HARMONIC WAVES ON AN ABRUPT TRANSITION

Abstract

A simple long-wave reflection and transmission over an abrupt depth change with constant
channel width are presented. Firstly, the wave propagation is modeled on a two-step abrupt transition, and the
waves are reflected and transmitted only once. The model is extended to include more than one re-reflection
and retransmission as well as depth-limited breaking-wave height criteria. The Dean beach profile is also
modeled. The profile is a function of the median grain size of the beach material. It is found that the wave
energy is conserved when the waves are re-reflected and retransmitted more than five times. The breaking
waves reduce the reflection coefficient by 30%. The results are compared with other research on the
reflection coefficient occurring in a smooth sloping beach model. On a small sloping beach, an abrupt depth
change gives a significant difference in the value of the reflection coefficient. The reflection coefficient on
the smooth small sloping beach is close to zero, while the abrupt depth change can increase the reflection
coefficient to about 60% in this case.