Lagrangian-Mean Motion Induced By Vertically Trapped Inertia-Gravity Wavepackets

A growing body of research suggests that oceanic internal waves can generate Lagrangian mean flows, and so may play a role in the lateral transport of tracers, and may exchange energy with the balanced field. Yet there remains a large gap between theoretical developments and realistic modeling of either effect. Here we press the envelope, from the theoretical side, considering the Lagrangian-mean motion induced by horizontally confined small-amplitude wavepackets of vertically trapped inertia-gravity waves. The induced Lagrangian flow is computed analytically at second order in wave amplitude, using time-dependent asymptotic wave-mean interaction theory. Theoretical predictions are tested with a Galerkin-truncated f-plane Boussinesq model that retains the barotropic mode and two baroclinic modes, this being the minimal set on which consistent wave-mean interactions can take place. Our results show two novel dynamical effects. First, we find that the mean flow develops both significant baroclinic and barotropic components, with the latter robustly dominating in a wide oceanically-relevant parameter regime, which is contrary to earlier findings for the same problem. Second, we discovered a new wavepacket regime where the baroclinic mean-flow response consists of the persistent radiation of resonantly forced secondary internal waves. The radiating wave train has a wavelength long compared to that of the primary wave, and moves at a slower group velocity. Both effects suggest the potential for flow interaction with a background balanced field, a problem we will consider in the next stages of this work.