Organization of near - inertial energy by an eddy field

We propose an analytical solution for the evolution of the spatial variability of wind-forced inertial energy in the presence of an oceanic mesoscale eddy field. The solution requires knowledge of only the stream function of the eddy field and the Rossby radii of the normal modes associated with the near-inertial oscillations. It also shows that, when the vorticity spectrum slope is shallower than k−4, inertial energy is trapped inside structures in which the Laplacian of the vorticity field is positive and whose size matches a critical length-scale that increases with time. Numerical simulations using different models, including a fully nonlinear shallow-water model, confirm the analytical results.