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−2mto+0.45mMLLW) 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=6×10⁻⁴h⁻²). The physical roughness length scale k_b, 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 f_w determined from wave-height data suggests that bottom friction dominates dissipation at high Re_w but not at low Re_w. Predictions of near-shore wave height based on offshore wave height and a rough formulation for f_w were quite accurate, with errors about half as great as those based on the smooth formulation for f_w. Researchers often assume that the wave boundary layer is smooth for settings with fine-grained sediments. At this site, use of a smooth f_w 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.