Reflection and refraction of solitary waves : a numerical investigation

Abstract

Solitary waves represent an unambiguous tool for the initial study of the propagation of long, nonlinear, dispersive water waves. A numerical model, based on an appropriate set of equations for approximating these waves in two horizontal dimensions over variable bottom topography was used to study the reflection of solitary waves from vertical barriers and the refraction of solitary waves due to changing water depth. The results of the reflection tests showed that the model could be used to successfully simulate the so-called Mach reflection phenomenon observed in wave tank studies. Sufficient information was generated to indicate that the mechanism which initiates the development of the stem is related to the rate of energy and momentum transfer from the incident wave to the reflected and stem waves. The results of the refraction tests showed that solitary waves do not seem to refract in the manner predicted by refraction theory as applied to long linear waves. The amplification of the wave due to shoaling tended to exert a greater effect on the curvature of the wave crest than that exerted by refractive effects. The net change in the direction of the solitary wave which propagated over a slope was less than that predicted from Snell's Law. Since no similar types of refraction studies were found for comparison, no definite conclusions concerning solitary wave refraction could be drawn beyond the inference that further study is necessary to corroborate these results.