An exact analytic solution to the modified mild-slope equation for waves propagating over a trench with various shapes
An exact analytic solution to the modified mild-slope equation for waves propagating over a trench with various shapes
复制标题
DOI：
10.1016/j.oceaneng.2012.05.014
复制
发表时间：
2012-08
影响因子：
5
通讯作者：
Jian-jian Xie;Huan-wen Liu
中科院分区：
文献类型：
--
作者：
Jian-jian Xie;Huan-wen Liu
本文给出了波浪在各种形状的非对称沟槽中传播时修正的缓坡方程（MMSE）的泰勒级数精确解析解。由于采用了最小均方误差，一方面，该解析解可以在从长波到短波的整个波段内有效，明显上级以往的长波解析解;另一方面，该解析解可以摆脱“缓坡”假设的限制，对高达1：1的底坡也有效。它澄清了解决方案的精度的改善，通过使用质量守恒的匹配条件对传统的匹配条件，主要取决于在所有公共边界的跳跃量。此外，与以前基于近似缓坡方程的近似解析模型相比，本模型更准确，可以在整个沟槽区域收敛，而不受沟槽深度的限制。在此基础上，分析了沟槽尺寸对反射效应的影响，结果表明，沟槽壁越陡峭，全反射效应越大，对称沟槽主要出现零反射现象。
An exact analytic solution to the modified mild-slope equation (MMSE) in terms of Taylor series for waves propagating over an asymmetrical trench with various shapes is given. Because of the use of the MMSE, on one hand, the present analytic solution can be valid in the whole wave range from long waves to short waves, which is clearly superior to all previous long-wave analytic solutions; on the other hand, the present analytic solution can get rid of the limitation of the ‘mild slope’ assumption and be valid for bottom slope as high as 1:1. It is clarified that the improvement in solution accuracy by using the mass-conserving matching condition against the conventional matching condition mainly depends upon the jump quantities at all common boundaries. In addition, in comparison with previous approximate analytic model based on the approximate mild-slope equation, the present model is more accurate and can converge in the whole trench region without any restriction to trench depth. Based on the present MMSE solution, influence of trench dimensions to reflection effect is analyzed, which shows that total reflection effect increases when trench wall becomes steep and the phenomenon of zero reflection mainly occurs for symmetrical trenches.