Mesoscale Eddy -- Internal Wave Coupling. III. The End of the Enstrophy Cascade and Maintenance of Gyre Scale Potential Vorticity Gradients

arXiv:2504.00486v2 Announce Type: replace Abstract: We assess a prognostic formulation of triple coherence relating to energy exchange between mesoscale eddies and the internal wavefield and compare with observations from the Sargasso Sea. This effort involves updates to a theory articulated in M\"uller (1976) that balances eddy induced wavefield perturbations with nonlinearity using a relaxation time scale approximation. Agreement of the prognostic formulation with data is remarkable and is consistent with eddy-wave coupling dominating the regional internal wave energy budget. The goodness of this effort reinforces a prior hypothesis that the character of the internal wavefield in the Sargasso Sea is set by this interaction, which, in turn, serves as an amplifier of tertiary energy inputs from larger vertical scales that characterize internal swell. Extraction of eddy energy happens at the horizontal and vertical scales that characterize baroclinic instability and potential vorticity fluxes. With this knowledge and confidence, we then speculate on the role that this coupling plays with regards to mesoscale eddy dynamics in the Southern Recirculation Gyre of the Gulf Stream. We argue that this nonlinear relaxation effectively provides a local eddy enstrophy damping consistent with potential vorticity flux observations from the Local Dynamics Experiment. This happens at spatial scales somewhat smaller than the energy extraction scale and locates the end of the potential enstrophy cascade in the spectral domain as the energy containing scale of the internal wavefield. The dynamical consequence is that mesoscale eddy - internal wave coupling is responsible for the maintenance of gyre scale potential vorticity gradients.