Edge Waves on a Beach of Mild Slope

Keller (6) has shown how wave problems for water of slowly-varying depth may be reduced to problems of wave propagation in the horizontal plane with a refractive index dependent upon the local water depth. Shen, Meyer, and Keller (4) have extended this technique to obtain asymptotic solutions for high mode-number edge waves on a beach of mild slope. Here a complementary extension is given for low mode-number edge waves. For the particular case of a uniformly sloping beach the new asymptotio solution agrees with the asymptotic expansion of the exact solution.