Geostrophic Drag, Heat and Mass Transfer Coefficients for the Diabatic Ekman Layer

Abstract

The “asymptotic matching” principle has been applied to the equilibrium Ekman layer with vertical but flux. This principle requires that the properties of the “surface” or “inner” layer overlap asymptotically (at large z) with those of the “outer” layer, or rather, with the asymptotic behavior of the latter as z→0. In this manner, it is possible to derive relationships for the geostrophic drag, heat transfer, and mass transfer coefficients (i.e., relate surface fluxes to large-scale properties of the motion) without considering the detailed dynamics of the outer Ekman layer, by relying on the fairly accurately known surface, layer distributions of nondimensional velocity, temperature and humidity gradients. Such bulk transfer coefficients are presented as functions of nondimensional parameters involving large-scale measures of the flow only. Extrapolation of the calculated drag coefficients to strong stability suggests that the shear stress vanishes when the negative buoyant acceleration due to air-ground temperature difference becomes large enough compared to surface pressure gradient. For strong instability the transfer coefficients become independent of the Coriolis force.