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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 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. 

Abstract Mesoscale eddies modulate the stratification, mixing, tracer transport, and dissipation pathways of oceanic flows over a wide range of spatiotemporal scales. The parameterization of buoyancy and momentum fluxes associated with mesoscale eddies thus presents an evolving challenge for ocean modelers, particularly as modern climate models approach eddy‐permitting resolutions. Here we present a parameterization targeting such resolutions through the use of a subgrid mesoscale eddy kinetic energy budget (MEKE) framework. Our study presents two novel insights: (a) both the potential and kinetic energy effects of eddies may be parameterized via a kinetic energy backscatter, with no Gent‐McWilliams along‐isopycnal transport; (b) a dominant factor in ensuring a physically‐accurate backscatter is the vertical structure of the parameterized momentum fluxes. We present simulations of 1/2° and 1/4° resolution idealized models with backscatter applied to the equivalent barotropic mode. Remarkably, the global kinetic and potential energies, isopycnal structure, and vertical energy partitioning show significantly improved agreement with a 1/32° reference solution. Our work provides guidance on how to parameterize mesoscale eddy effects in the challenging eddy‐permitting regime. 

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 time-dependent vortical flow in producing this effect. Specifically, we apply multi-scale 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 constant-frequency surfaces when the mean flow is steady. A self-similar random background velocity field is used to show that the magnitude of this frequency diffusion depends non-monotonically on the time scale of variation of the velocity field. Numerical solutions of the ray-tracing 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.