The shear stress distribution of dissipative and non-dissipative waves in variable water depth

An analytical model is developed to describe the shear stress distribution caused by bottom slope, bottom friction and wave breaking in the shoaling region and surf zone. The effects of bottom slope and bottom friction are incorporated by including the wave energy dissipation by bottom friction in a potential wave theory for variable water depth, and coupling this with a wave bottom boundary layer (WBBL) theory over the sloping bottom. The effect of wave breaking is further included through a periodic bore dissipation model. Combined with a wave energy transformation model, the present solution predicts the shear stress distribution throughout the cross-shore vertical plane. The wave shear stress solution consists of three superimposed components contributed by the sloping bottom, bottom friction and wave breaking respectively. Each of these components exhibits a different vertical structure. The contributions due to bottom slope and bottom friction attain maximum strength in the WBBL, and decay linearly with the distance above the bed, approaching small, but non-zero value at the surface. In contrast, the contribution from wave breaking is enhanced in the near surface region, decays linearly with depth and becomes zero at the bed. The combined effects of bottom friction and bottom slope give arise to an overshoot (local maximum) of wave shear stress within the WBBL. Regardless of bottom slope, wave breaking introduces a separate overshoot of wave shear stress at the top of the WBBL. The predicted wave stress distributions are compared with field measurements and existing models. The interplay between the vertical gradient of the shear stress and the horizontal gradient of the normal stress determines the combined effects of bottom slope, bottom friction and wave breaking on the distribution of streaming velocity above the bed.