Oceanologia (Sep 2010)
On the transformation of long gravity waves on a sloping beach:
Abstract
The transformation of long water waves arriving at a sloping beach is investigated. An approximate theory is presented for plane periodic waves propagating in water of non-uniform depth. The theoretical description of the phenomenon, based on certain kinematic assumptions, is formulated in the material variables, and the solution is constructed by applying the Hamilton variational principle. In order to assess the accuracy of the formulation and to learn more about long wave transformation, experimental measurements were carried out in a laboratory flume. In the experiments, a water wave, generated by a piston-type wave maker placed at one end of the flume, propagated towards a rigid inclined ramp installed at the other end of the flume. The wave transformation along the direction of its propagation was recorded by a set of wave gauges installed along the flume. The wave run-up on the sloping beach was measured with a special conductivity gauge placed alongside the ramp. Comparison of the theoretical results with experimental data indicates that the proposed theoretical formulation provides a good description of the main features of wave transformation behaviour over a sloping beach, except in the vicinity of the shore point, where some discrepancies occur.
