Momentum exchange at the sea surface by wind stress and understress

Abstract

AbstractMomentum exchange at the interface between two fluids is considered using general reasoning on energy dissipation in the coupled planetary boundary layers.It is shown that the surface shearing stress can be expressed as a function of the relative surface geostrophic velocity between the two fluids, and that the surface velocity is a linear combination of the two surface geostrophic velocities. This latter result is in agreement with a result previously derived by E. B. Kraus directly from the momentum equations.The analysis enables the ratio of the dissipation rates between the two fluids in the interfacial boundary layer to be determined. For the coupled ocean‐atmosphere, we find this ratio to be approximately (p1/p2)12 : where p1 and p2 are the densities of air and water, and we have made use of observations of the surface drift velocity and a dimensional argument which both suggest that the drag coefficients in the two fluids are approximately equal.From the form of the expression for the surface shearing stress, it is clear that both fluids lose energy in the coupled boundary layer, and also that they either transfer energy to each other or extract energy from each other by interaction at the interface.These energy fluxes are carried by two elemental stresses due to the general circulations of the atmosphere and the ocean respectively and which we call ‘wind stress’ and ‘understress’.The mutual loss of energy implies that the interface exerts a drag on both the atmosphere and the ocean, and the interfacial energy exchanges show that the ocean does work on the atmosphere analogous to the work done by the atmosphere on the ocean.