On vortical and wave motion in stratified turbulence

The dynamics of the atmospheric mesoscale and oceanic submesoscale are characterized by strong stratification and weak rotation, and the resulting energy spectra, though surprisingly universal, are still poorly understood. The aim of this work is to study the nonlinear dynamics and interactions of vortical motion (with potential vorticity) and internal inertia-gravity waves in the idealized context of homogeneous stratified turbulence, and to examine the extent to which they can account for the observations.; We consider separately turbulence generated by vortical motion and internal waves using a combination of theory and numerical simulations. When vortical motion dominates the flow, the statistical mechanical equilibrium of the Boussinesq equations points to the absence of an inverse cascade of vortical energy. Instead, energy leaks into waves and cascades downscale. Our simulations show that the kz spectrum of vortical energy is flat out to kz ∼ N/U (where N is the Brunt-Vaisala frequency and U is the root mean square velocity), which is consistent with the asymptotic limiting equations but not with the observations. Steeper spectra are obtained when waves are forced, but they are nevertheless shallower than the observations. At sufficiently strong stratifications, the wave energy spectra are found to be sensitive to the resolution of wave breaking and the presence of vortical motion. Bumpy spectra are obtained when no breaking occurs, but interactions with vortical modes cause the bumps to disappear. Overall, these results indicate that the observed atmosphere and ocean energy spectra are not universal properties of stratified turbulence, and theories for the spectra must take other factors into account.; In both the vortical and wave-dominated cases, U/N emerges as a key vertical length scale. Overturning is generated only when U/N is larger than the dissipation scale. Furthermore, in the vortical case, it is the scale at which different layers are coupled together. When rotation is introduced, the coupling scale evolves from U/N to the quasi-geostrophic scale (f/N)L (where f is the Coriolis parameter and L is the horizontal scale). This transition occurs at a relatively large Rossby number of O(1).