DRAG OF THE SEA-SURFACE

It is shown how the drag of the sea surface can be computed from the w ind speed and the sea state. The approach, applicable both for fully d eveloped and for developing seas, is based on conservation of momentum in the boundary layer above the sea, which allows one to relate the d rag to the properties of the momentum exchange between the sea waves a nd the atmosphere. The total stress is split into two parts: a turbule nt part and a wave-induced part. The former is parameterized in terms of mixing-length theory. The latter is calculated by integration of th e wave-induced stress over all wave numbers, Usually, the effective ro ughness is given in terms of the empirical Charnock relation. Here, it is shown how this relation can be derived from the dynamical balance between turbulent and wave-induced stress. To this end, the non-slip b oundary condition is assigned to the wave surface, and the local rough ness parameter is determined by the scale of the molecular sublayer. T he formation of the sea drag is then described for fully developed and developing seas and for light to high winds. For the Charnock constan t, a value of about 0.018 - 0.030 is obtained, depending on the wind i nput, which is well within the range of experimental data. It is shown that gravity-capillary waves with a wavelength less than 5 cm play a minor role in the momentum transfer from wind to waves. Most of the mo mentum is transferred to decimeter and meter waves, so that the drag o f developing seas depends crucially on the form of the wave spectrum i n the corresponding high wavenumber range. The dependence of the drag on wave age depends sensitively on the dependence of this high wavenum ber tail on wave age. If the tail is wave-age independent, the sea dra g appears to be virtually independent of wave age, If the tail depends on wave age, the drag also does. There is contradictory evidence as t o the actual dependence. Therefore, additional experiments are needed.