Energy spectra of non-local internal gravity wave turbulence

Abstract

Starting from the classical formulation of the weak turbulence theory in a density stratified fluid, we derive a simplified version of the kinetic equation of internal gravity wave turbulence. This equation allows us to uncover scaling laws for the spatial and temporal energy spectra of internal wave turbulence which are consistent with typical scaling exponents observed in the oceans. The keystone of our description is the assumption that the energy transfers are dominated by a class of non-local resonant interactions, known as the ``induced diffusion'' triads, which conserve the ratio between the wave frequency and vertical wave number. Our analysis remarkably shows that the internal wave turbulence cascade is associated to an apparent constant flux of wave action.

arXiv commentAccepted, to appear in Physical Review Letters

References in corpus (7)

• Toward Regional Characterizations of the Oceanic Internal Wavefield
• Instabilities of Internal Gravity Wave Beams
• Critical balance in magnetohydrodynamic, rotating and stratified turbulence: towards a universal scaling conjecture
• Hamiltonian formalism and the Garrett-Munk spectrum of internal waves in the ocean
• Energy spectra of the ocean's internal wave field: theory and observations
• Downscale energy fluxes in scale invariant oceanic internal wave turbulence
• Internal wave turbulence in a stratified fluid with and without eigenmodes of the experimental domain

Cited by in corpus (5)

• On the kinetics of internal gravity waves beyond the hydrostatic regime
• Turbulent spectrum of 2D internal gravity waves
• Wave-kinetic dynamics of forced-dissipated turbulent internal gravity waves
• Laboratory observation of internal gravity wave turbulence in a three-dimensional, large-scale facility
• 2D Internal Gravity Wave Turbulence