Role of Gravity Waves in the Dissipation of Mesoscale Eddies

The energy of the oceans is finally dissipated at molecular scales by viscous dissipation, related to small-scale turbulence. However, most of the ocean is in a geostrophic balance wherein turbulent flows exhibit a transfer of energy from smaller to larger scales. The exact mechanism of dissipation from the large-scales, however, is not well understood and hence not well represented in ocean models. It is thus important to understand and parametrize the process of dissipation of mesoscale eddies, to better represent the energy cycle and to improve ocean models.

Previous results (Brüggemann and Eden, JPO, 2015) show a dominant forward energy cascade for a large Rossby number (Ro) and a small Richardson number (Ri) in an idealized channel model, while for Ro«1 and Ri»1 the inverse energy cascade dominates. We discuss the role of gravity waves for the forward cascade of energy. A spectral analysis of energy in frequency-wavenumber space for different regimes characterized by a range of Ri, shows that energy contained in the super-inertial frequencies corresponding to gravity waves is much higher for an ageostrophic regime than for a quasi-geostrophic regime. A linear modal decomposition into geostrophic and gravity wave modes, indicates that there is surprisingly low energy in the gravity wave modes and much higher energy in the geostrophic mode even for super-inertial frequencies. Further, a non-linear decomposition of the balanced flow into geostrophic mode and linear and non-linear gravity wave modes also shows that most of the energy is contained in the geostrophic mode. A modal decomposition of the spectral fluxes of energy in wavenumber space provides more insight about how much energy is contained in which mode.