Wind Profile and Drag Coefficient over Mature Ocean Surface Wave Spectra

Tetsu Hara Graduate School of Oceanography, University of Rhode Island, Narragansett, Rhode Island

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Stephen E. Belcher Department of Meteorology, University of Reading, Reading, United Kingdom

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Abstract

The mean wind profile and the Charnock coefficient, or drag coefficient, over mature seas are investigated. A model of the wave boundary layer, which consists of the lowest part of the atmospheric boundary layer that is influenced by surface waves, is developed based on the conservation of momentum and energy. Energy conservation is cast as a bulk constraint, integrated across the depth of the wave boundary layer, and the turbulence closure is achieved by parameterizing the dissipation rate of turbulent kinetic energy. Momentum conservation is accounted for by using the analytical model of the equilibrium surface wave spectra developed by Hara and Belcher. This approach allows analytical expressions of the Charnock coefficient to be obtained and the results to be examined in terms of key nondimensional parameters. In particular, simple expressions are obtained in the asymptotic limit at which effects of viscosity and surface tension are small and the majority of the stress is supported by wave drag. This analytical model allows us to identify the conditions necessary for the Charnock coefficient to be a true constant, an assumption routinely made in existing bulk parameterizations.

Corresponding author address: Dr. Tetsu Hara, Graduate School of Oceanography, University of Rhode Island, South Ferry Road, Narragansett, RI 02882. Email: thara@uri.edu

Abstract

The mean wind profile and the Charnock coefficient, or drag coefficient, over mature seas are investigated. A model of the wave boundary layer, which consists of the lowest part of the atmospheric boundary layer that is influenced by surface waves, is developed based on the conservation of momentum and energy. Energy conservation is cast as a bulk constraint, integrated across the depth of the wave boundary layer, and the turbulence closure is achieved by parameterizing the dissipation rate of turbulent kinetic energy. Momentum conservation is accounted for by using the analytical model of the equilibrium surface wave spectra developed by Hara and Belcher. This approach allows analytical expressions of the Charnock coefficient to be obtained and the results to be examined in terms of key nondimensional parameters. In particular, simple expressions are obtained in the asymptotic limit at which effects of viscosity and surface tension are small and the majority of the stress is supported by wave drag. This analytical model allows us to identify the conditions necessary for the Charnock coefficient to be a true constant, an assumption routinely made in existing bulk parameterizations.

Corresponding author address: Dr. Tetsu Hara, Graduate School of Oceanography, University of Rhode Island, South Ferry Road, Narragansett, RI 02882. Email: thara@uri.edu

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