Inspired by spatiotemporal observations from satellites of the trajectories of objects drifting near the surface of the ocean in the National Oceanic and Atmospheric Administration’s “Global Drifter Program”, this paper develops data-driven stochastic models of geophysical fluid dynamics (GFD) with non-stationary spatial correlations representing the dynamical behaviour of oceanic currents. Three models are considered. Model 1 from Holm (Proc R Soc A 471:20140963, 2015) is reviewed, in which the spatial correlations are time independent. Two new models, called Model 2 and Model 3, introduce two different symmetry breaking mechanisms by which the spatial correlations may be advected by the flow. These models are derived using reduction by symmetry of stochastic variational principles, leading to stochastic Hamiltonian systems, whose momentum maps, conservation laws and Lie–Poisson bracket structures are used in developing the new stochastic Hamiltonian models of GFD.

中文翻译：

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拉格朗日流体流动中具有非平稳空间相关性的随机几何模型。

受国家海洋与大气管理局“全球漂移者计划”中卫星漂移至海洋表面的轨迹的时空观测启发，本文开发了具有非平稳性的数据驱动的地球物理流体动力学（GFD）随机模型。代表洋流动力学行为的空间相关性。考虑了三种模型。回顾了Holm的模型1（Proc R Soc A 471：20140963，2015），其中空间相关性与时间无关。称为模型2和模型3的两个新模型引入了两种不同的对称破坏机制，通过这些机制，流量可以对空间相关性进行平移。这些模型是根据随机变分原理的对称性归约得出的，从而得出了随机哈密顿系统，其动量图