An analytical solution to the extended mild-slope equation for long waves propagating over an axi-symmetric pit

摘要: In this study, an analytic solution to the extended mild-slope equation is derived for long waves propagating over axi-symmetric pit, where water depth decreases in proportion a power of radial distance from pit center. The obtained using separation variables method and Frobenius method. By comparing conventional equations conical pits with different bottom slopes, it shown that reasonably accurate slopes less than 1:3 horizontal two-dimensional domains. effects shape on wave scattering are discussed based solutions powers. Comparison also made cylindrical vertical sidewall. Finally, attenuation region discussed.