In this paper we propose a stochastic model reduction procedure for deterministic equations from geophysical fluid dynamics. Once large-scale and small-scale components of the dynamics have been identified, our method consists in modelling stochastically the small scales and, as a result, we obtain that a transport-type Stratonovich noise is sufficient to model the influence of the small scale structures on the large scales ones. This work aims to contribute to motivate the use of stochastic models in fluid mechanics and identifies examples of noise of interest for the reduction of complexity of the interaction between scales. The ideas are presented in full generality and applied to specific examples in the last section.

中文翻译：

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小尺度扰动的随机建模

在本文中，我们提出了一种用于地球物理流体动力学确定性方程的随机模型简化程序。一旦确定了动力学的大尺度和小尺度分量，我们的方法就在于对小尺度进行随机建模，因此，我们获得传输型 Stratonovich 噪声足以对小尺度的影响进行建模大规模的结构。这项工作旨在促进在流体力学中使用随机模型，并确定感兴趣的噪声示例，以降低尺度之间相互作用的复杂性。这些想法是完全通用的，并应用于最后一节中的具体示例。