Effect of g-jitter on the spectrum of excitations of a free fluid surface: Stochastic formulation

We present a theoretical investigation of the effects that residual accelerations onboard spacecraft can have on the spectrum of excitations of a free fluid surface. We model the high frequency, large-amplitude components of such residual accelerations (sometimes called g-jitter) as a stochastic or random process. We calculate, to lowest order in ail expansion in the correlation time of g-jitter, the dynamical equation satisfied by the average surface displacement from planarity. The average is taken over an ensemble of realizations of the fluctuating residual acceleration. We conclude that the dispersion relation for surface waves is modified: it includes a contribution proportional to the mean square g-jitter and tile square of its correlation time.