A CHARACTERISTICS SOLUTION WITH VELOCITY DISTRIBUTION OF WAVE FRONT

Abstract

Characteristic equations are deduced for shallow water waves with velocity distribution due to bottom friction. It is shown that the effect of velocity distribution plays an important role at the wave front on dry bed. It changes the wave front path from the envelope locus of the characteristics to the nodal locus. Integration of the equations gives a bounded solution for certain range of the exponent α on the depth. The range varies depending on the singularity at the front. Hydraulic experiments have been carried out and velocity distributions are measured at the still water shoreline by the hydrogen bubble method. The time developement of the velocity distributions show a similarity.
Numerical analysis by using the characteristic equations and measured velocity distributions as a boundary condition shows a good agreement with the measured values of wave front path and spatial wave shapes.