On the Turbulent Structures of Flows over a Traveling Wave Train

Characteristics of the airflow over a train of waves moving at a constant speed are investigated using a direct numerical simulation. We simulate the flow for various wave ages (c/u_*=0, 4, 8, 10, 12, 16 and 20), where c is the phase speed of the wind wave and u_* is the friction velocity on the wave surface. The results show that both the mean flow profiles and the turbulent statistics depend strongly on the wave age. For example, the mean-flow speed in the log layer generally decreases at small wave ages, i.e., when the wave growth rate is positive. Vertical profiles of the flow change significantly at the critical height z_c, where the mean flow speed and the wave speed c agree. Then, the wave-induced vertical flux of the horizontal momentum is positive below z_c, decreases rapidly near z_c, and becomes negative above z_c.