| 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,... |
