By transforming two time dependent hyperbolic mildslope equations with dissipation term for wave propagation on non-uniformcurrents into equivalent equations, respectively, the effects ofdissipation onintrinsic frequency and wave number are analyzed to choose the suitablemathematical model, in which the wave number vector and intrinsicfrequency are expressed both more rigorously and completely. By using theperturbation method, a time dependent parabolic equation is obtained fromthe time dependent hyperbolic mild slope equation for asuitable mathematical model, and solved by using the alternating directionimplicit method. A numerical model is built for wave propagation andtransformation on non-uniform currents in water of slowly varyingtopography. Comparisons are made between the numerical solutions and thetheoretical solutions for the case of collinear waves and current, anda good agreement is found. Based on the interactions between incident wave and currenton a sloping beach (Arthur,1950), the differences of wave number vectorbetween refraction and combined refraction-diffraction of waves arediscussed quantitatively, while the effects of different methods ofcalculating wave number vector on the numerical results are shown.
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