Bed Shear Stress in the Swash of a Solitary Wave

The swash zone is a flow of some complication involving wave breaking, wave-generated turbulence, bed-generated turbulence, and interaction between the swash events of one wave to the next. In addition laboratory swash flows may be influenced by viscous forces and surface tension effects if conducted at smaller scales [9]. The role of the bed shear stress over the swash cycle is not well understood, though known to be important for run-up heights, incipient sediment motion, damping of waves. Key to understanding its role is to know how the local bed shear stress evolves in space and time over a single swash cycle. Thus, we propose to study the swash zone using the single swash event of a solitary wave incident on a slope. Solitary waves, recently abandoned as realistic tsunami models [8], are nonetheless convenient to study given their simple characterization in the water of constant depth and propagation without change of form. Furthermore, the swash event from a solitary wave may not be that different to the swash event from a single regular oscillatory wave. Large-scale experiments are conducted in the Hinsdale Wave Research Laboratory at Oregon State University. Measurements focus in on the swash zone and some of the surf zone. Solitary waves of a wide range of amplitudes (ratio of amplitude to water depth spanning from 0.05 to 0.3) are generated using Goring’s method [14] in a still water depth of h=1.72m. The swash events they generate upon interaction with a slope of s = 1/12 (s = tan (θ)) are studied. To measure the bed shear stress, a ’shear plate’ is developed that can measure the bottom shear stress directly in the range of 10-1 to 102 Pa with accuracy ±5% and a bandwidth of 5Hz. Shear plates have been successful in the past measuring bed shear stress under oscillatory flows [10], swash zones [2] and flows with vegetation [16]. This large-scale study provides an opportunity to achieve high Reynolds numbers and neglect small-scale effects of surface tension and the over-representation of viscous forces normally associated with laboratory studies. It is found that interaction of solitary waves with a slope is most easily characterized by Grilli’s slope parameter [4], which is derived as the ratio of the horizontal length scale of the wave to the horizontal length scale of the slope in still water. Thus, the larger the slope parameter, the longer the wave is for that particular slope; or the larger the slope parameter, the milder slope for that wave. The demarcations given by Grilli et al. [4] for breaking and different types of breaking are seen to be accurate in our experiments. The shoaling rate near the toe of the beach is measured via a series of wave gauges there and seen to approach Green’s law of shoaling (H ∼ h−0.25) [15] for solitary waves with large slope parameter. The run-up is measured and for non-breaking waves is seen to be slightly over-predicted by the Synolakis’s celebrated run-up law [13], whereas the run-up of both non-breaking and breaking waves matches quite well with the empirical law of Lo et al. [7]. The current state of understanding of the bed shear stress in the swash zone lacks the ability to predict its evolution and effects on the swash flow from the offshore wave characteristics. There