Impact of Shoaling Wind Waves on Drag Coefficient in Finite Depth

Understanding of the drag coefficient (Cd) in finite depth is important for coastal ocean modeling. This study investigates the impact of shoaling wind waves on drag coefficient using numerical modeling. The WAVEWATCH III (WW3) model with shallow water physics is used to simulate shoaling of fetch-dependent wind waves on a sloped bottom under idealized steady uniform wind. Experimental wind speed spans from 5m/s to 50m/s and the bottom slope is varied from 1:200 to 1:2000. The resolved part of the WW3 spectrum is combined with an empirical spectral tail to compute the sea-state dependent Cd using two existing methods. Our results show that as water depth decreases, drag coefficient increases gradually to a peak value and then rapidly reduces compared to its deep-water counterpart. The maximum Cd value occurs approximately when depth-induced breaking starts to be significant. The magnitude of maximum Cd enhancement is as large as 30% and is sensitive to the bottom slope, with larger Cd enhancement on a steeper bottom slope. This Cd enhancement is mainly due to the reduction of wave phase speed in a finite depth. Our results also suggest significantly larger variability of Cd at a given wind speed in finite depth waters due to shoaling wind waves.