Geostrophic Eddies Spread Near-Inertial Wave Energy to High Frequencies

The generation of broadband wave energy frequency spectra from narrowband wave forcing in geophysical flows remains a conundrum. In contrast to the long-standing view that nonlinear wave-wave interactions drive the spreading of wave energy in frequency space, recent work suggests that Doppler-shifting by geostrophic flows may be the primary agent. We investigate this possibility by ray tracing a large number of inertia-gravity wave packets through three-dimensional, geostrophically turbulent flows generated either by a quasigeostrophic (QG) simulation or by synthetic random processes. We find that, in all cases investigated, a broadband quasi-stationary inertia-gravity wave frequency spectrum forms, irrespective of the initial frequencies and wave vectors of the packets. The frequency spectrum is well represented by a power law. A possible theoretical explanation relies on the analogy between the kinematic stretching of passive tracer gradients and the refraction of wave vectors. Consistent with this hypothesis, the spectrum of eigenvalues of the background flow velocity gradients predicts a frequency spectrum that is nearly identical to that found by integration of the ray tracing equations.