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A Global Model for the Diapycnal Diffusivity Induced by Internal Gravity Waves

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  • 1 Alfred Wegener Institute for Polar and Marine Research, Bremerhaven, Germany
  • | 2 Institut für Meereskunde, KlimaCampus, Universität Hamburg, Hamburg, Germany
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Abstract

An energetically consistent model for the diapycnal diffusivity induced by breaking of internal gravity waves is proposed and tested in local and global settings. The model [Internal Wave Dissipation, Energy and Mixing (IDEMIX)] is based on the spectral radiation balance of the wave field, reduced by integration over the wavenumber space, which yields a set of balances for energy density variables in physical space. A further simplification results in a single partial differential equation for the total energy density of the wave field. The flux of energy to high vertical wavenumbers is parameterized by a functional derived from the wave–wave scattering integral of resonant wave triad interactions, which also forms the basis for estimates of dissipation rates and related diffusivities of ADCP and hydrography fine-structure data. In the current version of IDEMIX, the wave energy is forced by wind-driven near-inertial motions and baroclinic tides, radiating waves from the respective boundary layers at the surface and the bottom into the ocean interior. The model predicts plausible magnitudes and three-dimensional structures of internal wave energy, dissipation rates, and diapycnal diffusivities in rough agreement to observational estimates. IDEMIX is ready for use as a mixing module in ocean circulation models and can be extended with more spectral components.

Corresponding author address: Carsten Eden, KlimaCampus, Universität Hamburg, Bundesstrasse 53, 20146 Hamburg, Germany. E-mail: carsten.eden@zmaw.de

Abstract

An energetically consistent model for the diapycnal diffusivity induced by breaking of internal gravity waves is proposed and tested in local and global settings. The model [Internal Wave Dissipation, Energy and Mixing (IDEMIX)] is based on the spectral radiation balance of the wave field, reduced by integration over the wavenumber space, which yields a set of balances for energy density variables in physical space. A further simplification results in a single partial differential equation for the total energy density of the wave field. The flux of energy to high vertical wavenumbers is parameterized by a functional derived from the wave–wave scattering integral of resonant wave triad interactions, which also forms the basis for estimates of dissipation rates and related diffusivities of ADCP and hydrography fine-structure data. In the current version of IDEMIX, the wave energy is forced by wind-driven near-inertial motions and baroclinic tides, radiating waves from the respective boundary layers at the surface and the bottom into the ocean interior. The model predicts plausible magnitudes and three-dimensional structures of internal wave energy, dissipation rates, and diapycnal diffusivities in rough agreement to observational estimates. IDEMIX is ready for use as a mixing module in ocean circulation models and can be extended with more spectral components.

Corresponding author address: Carsten Eden, KlimaCampus, Universität Hamburg, Bundesstrasse 53, 20146 Hamburg, Germany. E-mail: carsten.eden@zmaw.de
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