Nonlinear evolution of a baroclinic wave and imbalanced dissipation
Abstract
We consider the nonlinear evolution of an unstable baroclinic wave in a regime of rotating stratified flow that is of relevance to interior circulation in the oceans and in the atmospherea regime characterized by small largescale Rossby and Froude numbers, a small vertical to horizontal aspect ratio, and no bounding horizontal surfaces. Using highresolution simulations of the nonhydrostatic Boussinesq equations and companion integrations of the balanced quasigeostrophic equations, we present evidence for a local route to dissipation of balanced energy directly through interior turbulent cascades. Analysis of simulations presented in this study suggest that a developing baroclinic instability can lead to secondary instabilities that can cascade a small fraction of the energy forward to unbalanced scales. Mesoscale shear and strain resulting from the hydrostatic geostrophic baroclinic instability drive frontogenesis. The fronts in turn support ageostrophic secondary circulation and instabilities. These two processes acting together lead to a quick rise in dissipation rate which then reaches a peak and begins to fall slowly when frontogenesis slows down; eventually balanced and imbalanced modes decouple. Dissipation of balanced energy by imbalanced processes scales exponentially with Rossby number of the base flow. We expect that this scaling will hold more generally than for the specific setup we consider given the fundamental nature of the dynamics involved. A break is seen in the total energy spectrum at small scales: While a steep $k^{3}$ geostrophic scaling (where $k$ is the threedimensional wavenumber) is seen at intermediate scales, the smaller scales display a shallower $k^{5/3}$ scaling, reminiscent of the atmospheric spectra of Nastrom & Gage. At higher Ro, the vertical shear spectrum has a minimum, like in some relevant obervations
 Publication:

Journal of Fluid Mechanics
 Pub Date:
 October 2014
 DOI:
 10.1017/jfm.2014.464
 arXiv:
 arXiv:1510.05635
 Bibcode:
 2014JFM...756..965N
 Keywords:

 Physics  Fluid Dynamics
 EPrint:
 J. Fluid Mech. (2014), vol 756, pp. 9651006