STABILITY OF A FLUID SURFACE IN A MICROGRAVITY ENVIRONMENT

We introduce a stochastic model to analyze in quantitative detail the effect of the high-frequency components of the residual accelerations onboard spacecraft (often called g jitter) on the motion of a fluid su rface. The residual acceleration field is modeled as a narrow-band noi se characterized by three independent parameters: its intensity G2, a dominant frequency OMEGA, and a characteristic spectral width tau-1. T he white noise limit corresponds to OMEGAtau-->0, with G2tau finite, a nd the limit of a periodic g jitter (or deterministic limit) can be re covered for OMEGAtau-->infinity, G2 finite. Analysis of the linear res ponse of a fluid surface subjected to a fluctuating gravitational fiel d leads to the stochastic Mathieu equation driven by both additive and multiplicative noise. We discuss the stability of the solutions of th is linear equation in the two limits of white noise and deterministic forcing, and in the general case of narrow-band noise. The results are then applied to typical microgravity conditions.