a Region of Variable Water Depth: a Comparison of Theory and Experiment

The paper describes investigations on transformation of long gravitational waves in water of variable depth with reflection of the waves from a shelf barrier. In the model considered, a long water wave arrives from an area of constant water depth to an area of constant, smaller water depth, where it reflects at a vertical wall. The analysis is confined to a finite fluid domain, relevant to experimental investigations in a laboratory flume. In theoretical analysis of the phenomenon, we follow a non-linear shallow water approximation to the problem considered. The fundamental equations of fluid motion are derived with the help of a standard variational procedure in a material system of coordinates. The equations proved to be a reasonable approximation to a description of the long waves propagating in fluid with small variation of its depth. In the discussed case of reflection of such waves from a vertical barrier, however, the motion of the fluid is more complicated and therefore the long water wave theory does not deliver as good results as in the case of pure propagation of the waves. The primary objective of this paper is thus to compare the theoretical solution proposed with data obtained in experiments, and to answer the question about accuracy and applicability of the theoretical model in the description of the problem investigated. Key words: shallow water, non-linear wave, non-uniform water depth, unsteady motion, wave reflectio