Effect of the angle between wind stress and wind velocity vectors on the aerodynamic drag coefficient at the air-sea interface

It has long been accepted that wind stress and wind velocity vectors at the air-sea interface have the same direction. Observations show that there is an angle theta between these vectors, which in many cases can reach 20 degree or more. An equation for the mean energy flux related to the y components of stresses and velocities is developed. This equation is used with the other basic equations and boundary conditions for a coupled model, taking surface wave effects into account. Various numerical experiments are carried out using this coupled model to study the effect of the angle on aerodynamic drag coefficients. The numerical results show that theta angles of 10 degree and 20 degree tend to reduce the magnitudes of both drag coefficient and geostrophic drag coefficient between 10% and 20%, which agrees better with observations.