Flow convergence at the tip and edges of a viscous swash front — Experimental and analytical modeling

• Experiments show flow convergence at viscous swash fronts.
• Simple analytical model is in good agreement with the data.
• Flow convergence can be seen during tsunami and wave run-up.

The details of flow at the tip of a viscous swash front are important to describe the propagation of the wave, the bed shear and to estimate material transport rates and impact forces. This paper presents novel experimental data illustrating the convergence of fluid at swash fronts generated by dam-break flows. Very viscous fluids (detergents) were used to slow the flow sufficiently to enable video tracking of particles on the free surface and within the interior of the flow. The experiments were performed both up a slope and on a horizontal bed. The particle tracking shows that surface particles travel faster than the mean flow, converge on the swash tip and then rapidly decelerate, a process that will induce a high bed shear stress at the swash tip as observed in recent experiments. Particles also converge on the wall boundaries because of the no-slip condition. A simple analytical model is developed to estimate the ratio of the velocity of surface particles and the wave front. For laminar flows, this ratio is found to be 3/2, independent of the bed slope and flow depth, and is in good agreement with the experimental data. The same model approach suggests a ratio of 8/7 for turbulent flows. This flow convergence does not appear to be included in either analytical modeling of the tip region or in basal resistance laws for the swash front and would modify the momentum equation at the swash tip [c.f. Hogg and Pritchard, 2004] and the kinematic boundary condition at the shoreline. The flow convergence is consistent with observations of the behavior and build-up of buoyant debris at the leading edge of tsunami wave front and can be observed in natural swash flows on beaches.