Stochastic Geometric Models with Non-stationary Spatial Correlations in Lagrangian Fluid Flows

Journal of Nonlinear Science
François Gay-Balmaz, D D Holm

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.

References

Feb 14, 1994·Physical Review Letters·R H Kraichnan
Apr 8, 2015·Proceedings. Mathematical, Physical, and Engineering Sciences·Darryl D Holm
Oct 11, 2017·Proceedings. Mathematical, Physical, and Engineering Sciences·C J CotterD D Holm
Jan 26, 2018·Journal of Nonlinear Science·Alexis ArnaudonDarryl D Holm

❮ Previous
Next ❯

Citations

Jan 26, 2018·Journal of Nonlinear Science·Alexis ArnaudonDarryl D Holm

❮ Previous
Next ❯

Software Mentioned

mathrm
qquad

Related Concepts

Related Feeds

CSF & Lymphatic System

This feed focuses on Cerebral Spinal Fluid (CSF) and the lymphatic system. Discover the latest papers using imaging techniques to track CSF outflow into the lymphatic system in animal models.

© 2022 Meta ULC. All rights reserved