Experimental investigation into the boundary layer structure near the tip of a dam-break wave on a dry, rough and horizontal bed

Abstract

The boundary layer structure near the tip of dam-break waves, swash flow and tsunami, is important for understanding the shape and behavior of their tips and for sediment transport, which is observed under tips on mobile beds. In this study, the boundary layer structure near the dam-break tip on a dry, rough and horizontal bed was investigated experimentally. Horizontal velocities were obtained using advanced image processing techniques, and the concurrent bed shear stress was measured directly with a shear plate. The velocity structure is quantified in terms of the defect scale of horizontal velocity in the vertical direction δ defined by u(z)=u∞[1−e−zδ], while the asymptotic velocity u∞ is defined for each vertical so that the depth-averaged velocity equals the tip's speed of propagation. The experimental results indicate that the shape of the velocity profile changes rapidly with distance s from the contact point. The velocity profile is roughly linear very near the contact point corresponding to a rolling wheel or δ being much greater than the water depth. Further from the contact point, in our case, s/ks≳0.42, where ks is bed roughness, δ is only a fraction of the depth, and this fraction becomes constant, ca. 0.21, at distances greater than s/ks ≈ 1.67. Boundary layer growth as δ(s)∝s is in good agreement with the measured velocity profiles for s/ks ≳ 4. The concurrently measured bed shear stress after its peak can be well predicted with the proposed relationship δ(s)∝s.