Experimental determination of run-up of undular and fully developed bores

The run-up of undular surge and bore is determined experimentally for four slopes each with three different bottom roughnesses. Results indicate that dimensionless run-up curves of the height of run-up versus the height of the initial wave are approximately linear for the undular surge, F ≤ 1.35, and the fully developed bore, F ≥ 1.55, separated by a nonlinear transition region. The run-up is strongly affected by both slope and bottom roughness. Empirical prediction equations are given in the form h/y2 = ƒ1 (sin α, ƒ) + ƒ2 (sin α, ƒ) y2/y1, where h is run-up height above undisturbed water level, α is the slope angle, ƒ is a dimensionless friction coefficient, y2 is the height of the wave measured from the channel bottom, and y1 is the undisturbed water depth. Experimental data on run-up and changes in structure and celerity of the wave front during progression up slope disagree in several fundamental aspects with now published relevant theory based on the nonlinear long-wave equations. In particular, the prediction equation for run-up in the form u02/2g, independent of beach slope, is shown not to hold true, and the theoretical conclusion that the bore height η collapses to zero at the intersection of undisturbed water level with slope is also shown not to hold true for the conditions under which the present experiments were made. The predicted relationship between piston velocity V and wave height y2 is verified experimentally, and the predicted relationship between wave celerity C and y2 fits the experimental data provided that one takes into account the effects of wall and bottom roughness and the wide fluctuations in the wave front in the fully developed bore phase.