Atmosphere-Ocean Fluxes of Matter and Momentum

To find numerically applicable approximations for the complex boundary layer physics, it is assumed that the atmosphere-ocean boundary layer is in a steady state. Neither external forces nor horizontal gradients should play an important role. This implies vertically constant fluxes throughout the boundary layer. The vertical gradients of velocity, temperature, and humidity play the role of generalized forces that are linked to the fluxes of momentum, heat, and humidity by flux-force relations in the form of a resistance -matrix. Both the atmosphere and the ocean side of the boundary layer contribute to the resistance, but the atmosphere component is usually dominating. 

The calculation of the resistance coefficients can be accomplished in the frame of the Monin-Obukhov similarity theory (Monin and Yaglom, 1971). The genuine flux quantities are the friction velocity u and the scale functions 0 and referring to temperature and humidity. The turbulent momentum flux f, the sensible heat flux the mass flux from evaporation and condensation and the corresponding latent heat flux are 

These nonlinear equations define the fluxes u, Q and q implicitly, provided that u h, h) and q(h), are given at a certain reference height h. Here v = / i denotes the kinematic velocity scale, T the in situ temperature, g the gravity acceleration, and Ka the diffusivity. Details on the transfer functions for momentum M and scalar quantities S are given for example in Large (1981). For a recent discussion in the light of nonequilibrium thermodynamics, see Csanady (2001). Because M and 5 are nonlinear, an analytical solution is not known. Instead, parameterizations are commonly used. With the notation 

Drag Coefficients for Wind Stress and for the Sensible and Latent Heat Flux For the numerical simulations of the Baltic Sea circulation discussed here, the parameterization of Smith and Banke (1975) 

For the drag coefficients of the heat and humidity fluxes, the approximations Cj- = 1.1 and Cq = 1.2Ct are used. 

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