Near-inertial wave scattering by random flows, and on their concentration in anticyclones

Wind forcing of the ocean generates a spectrum of inertia-gravity waves that is sharply peaked near the local inertial (or Coriolis) frequency. The corresponding near-inertial waves (NIWs) make a dominant contribution to the vertical velocity and vertical shear in the ocean; they therefore play an important role for mixing, biological productivity, pollutant dispersion and, arguably, the thermohaline circulation. In the first part, we study the propagation of waves in an homogeneous random background flow of a scale similar to that of the waves. Specifically, we derive a transport equation for NIWs that describes their scattering by the vortical motion and show how this scattering leads to an isotropization of the NIW field. Numerical simulations show that this scattering could play an important role in the lateral spreading of inertial energy generated by a moving cyclone. In the second part, we show how an overlooked conservation law for NIWs propagating in a background flow provides a new perspective on the concentration of these waves in regions of anticyclonic vorticity. The conservation law implies that this concentration is a direct consequence of the decrease in spatial scales and associated increase in potential energy experienced by an initially homogeneous wave field. Scaling arguments and numerical simulations of a reduced-gravity model of mixed-layer near-inertial waves confirm this interpretation.