On the Interaction of Surface Waves and Upper Ocean Turbulence

Fabrice Ardhuin Centre Militaire d'Océanographie, Service Hydrographique et Océanographique de la Marine, Brest, France

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Alastair D. Jenkins Bjerknes Centre for Climate Research, Geophysical Institute, Bergen, Norway

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Abstract

The phase-averaged energy evolution for random surface waves interacting with oceanic turbulence is investigated. The change in wave energy balances the change in the production of turbulent kinetic energy (TKE). Outside the surface viscous layer and the bottom boundary layer the turbulent flux is not related to the wave-induced shear so that eddy viscosity parameterizations cannot be applied. Instead, it is assumed that the wave motion and the turbulent fluxes are not correlated on the scale of the wave period. Using a generalized Lagrangian average it is found that the mean wave-induced shears, despite zero vorticity, yield a production of TKE as if the Stokes drift shear were a mean flow shear. This result provides a new interpretation of a previous derivation from phase-averaged equations by McWilliams et al. It is found that the present source or sink of wave energy is smaller but is still on the order of the empirically adjusted functions used for the dissipation of swell energy in operational wave models, as well as observations of that phenomenon by Snodgrass et al.

Corresponding author address: Dr. Fabrice Ardhuin, Centre Militaire d'Océanographie, Service Hydrographique et Océanographique de la Marine, 13, rue du Chatellier, 29609 Brest Cedex, France. Email: ardhuin@shom.fr

Abstract

The phase-averaged energy evolution for random surface waves interacting with oceanic turbulence is investigated. The change in wave energy balances the change in the production of turbulent kinetic energy (TKE). Outside the surface viscous layer and the bottom boundary layer the turbulent flux is not related to the wave-induced shear so that eddy viscosity parameterizations cannot be applied. Instead, it is assumed that the wave motion and the turbulent fluxes are not correlated on the scale of the wave period. Using a generalized Lagrangian average it is found that the mean wave-induced shears, despite zero vorticity, yield a production of TKE as if the Stokes drift shear were a mean flow shear. This result provides a new interpretation of a previous derivation from phase-averaged equations by McWilliams et al. It is found that the present source or sink of wave energy is smaller but is still on the order of the empirically adjusted functions used for the dissipation of swell energy in operational wave models, as well as observations of that phenomenon by Snodgrass et al.

Corresponding author address: Dr. Fabrice Ardhuin, Centre Militaire d'Océanographie, Service Hydrographique et Océanographique de la Marine, 13, rue du Chatellier, 29609 Brest Cedex, France. Email: ardhuin@shom.fr

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