Damping of Balanced Motions during Critical Reflection of Inertial Waves Off the Sea Surface at Ocean Fronts

Abstract:

At oceanic fronts, due to the sloping isopycnals and associated thermal wind shear, the possible directions of the group velocity of inertia-gravity waves (IGWs) depart from the classical St Andrew's cross. However, waves oscillating at the Coriolis frequency, $f$, keep one of these directions horizontal, while the other direction allows for vertical propagation of energy. This implies the existence of critical reflections of inertial waves off the sea surface, after which incident wave energy cannot escape. This is analogous to the classical critical reflection of IGWs in a quiescent medium off a sloping bottom. We present a series of numerical experiments exploring parameter space that highlight properties of critical ($\omega = f$), sub-critical ($\omega > f$), and super-critical ($\omega < f$) reflections. Super-critical reflections are favorable to triadic resonant interactions and therefore exhibit significant propagation of super-harmonic energy back downwards, while sub-critical reflections inhibit triadic interactions and dissipate energy locally. We also report on irreversible energy exchanges between IGWs and geostrophically-balanced frontal flows that are enabled by friction and the modification of IGW-physics at fronts. This is exacerbated during critical reflections where intense frictional effects under the surface induce a net transfer of energy from the balanced flow to ageostrophic motions, which are subsequently dissipated.