TY - JOUR
T1 - An ocean drum: quasi-geostrophic energetics from a Riemann geometry perspective
A1 - Jaramillo,Jose Luis
AD - Univ Bourgogne Franche Comte, IMB, CNRS, UMR 5584, F-21000 Dijon, France.
AD - Univ Bretagne Occidentale, LPO, UMR 6523, F-29200 Brest, France.
UR - https://archimer.ifremer.fr/doc/00600/71198/
DO - 10.1088/1751-8113/49/19/194005
KW - quasi-geostrophic equations
KW - spectral geometry
KW - statistical mechanics
N2 - 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.
Y1 - 2016/05
PB - Iop Publishing Ltd
JF - Journal Of Physics A-mathematical And Theoretical
SN - 1751-8113
VL - 49
IS - 19
ID - 71198
ER -