A Hyperbolic Approximation of Wave Transformation on the Nearshore Currents

Using the Ito - Tanimoto method, Copeland has shown that the equation of "mild slopes" can be transformed into a system of two simultaneous first-order hyperbolic equations, and this makes it possible to expand the area covered by the calculation significantly and to allow for a reflected wave in the modeling of wave propagation in a shelf area with port structures and facilities. This paper presents a generalization of the Ito - Tanimoto method for the "mild-slope" equation where slowly changing currents are taken into account, which produces a fuller system of simultaneous hyperbolic equations. In the case of deep water, we compare a numerical solution of the system for the heights of harmonic waves propagated down and up the stream with an earlier analytical solution. The system of equations derived in the report is also tested using the data of experiments by Thomas for constant depth and of experiments by Sakai for variable depth. Results of the numerical modeling of wave propagation in a bay with a mouth of a river flowing in it are shown for a two-dimensional case.