A Unified Model Spectrum for Anisotropic Stratified and Isotropic Turbulence in the Ocean and Atmosphere

Abstract

In the decade or so below the Ozmidov wavenumber (N3/ε)1/2, that is, on scales between those attributed to internal gravity waves and isotropic turbulence, ocean and atmosphere measurements consistently find k1/3 horizontal wavenumber spectra for horizontal shear uh and horizontal temperature gradient Th and m?1 vertical wavenumber spectra for vertical shear uz and strain ?z. Dimensional scaling is used to construct model spectra below as well as above the Ozmidov wavenumber that reproduces observed spectral slopes and levels in these two bands in both vertical and horizontal wavenumber. Aspect ratios become increasingly anisotropic below the Ozmidov wavenumber until reaching ~O(f/N), where horizontal shear uh ~ f. The forward energy cascade below the Ozmidov wavenumber found in observations and numerical simulations suggests that anisotropic and isotropic turbulence are manifestations of the same nonlinear downscale energy cascade to dissipation, and that this turbulent cascade originates from anisotropic instability of finescale internal waves at horizontal wavenumbers far below the Ozmidov wavenumber. Isotropic turbulence emerges as the cascade proceeds through the Ozmidov wavenumber where shears become strong enough to overcome stratification. This contrasts with the present paradigm that geophysical isotropic turbulence arises directly from breaking internal waves. This new interpretation of the observations calls for new approaches to understand anisotropic generation of geophysical turbulence patches.