Buoyancy driven convection induced by a fluctuating acceleration field is studied in a two dimensional square cavity. This is a simplified model of, for example, fluid flow in a directional solidification cell subject to external accelerations, such as those encountered in a typical microgravity environment (g-jitter). The effect of both deterministic and stochastic acceleration modulations normal to the initial density gradient are considered. In the latter case, the acceleration field is modeled by narrow band noise defined by a characteristic frequency Ω, a correlation time τ, and an intensity G². If the fluid is quiescent at t=0 when the acceleration field is initiated, the ensemble average of the voracity at the center of the cavity remains zero for all times. The mean squared vorticity 〈ξ ²〉, however, is seen to exhibit two distinct regimes: For t≪τ, 〈ξ²〉 oscillates in time with frequency Ω. For t≫τ, 〈ξ²〉 grows linearly in time with an amplitude equal to R²Pr/(1 + (Ωτ))², where R is a new dimensionless number which reduces to the Rayleigh number in the case of a constant gravity, and Pr is Prandtl number. At yet later times, viscous dissipation at the walls of the cavity leads to saturation, with 〈ξ²〉_sat={(Pr τ+1)R²/[(Pr π+1)²+Ω²τ²]}.