A stochastic formulation is introduced to study the large amplitude and high‐frequency components of residual accelerations found in a typical microgravity environment (or g‐jitter). The linear response of a fluid surface to such residual accelerations is discussed in detail. The analysis of the stability of a free fluid surface can be reduced in the underdamped limit to studying the equation of the parametric harmonic oscillator for each of the Fourier components of the surface displacement. A narrow‐band noise is introduced to describe a realistic spectrum of accelerations, that interpolates between white noise and monochromatic noise. Analytic results for the stability of the second moments of the stochastic parametric oscillator are presented in the limits of low‐frequency oscillations, and near the region of subharmonic parametric resonance. Based upon simple physical considerations, an explicit form of the stability boundary valid for arbitrary frequencies is proposed, which interpolates smoothly between the low frequency and the near resonance limits with no adjustable parameter, and extrapolates to higher frequencies. A second‐order numerical algorithm has also been implemented to simulate the parametric stochastic oscillator driven with narrow‐band noise. The simulations are in excellent agreement with our theoretical predictions for a very wide range of noise parameters. The validity of previous approximate theories for the particular case of Ornstein–Uhlenbeck noise is also checked numerically. Finally, the results obtained are applied to typical microgravity conditions to determine the characteristic wavelength for instability of a fluid surface as a function of the intensity of residual acceleration and its spectral width.

中文翻译：

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研究由窄带噪声驱动的参数振荡器，以模拟流体表面对时间相关加速度的响应

引入了一种随机公式来研究在典型情况下发现的剩余加速度的大幅度和高频分量 微重力环境（或g抖动）。a的线性响应流体表面对于这种残余加速度的详细讨论。的分析 自由的稳定性 流体表面 可以减少欠阻尼极限来研究 方程 参数谐波的 震荡器 对于每个傅立叶分量 表面移位。窄带噪声 引入以描述现实的加速度谱，在 白噪声 和单色 噪声。 随机参数第二矩稳定性的解析结果 震荡器 呈现在低频范围内 振荡 在次谐波参数区域附近 谐振。 基于简单的物理考虑，提出了一种适用于任意频率的稳定边界的显式形式，该形式可以在低频和附近频率之间平滑插值 谐振没有可调整参数的极限，并外推到更高的频率。还采用了二阶数值算法来模拟参数随机震荡器 窄带驱动 噪声。 这些模拟与我们对范围广泛的理论预测非常吻合 噪声参数。先前的近似理论对于特定的Ornstein–Uhlenbeck案例的有效性噪声也通过数字检查。最后，将获得的结果应用于典型微重力 确定不稳定性的特征波长的条件 流体表面 残余加速度的强度及其频谱宽度的函数。