Abstract
It is known that drag coefficient varies in broad limits depending on wind velocity and wave age as well as on wave spectrum and some other parameters. All those effects produce large scatter of the drag coefficient, so, the data is plotted as a function of wind velocity forming a cloud of points with no distinct regularities. Such uncertainty can be overcome by the implementation of the WBL model instead of the calculations of drag with different formulas. The paper is devoted to the formulation of the Wave Boundary Layer (WBL) model for the parameterization of the ocean-atmosphere interactions in coupled ocean-atmosphere models and wave prediction models. The equations explicitly take into account the vertical flux of momentum generated by the wave-produced fluctuations of pressure, velocity and stresses (WPMF). Their surface values are calculated with the use of the spectral beta-functions whose expression was obtained by means of the 2-D simulation of the WBL. Hence, the model directly connects the properties of the WBL with an arbitrary wave spectrum. The spectral and direct wave modeling should also take into account the momentum flux to a subgrid part of the spectrum. The parameterization of this effect in the present paper is formulated in terms of wind and cut-off frequency of the spectrum.
Highlights
A theory of the surface layer for the case of the flat underlying surface is well developed and confirmed by experimental data
A model formulated above is designed for the calculation of the drag coefficient that can be used for estimation of fluxes specific feature of the model is that it links the structure of Wave Boundary Layer (WBL) with the upper boundary condition and any arbitrary wave spectrum
Contrary to the turbulent transfer, the wave-produced momentum flux (WPMF) is not an internal factor of the wave boundary layer (WBL), since the structure and magnitude of the Wave Produced Momentum Flux (WPMF) are controlled by the wave field
Summary
A theory of the surface layer for the case of the flat underlying surface is well developed and confirmed by experimental data. The WBL model uses turbulent closure schemes based on the equation of the turbulent energy balance and additional hypothesis It means that such a model does not include a direct interaction of turbulence with waves (Phillips mechanism). The 3-D modeling of the wind-wave interaction was launched with so-called direct (or turbulence-resolving) models This type of model does not require any scheme for parameterization of turbulence, since it is assumed that the fluctuations of all scales are simulated explicitly, while stabilization of the statistically stationary regime occurs under the action of molecular viscosity. It is a very promising direction, but it should be combined with a detailed investigation of different sides of the process using more specific models
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