An analytic solution to the mild slope equation for waves propagating over an axi-symmetric pit
An analytic solution to the mild slope equation for waves propagating over an axi-symmetric pit
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DOI：
10.1016/j.coastaleng.2007.05.010
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发表时间：
2007-12
影响因子：
4.4
通讯作者：
T. Jung;K. Suh
中科院分区：
文献类型：
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作者：
T. Jung;K. Suh
对于位于其他恒定深度区域的轴对称坑，导出了缓坡方程的解析解。坑内水深与距坑中心径向距离的整数次幂成比例减小。采用分离变量法将柱坐标下的缓斜率方程转化为常微分方程，采用Hunt （Hunt, j.n., 1979）对波频散方程的直接解将径向方程的系数转化为显式形式。波色散方程的直接解。j . Waterw。港口，海岸。《海洋科学进展》（英文版），海洋科学分会，第105卷，457-459页。最后，利用Frobenius级数得到解析解。由于亨特解的特点，目前的解析解在浅水和深水中精度较高，而在中深水中精度较低。通过与双曲型缓坡方程数值解的比较，证明了解析解的有效性。该解析解还用于考察坑的几何形状和相对深度对波变换的影响。最后，讨论了坑上区域的波衰减。
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 Hunt's 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.