Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics

@inproceedings{Cotter2017StochasticPD,
  title={Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics},
  author={Colin J. Cotter and Georg A. Gottwald and Darryl D. Holm},
  booktitle={Proceedings. Mathematical, physical, and engineering sciences},
  year={2017}
}
In Holm (Holm 2015 Proc. R. Soc. A471, 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow… CONTINUE READING
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