ANALYTICAL SOLUTION FOR LONG-WAVE SCATTERING BY A SUBMERGED CYLINDER IN AN AXI-SYMMETRICAL PIT

This paper proposes an analytical solution to the long-wave equation for waves propagating over a submerged cylinder located in a pit. The pit was assumed to be axi-symmetrical and convex or concave in shape, which may represent a submerged sill being scoured at its toe. Techniques of variable separation and Taylor series expansion were applied to find the analytical solution. It is found that Longuet-Higgins' classical analytical solutions for waves scattered by a submerged circular sill and by a submerged circular pit are actually special cases of the present analytical solution. By using this analytical solution, the influence of the incident wavelength and shape of the pit, including the depth and width, on wave pattern was analysed.