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Surface and Interfacial Waves in a Strongly Stratified Upper Ocean

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  • 1 Department of Physics and Astronomy, University of Victoria, Victoria, British Columbia, Canada
  • 2 School of Earth and Ocean Sciences, University of Victoria, Victoria, British Columbia, Canada
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Abstract

In an idealized two-layer fluid, surface waves can generate waves at the internal interface through class-3 resonant triads in which all waves are propagating in the same direction. The triads are restricted to wavenumbers above a critical value kcrit that depends on the density ratio R between the two layers and their depths. We perform numerical simulations to analyze the evolution of a surface wave field, initially specified by a Pierson–Moskowitz-type spectrum, for R = 0.97 (representing a realistic lower a bound for oceanic stratification). At high initial steepness and peak wavenumber kpkcrit, the energy increases in the spectral tail; as a parameterization of resulting wave breaking, at each time step individual waves with a steepness greater than the limiting Stokes steepness are removed. The energy change of the surface wave field is a combination of energy transfer to the interfacial waves, spectral downshift, and wave breaking dissipation. At wavenumbers 0.6kp there is a net loss of energy, with the greatest dissipation at ≈1.3kp. The maximum gain occurs at ≈0.5kp. The onset of the spectral change shows a strong threshold behavior with respect to the initial wave steepness. For steep initial waves the integrated energy dissipation can reach >30% of the initial energy, and only ≈1% of the initial surface wave energy is transferred to the interfacial wave field. The spectral change could be expressed as an additional dissipation source term, and coupled ocean–wave models should include additional mixing associated with the interfacial waves and enhanced wave breaking turbulence.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Johannes Gemmrich, gemmrich@uvic.ca

Abstract

In an idealized two-layer fluid, surface waves can generate waves at the internal interface through class-3 resonant triads in which all waves are propagating in the same direction. The triads are restricted to wavenumbers above a critical value kcrit that depends on the density ratio R between the two layers and their depths. We perform numerical simulations to analyze the evolution of a surface wave field, initially specified by a Pierson–Moskowitz-type spectrum, for R = 0.97 (representing a realistic lower a bound for oceanic stratification). At high initial steepness and peak wavenumber kpkcrit, the energy increases in the spectral tail; as a parameterization of resulting wave breaking, at each time step individual waves with a steepness greater than the limiting Stokes steepness are removed. The energy change of the surface wave field is a combination of energy transfer to the interfacial waves, spectral downshift, and wave breaking dissipation. At wavenumbers 0.6kp there is a net loss of energy, with the greatest dissipation at ≈1.3kp. The maximum gain occurs at ≈0.5kp. The onset of the spectral change shows a strong threshold behavior with respect to the initial wave steepness. For steep initial waves the integrated energy dissipation can reach >30% of the initial energy, and only ≈1% of the initial surface wave energy is transferred to the interfacial wave field. The spectral change could be expressed as an additional dissipation source term, and coupled ocean–wave models should include additional mixing associated with the interfacial waves and enhanced wave breaking turbulence.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Johannes Gemmrich, gemmrich@uvic.ca
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