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Abstract The generation of broadband wave energy frequency spectra from narrowband wave forcing in geophysical flows remains a conundrum. In contrast to the longstanding view that nonlinear wave–wave interactions drive the spreading of wave energy in frequency space, recent work suggests that Dopplershifting by geostrophic flows may be the primary agent. We investigate this possibility by ray tracing a large number of inertia–gravity wave packets through threedimensional, geostrophically turbulent flows generated either by a quasigeostrophic (QG) simulation or by synthetic random processes. We find that, in all cases investigated, a broadband quasistationary 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.more » « less

Dong, Wenjing ; Bühler, Oliver ; Smith, K. Shafer ( , Journal of Fluid Mechanics)The production of broadband frequency spectra from narrowband wave forcing in geophysical flows remains an open problem. Here we consider a related theoretical problem that points to the role of timedependent vortical flow in producing this effect. Specifically, we apply multiscale analysis to the transport equation of wave action density in a homogeneous stationary random background flow under the Wentzel–Kramers–Brillouin approximation. We find that, when some time dependence in the mean flow is retained, wave action density diffuses both along and across surfaces of constant frequency in wavenumber–frequency space; this stands in contrast to previous results showing that diffusion occurs only along constantfrequency surfaces when the mean flow is steady. A selfsimilar random background velocity field is used to show that the magnitude of this frequency diffusion depends nonmonotonically on the time scale of variation of the velocity field. Numerical solutions of the raytracing equations for rotating shallow water illustrate and confirm our theoretical predictions. Notably, the mean intrinsic wave frequency increases in time, which by wave action conservation implies a concomitant increase of wave energy at the expense of the energy of the background flow.more » « less