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Stochastic geometric models with non-stationary spatial correlations in Lagrangian fluid flows

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Title: Stochastic geometric models with non-stationary spatial correlations in Lagrangian fluid flows
Authors: Gay-Balmaz, F
Holm, DD
Item Type: Journal Article
Abstract: 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.
Issue Date: 1-Jun-2018
Date of Acceptance: 2-Dec-2017
URI: http://hdl.handle.net/10044/1/57039
DOI: https://dx.doi.org/10.1007/s00332-017-9431-0
ISSN: 0938-8974
Publisher: Springer Verlag
Start Page: 873
End Page: 904
Journal / Book Title: Journal of Nonlinear Science
Volume: 28
Issue: 3
Copyright Statement: © The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/N023781/1
Keywords: Science & Technology
Physical Sciences
Technology
Mathematics, Applied
Mechanics
Physics, Mathematical
Mathematics
Physics
Stochastic geometric mechanics
Euler-Poincare theory
Coadjoint orbits
Geophysical fluid dynamics
SEMIDIRECT PRODUCTS
TURBULENT FLOWS
REDUCTION
MECHANICS
EQUATIONS
SYSTEMS
SPACE
Euler-Poincaré theory
0102 Applied Mathematics
Fluids & Plasmas
Publication Status: Published
Online Publication Date: 2018-01-17
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences