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@article{Gay-Balmaz:2018:10.1007/s00332-017-9431-0,
author = {Gay-Balmaz, F and Holm, DD},
doi = {10.1007/s00332-017-9431-0},
journal = {Journal of Nonlinear Science},
pages = {873--904},
title = {Stochastic geometric models with non-stationary spatial correlations in Lagrangian fluid flows},
url = {http://dx.doi.org/10.1007/s00332-017-9431-0},
volume = {28},
year = {2018}
}

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TY  - JOUR
AB  - 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.
AU  - Gay-Balmaz,F
AU  - Holm,DD
DO  - 10.1007/s00332-017-9431-0
EP  - 904
PY  - 2018///
SN  - 0938-8974
SP  - 873
TI  - Stochastic geometric models with non-stationary spatial correlations in Lagrangian fluid flows
T2  - Journal of Nonlinear Science
UR  - http://dx.doi.org/10.1007/s00332-017-9431-0
UR  - http://hdl.handle.net/10044/1/57039
VL  - 28
ER  -

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