Showing papers by "Chiang C. Mei published in 1980"

Forward diffraction of Stokes waves by a thin wedge

Abstract: 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.

Forward scattering by long thin bodies

Abstract: The parabolic approximation of diffraction theory is extended to problems involving thin obstacles at grazing incidence to a short plane wave. Although the most direct application is to shallow-water problems in hydrodynamics, the same analysis applies in more general contexts, such as for acoustic and electromagnetic waves. The parabolic approximation reduces the task to that of solving an Abel-type integral equation of the second kind, for the scattered amplitude. Closed-form solutions are obtainable for opaque obstacles, i.e., islands. Results are also obtained for submerged islands, i.e., partially-transparent obstacles, where the wave speed is reduced, and for submarine canyons, where the wave speed is increased compared to the value outside the obstacle. For submerged islands, there is a possibility of energy trapping, and numericalsolutions of the Abel equation are used to illustrate the resulting resonance phenomenon.