Narrow band noise as a model of time-dependent accelerations: study of the stability of a fluid surface in a microgravity environment

Abstract

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 fluid motion. The residual acceleration field is modeled as a narrow band noise characterized by three independent parameters: its intensity $G^{2}$, a dominant frequency $Ω$, and a characteristic spectral width $τ^{-1}$. The white noise limit corresponds to $Ωτ\rightarrow 0$, with $G^{2} τ$ finite, and the limit of a periodic g-jitter (or deterministic limit) can be recovered for $Ωτ\rightarrow \infty$, $G^{2}$ finite. The analysis of the response of a fluid surface subjected to a fluctuating gravitational field leads to the stochastic Mathieu equation driven by both additive and multiplicative noise. We discuss the stability of the solutions of this 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.