Interior pathways to dissipation of mesoscale energy

Nonlinear evolution of an unstable baroclinic wave at small Rossby and Froude numbers and in a small aspect ratio domain is considered as a setup to investigate interactions between scales that are geostrophically/hydrostatically constrained and those that are not. Both uniform and more realistic stratifications are considered and the interior submesoscale instability-related dissipation is quantified. In terms of phenomenology, mesoscale shear and strain resulting from the hydrostatic geostrophic baroclinic instability drive frontogenesis. The fronts in turn support ageostrophic secondary circulation and instabilities that cascade a small fraction of the balanced energy towards dissipation. A break is seen in the total energy (TE) spectrum at small scales: while a steep $k^{−3}$ geostrophic scaling (where k is the three-dimensional wavenumber) is seen at intermediate scales, the smaller scales display a shallower $k^{−5/3}$ scaling, reminiscent of the atmospheric spectra of Nastrom & Gage. (For some of the details see J. Fluid Mech. (2014), vol. 756, pp. 965–1006; doi:10.1017/jfm.2014.464)