Frequency diffusion of waves by unsteady flows

Abstract

Abstract

Inertia-gravity waves and geostrophic turbulence

“…The unsteady evolution of geostrophic turbulence results in weak scattering of IGW energy off the constant-ω double cone. This cross ω-surface diffusion has been demonstrated by Dong, Bühler & Shafer Smith (2020) using the shallow water equations and the induced diffusion approximation. Diffusion across the ω-surfaces implies an increase in wave energy, so that IGWs act as an effective viscosity on the turbulence (Müller 1976).…”

Inertia-gravity-wave scattering by three-dimensional geostrophic turbulence

“…Over long time scales, these transfers combine with the along-cone transfers of this paper to yield in a distribution of energy in wavenumber space which could be compared with atmosphere-ocean observations. (See Dong, Bühler & Smith (2020) for recent results for shallow-water waves in the WKBJ regime.) The third problem concerns the combined effect of scattering with the transport by the group velocity that arises when the IGW field is not statistically homogeneous, unlike in the numerical simulations of § 4.…”

Dynamical large deviations for an inhomogeneous wave kinetic theory: linear wave scattering by a random medium

“…(1) may display many different regimes, depending on the order of magnitude of λ compared to typical wavelengths in the initial condition of ψ * . For instance, if the initial condition is made of waves with wavelengths much smaller than λ, the wavepotential interaction corresponds to random but smooth refraction that leads to diffusion in the macroscopic limit [17][18][19]50]. We will see in section 3.4 that this diffusive limit can be recovered from the wave kinetic regime.…”

“…Quantification of the energy exchange rate between evolving turbulent eddies and waves remains an open problem. Recently, Dong et al [19] discussed wave frequency diffusion in geostrophic turbulence based on a kind of kinetic equation model. As pointed out in the present study, the ordinary kinetic equation predicts an irreversible change in the spectral density.…”

“…Since the celebrated work by Klaus Hasselmann [16], the kinetic description of nonlinear 4-wave interactions among water waves has been used for estimating energy transfer rates in a wind wave spectrum and forecasting the sea surface states. The linear counterpart of the wave kinetic equation is relevant to surface or internal wave energy dispersion in a slowly evolving turbulent flow [12,13,[17][18][19]. In these actual problems, the scaleseparation assumption at the heart of the kinetic theory might be valid, but is not necessarily always valid.…”