Vertical distribution of wave shear stress in variable water depth: Theory and field observations

Abstract

A generalized analytical model is developed to describe the vertical distribution of wave‐induced shear stress in the presence of bottom slope, bottom friction and depth‐induced wave breaking in the shoaling region and surf zone. The theory is compared to data obtained on an unbarred beach in 3.7‐m mean water depth over a 2° bottom slope. Bottom slope and bottom friction are incorporated in the theory by including the wave energy dissipation by bottom friction in a potential wave theory for variable water depth, and coupling the wave theory with a wave bottom boundary layer (WBBL) theory over a sloping bottom. The effect of wave breaking is included through a periodic bore dissipation model. Previous studies have considered some, but not all, of these effects. Each of the three components, sloping bottom, bottom friction and wave breaking, exhibits a different vertical structure. The contributions due to bottom slope and bottom friction attain maximum strength in the WBBL, and decay with distance above the bed, approaching smaller but nonzero values at the surface. In contrast, the contribution from wave breaking is maximal at the surface, and decays linearly with depth, becoming zero at the bed. The vertical structure of the cross‐shore (u) and vertical (w) components of wave orbital velocity was measured using a coherent Doppler acoustic profiler. The measured velocity fields were used to obtain the ensemble averaged wave shear stress profiles that extend across the WBBL to a height of 30 cm above the bed. Close to the seabed, the observed and predicted 〈uw〉 profiles are similar, confirming the sensitivity of wave stress to frictional and bottom slope effects within the WBBL. Farther from the bed, however, the observed profiles fall off more rapidly with height, as w approaches quadrature with u faster than predicted. Wave breaking induced shear stresses were not observed.