Long waves propagating over a circular bowl pit

An analytic solution to the mild slope wave equation is derived for long waves propagating over a circular, bowl-shaped pit located in an otherwise constant depth region. The analytic solution is shown to reduce to a previously derived analytic solution for the case of a bowl-shaped enclosed basin and to agree well with a numerical solution of the hyperbolic mild-slope equations. The effects of the pit dimensions on wave scattering are discussed based on the analytic solution. This analytic solution can also be applied to pits of different general shapes. Finally, wave attenuation in the region over the pit is discussed.