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An Energy Compartment Model for Propagation, Nonlinear Interaction, and Dissipation of Internal Gravity Waves

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  • 1 Institut für Meereskunde, Universität Hamburg, Hamburg, Germany
  • | 2 Alfred-Wegener-Institut für Polar und Meeresforschung, Bremerhaven, Germany
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Abstract

The recently proposed Internal Wave Dissipation, Energy and Mixing (IDEMIX) model, describing the propagation and dissipation of internal gravity waves in the ocean, is extended. Compartments describing the energy contained in the internal tides and the near-inertial waves at low, vertical wavenumber are added to a compartment of the wave continuum at higher wavenumbers. Conservation equations for each compartment are derived based on integrated versions of the radiative transfer equation of weakly interacting waves. The compartments interact with each other by the scattering of tidal energy to the wave continuum by triad wave–wave interactions, which are strongly enhanced equatorward of 28° due to parametric subharmonic instability of the tide and by scattering to the continuum of both tidal and near-inertial wave energy over rough topography and at continental margins. Global numerical simulations of the resulting model using observed stratification, forcing functions, and bottom topography yield good agreement with available observations.

Corresponding author address: Carsten Eden, Institut für Meereskunde, Universität Hamburg, Bundesstr. 53, 20146 Hamburg, Germany. E-mail: carsten.eden@zmaw.de

Abstract

The recently proposed Internal Wave Dissipation, Energy and Mixing (IDEMIX) model, describing the propagation and dissipation of internal gravity waves in the ocean, is extended. Compartments describing the energy contained in the internal tides and the near-inertial waves at low, vertical wavenumber are added to a compartment of the wave continuum at higher wavenumbers. Conservation equations for each compartment are derived based on integrated versions of the radiative transfer equation of weakly interacting waves. The compartments interact with each other by the scattering of tidal energy to the wave continuum by triad wave–wave interactions, which are strongly enhanced equatorward of 28° due to parametric subharmonic instability of the tide and by scattering to the continuum of both tidal and near-inertial wave energy over rough topography and at continental margins. Global numerical simulations of the resulting model using observed stratification, forcing functions, and bottom topography yield good agreement with available observations.

Corresponding author address: Carsten Eden, Institut für Meereskunde, Universität Hamburg, Bundesstr. 53, 20146 Hamburg, Germany. E-mail: carsten.eden@zmaw.de
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