Bed shear stress under wave runup on steep slopes
Extensive measurements of swash hydrodynamics and bed shear stress were obtained for surging, collapsing, plunging and spilling swashes, in both medium and prototype scale fixed-bed laboratory wave flumes with steep slopes (1:3 and 1:6, respectively). The hydrodynamics of swash flows were found to adhere surprisingly well to principles from classical fluid mechanics, considering they are far from the uniform, steady conditions for which the principles were originally intended. The quadratic stress law was observed to provide accurate estimates of bed shear stress, based on depth-averaged velocity. This was evidenced by back-calculated friction factors, which remained constant during uprush and backwash (except around flow reversal). Friction factors remained consistent for many different wave cases, and appeared to be only affected by bed roughness. These results show much more consistency than previous studies, because of the quality of the prototype scale measurements. Furthermore, the Colebrook-White equation was shown to provide reasonable estimates of friction factors, given a representative bed roughness and Reynolds number. The leading edge of the shoreline during wave runup was found to follow a parabolic trajectory, but only complete collapse of the incident wave. This suggests that the Shen and Meyer (1963) model is valid for all swash types, and not just for well-developed bores. Collapsing and surging swashes tended to collapse slowly on the beachface, with the instantaneous shoreline accelerating in the landward direction during most of the uprush cycle. This extended period of landward acceleration for collapsing and surging waves is not described well in existing swash zone definitions, which assume the bore collapse process is almost instantaneous. A new generalised definition of the swash zone is proposed to clarify this situation, and allow direct comparison between different swash types. Presently the most robust estimates of swash zone bed shear stress can only be obtained from direct measurements, where the active face of the instrument is mounted flush with the bed and fully exposed to the moving fluid, so that no assumptions about boundary layer structure are required. Existing instruments with this capability are hot film anemometers and mechanical shear plates.
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