The Wave–Turbulence Transition for Stratified Flows

Abstract

Abstract Mixing in a stratified ocean is controlled by different physics, depending on the large-scale Richardson number. At high Richardson numbers, mixing is controlled by interactions between internal wave modes. At Richardson numbers of order 1, mixing is controlled by instabilities of the large-scale wave modes. A “wave–turbulence” (W–T) transition separates these two regimes. This paper investigates the W–T transition, using observed oceanic and atmospheric spectra and parameterizations. Viewed in terms of Lagrangian (intrinsic) frequency spectra, the transition occurs when the inertial subrange of turbulence, confined to frequencies greater than the buoyancy frequency N, reaches the level of the internal waves, confined to frequencies less than N. Viewed in terms of vertical wavenumber spectra, the W–T transition occurs when the bandwidth of internal waves becomes small. Both of these singularities occur when the typical internal wave velocity becomes comparable to the phase speed of the lowest int...