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.
Authors retain copyright and grant the Proceedings right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this Proceedings.