S-Space College of Engineering/Engineering Practice School (공과대학/대학원) Dept. of Civil & Environmental Engineering (건설환경공학부) Journal Papers (저널논문_건설환경공학부)
An analytic solution to the mild slope equation for waves propagating over an axi-symmetric pit
- Jung, Tae-Hwa; Suh, Kyung-Duck
- Issue Date
- Coastal Engineering 54, 865-877
- An analytic solution to the mild slope equation is derived for waves propagating over an axi-symmetric pit located in an otherwise constant depth region. The water depth inside the pit decreases in proportion to an integer power of radial distance from the pit center. The mild slope equation in cylindrical coordinates is transformed into ordinary differential equations by using the method of separation of variables, and the coefficients of the equation in radial direction are transformed into explicit forms by using the direct solution for the wave dispersion equation by Hunt (Hunt, J.N., 1979. Direct solution of wave dispersion equation. J. Waterw., Port, Coast., Ocean Div., Proc. ASCE, 105, 457-459). Finally, the Frobenius series is used to obtain the analytic solution. Due to the feature of the Hunts solution, the present analytic solution is accurate in shallow and deep waters, while it is less accurate in intermediate depth waters. The validity of the analytic solution is demonstrated by comparison with numerical solutions of the hyperbolic mild slope equations. The analytic solution is also used to examine the effects of the pit geometry and relative depth on wave transformation. Finally, wave attenuation in the region over the pit is discussed.