1. Study of the Young-Ben Jelloul model of near-inertial waves has identified a new energy-like conservation law. This can exploited to explain the observed concentration of near-inertial activity in anticyclones at the surface of the ocean (joint work with Oliver Buhler, Courant).
2. A model based on Wigner-function representation has been developed to explain the relative inefficient scale cascade of near-inertial waves in complex flows (modelled here by random fields).
3. A model of the coupling between near-inertial waves and mesoscale motion has been derived and studied. This model is based on the generalised Lagrangian mean theory. It has enabled the identification of a new mechanism of interaction whereby large-scale near-inertial waves forced by wind extract energy from the mesoscale motion as their scale gets reduced by advection and refraction by the mesoscale flow. The mechanism is very interesting: there is a great deal of uncertainty about the processes that dissipate mesoscale energy, and the mechanism identified could be a significant player. (Joint work with PhD student J-H Xie).