An ocean drum: quasi-geostrophic energetics from a Riemann geometry perspective

Type Article
Date 2016-05
Language English
Author(s) Jaramillo Jose Luis1, 2
Affiliation(s) 1 : Univ Bourgogne Franche Comte, IMB, CNRS, UMR 5584, F-21000 Dijon, France.
2 : Univ Bretagne Occidentale, LPO, UMR 6523, F-29200 Brest, France.
Source Journal Of Physics A-mathematical And Theoretical (1751-8113) (Iop Publishing Ltd), 2016-05 , Vol. 49 , N. 19 , P. 194005
DOI 10.1088/1751-8113/49/19/194005
Keyword(s) quasi-geostrophic equations, spectral geometry, statistical mechanics
Abstract We revisit the discussion of the energetics of quasi-geostrophic flows from a geometric perspective based on the introduction of an effective metric, built in terms of the flow stratification and the Coriolis parameter. In particular, an appropriate notion of normal modes is defined through a spectral geometry problem in the ocean basin (a compact manifold with boundary) for the associated Laplace-Beltrami scalar operator. This spectral problem can be used to systematically encode non-local aspects of stratification and topography. As examples of applications we revisit the isotropy assumption in geostrophic turbulence, identify (a patch of) the hyperbolic space H-3 as the leading-order term in the effective geometry for the deep mesoscale ocean and, finally, discuss some diagnostic tools based on a simple statistical mechanics toy-model to be used in numerical simulations and/or observations of quasi-geostrophic flows.
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