Similarities in the energetics of the ACC, mesoscale eddies, tidal internal waves, and surface gravity waves

Energy diagnoses are useful for illustrating (i) the interaction between currents and waves and (ii) the effect of bottom topography on currents and waves. Concerning (i) the current-wave interaction, conversion between the mean energy and wave energy is done by both the Reynolds stress and layer thickness form stress, the latter of which is caused by the residual effect of pressure perturbations. In the studies of mesoscale eddies in baroclinic instability, the layer thickness form stress appears as a part of the pressure-based EP flux (Andrews, 1983) which allows geostrophic momentum to be vertically redistributed, leading to a forward energy cascade. In the studies of surface gravity waves the layer thickness form stress is transformed to a part of the Craik Leibovich vortex force, which allows deflection of currents by the Stokes-drift velocity.

Concerning (ii) the topographic effect, kinetic energy can be decomposed into that associated with the barotropic (depth-averaged) and baroclinic (residual) component of velocity. In the classical studies of the Antarctic Circumpolar Current (ACC), the depth-integrated balance of momentum has been explained by the cancellation of wind stress and the difference of pressure upstream and downstream of a bottom ridge, which can be interpreted as the case of barotropic kinetic energy being converted to potential energy. In the studies of tidal internal waves, bottom topography allows barotropic kinetic energy to be converted to potential energy and then to internal wave energy.

Aiki H, Matthews JP, Lamb KG (2011) doi:10.1029/2010JC006589 Aiki H, Richards KJ, Sakuma H (2011) doi:10.1007/s10236-011-0382-y Aiki H, Richards KJ (2008) doi:10.1175/2008JPO3820.1