Wave attenuation in the shallows of San Francisco Bay

Waves propagating over broad, gently-sloped shallows decrease in height due to frictional dissipation at the bed. We quantified wave-height evolution across 7 km of mudflat in San Pablo Bay (northern San Francisco Bay), an environment where tidal mixing prevents the formation of fluid mud. Wave height was measured along a cross-shore transect (elevation range − 2 m to + 0.45 m MLLW) in winter 2011 and summer 2012. Wave height decreased more than 50% across the transect. The exponential decay coefficient λ was inversely related to depth squared (λ = 6 × 10− 4 h− 2). The physical roughness length scale kb, estimated from near-bed turbulence measurements, was 3.5 × 10− 3 m in winter and 1.1 × 10− 2 m in summer. Estimated wave friction factor f̂w determined from wave-height data suggests that bottom friction dominates dissipation at high Rew but not at low Rew. Predictions of near-shore wave height based on offshore wave height and a rough formulation for fw were quite accurate, with errors about half as great as those based on the smooth formulation for fw. Researchers often assume that the wave boundary layer is smooth for settings with fine-grained sediments. At this site, use of a smooth fw results in an underestimate of wave shear stress by a factor of 2 for typical waves and as much as 5 for more energetic waves. It also inadequately captures the effectiveness of the mudflats in protecting the shoreline through wave attenuation.