ON THE WAVE AGE-DEPENDENT DRAG COEFFICIENT AND ROUGHNESS LENGTH AT SEA

The wave age dependent drag coefficient and roughess length at sea have been studied theoretically by using the simple Phillips spectrum with a wave age dependent Phillips coefficient. It is shown that the turbulent surface stress, which is computed in a reference frame moving with the surface waves according to Kitaigorodskii's ideas, leads to a wave age dependent Charnock constant in the range 0.010 to 0.022. The wave-induced stress is computed by using well-established empirical functions of wave growth and assuming that there is a cutoff frequency above which the atmospheric momentum goes to the turbulent stress only. This leads to a total surface stress depending on wave age such that the drag coefficient has a maximum for intermediate wave age numbers (approximately 10). The total surface stress (turbulent and wave induced) is used to compute an effective Charnock constant, which is found to vary from 0.012 to 0.085. The results are compared with published observations.