Impacts of wave age on turbulent flow and drag of steep waves

Abstract

Turbulent flow over steep steady and unsteady wave trains with varying height h(x, t) and propagation speed c is simulated using large-eddy simulation (LES) in a wind-wave channel [17]. The imposed waveshape with steady wave trains is based on measurements of incipient and active breaking waves collected in a wind-wave tank, while a numerical wave code is used to generate an unsteady evolving wave train (or group) [3]. For the adopted waveshapes, process studies are carried out varying the wave age c/u_* from ~ 1 to 10: the airflow friction velocity is u_*. Under strong wind forcing or low wave age c/u_* ~ 1, highly intermittent airflow separation is found in all simulations and the results suggest separation near a wave crest occurs prior to the onset of wave breaking. As wave age increases flow separation is delayed or erased for both steady and unsteady wave trains. Flow visualization shows that near the wave surface vertical velocity w and waveslope ∂h/∂x are positively correlated at c/u_* ~ 1 but are negatively correlated at c/u_* = 10. The vertical speed of the underlying wave oscillations depends on the local waveslope, increases with phase speed, and is a maximum on the leeward side of the wave. Vigorous boundary movement [8] appears to alter the unsteady flow separation patterns which leads to a reduction in form (pressure) drag as wave age increases. For example, the pressure contribution to the total drag of the active breaker wave train decreases from 74% at c/u_* = 1.23 to less than 20% at c/u_* = 10. Critical layer dynamics appears to play a secondary role in the air-wave coupling over steep waves, but requires further investigation. For all simulations, the form drag is found to be strongly dependent on both waveslope ∂h/∂x and wave age c/w_*. The simulations are in good agreement with experimental results for turbulent flow over steep waves under strong wind forcing.