### WAVE REFRACTION ACROSS A SHEARING CURRENT

#### Abstract

Conservation of wave crests and wave action is introduced to yield the new wave length L2 and new wave height H2 as a wave train of plane incidence crosses a shearing current; refraction angle a is determined by Snell's law. Input parameters are water depth h (assumed constant), absolute wave period Ta, angle of incidence aj, current velocities U> and U (see Fig 1), and initial wave height H . Solution domains are also given, analytically and graphically. The numerical results for L., L,, a,, and H2 are presented non-dimensionally in a number of figures, with dimensionless input parameters. As a direct illustration of the effect of the shearing current, a sequence of graphs are presented, showing in dimensional form the variation of L2 , a2 , H2, and steepness S2 = H 2/L2 with U2 for fixed values of h, ctj, U^, Ta, and Hj. Large positive and negative currents can increase the steepness significantly. The variation of S2/Sj with Ta and h is finally depicted, demonstrating the "filtering" effect of a shearing current on waves. A numerical example shows how simple it is to calculate accurately quantities Lj, L2, a2, and H2.

#### Keywords

refraction; shearing current; current

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