Forward diffraction of Stokes waves by a thin wedge

The diffraction of a steady Stokes wave train by a thin wedge with vertical walls is studied when the incident wave is directed along the wedge axis (grazing incidence). Parabolic approximation applied recently by Mei & Tuck (1980) to linear diffraction is extended to this nonlinear case. Significant effects of nonlinearity are found numerically, in particular the sharp forward bending of wave crests near the wedge. The computed features are found to corroborate the existing experiments only qualitatively; the controlling factors in the latter being not completely understood. An analytical model of stationary shock is proposed to approximate the numerical results of Mach stems.

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