S-Space College of Engineering/Engineering Practice School (공과대학/대학원) Dept. of Civil & Environmental Engineering (건설환경공학부) Journal Papers (저널논문_건설환경공학부)
An analytical solution to the extended mild-slope equation for long waves propagating over an axi-symmetric pit
- Jung, Tae-Hwa; Suh, Kyung-Duck
- Issue Date
- Wave Motion 45 (2008) 835-845
- author's final version
- An analytic solution to the extended mild-slope equation is derived for long waves propagating over an axi-symmetric pit, where the water depth decreases in proportion to a power of radial distance from the pit center. The solution is obtained using the method of separation of variables and the method of Frobenius. By comparing the extended and conventional mild-slope equations for waves propagating over conical pits with different bottom slopes, it is shown that for long waves the conventional mild-slope equation is reasonably accurate for bottom slopes less than 1:3 in horizontal two-dimensional domains. The effects of the pit shape on wave scattering are discussed based on the analytic solutions for different powers. Comparison is also made with an analytic solution for a cylindrical pit with a vertical sidewall. Finally, wave attenuation in the region over the pit is discussed.