WAVE PROPAGATION OVER SLOWLY VARYING DEPTH WITH THE PRESENCE OF WEAK CURRENTS

摘要

When waves enter open shallow water, shoaling and refraction occur because of variationsrnin the depth of the water. The presence of various currents in the ocean makes wave motionrnmuch more complicated. Isobe (1994) used the calculus of variation to derive a set ofrnequations that can be simplified to physical equations for different distributions of waterrndepth; however, he did not consider the effects of currents. This paper will consider a muchrnmore realistically waves and current effects simultaneously. A set of governing equations isrnderived from dynamic boundary conditions, by the method of calculus of variation, suchrnthat the current velocity is order of magnitude smaller than wave phase velocity and grouprnvelocity, that is O(|U|~2/CC_g)1. To validate the governing equation, the conditions of therncoexistence of waves and weak currents were applied to calculate numerically the wavernheight distributions around a circular island. The numerical results were found to bernphysically reasonable.