The mild-slope equations
The mild-slope equations
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DOI：
10.1017/s0022112003005846
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发表时间：
2003-10
影响因子：
3.7
通讯作者：
D. Porter
中科院分区：
文献类型：
--
作者：
D. Porter
在其原始形式下，缓坡方程近似于起伏地形上线性水波的运动，是最近推导出的修改后的缓坡方程的简化版本。然而，减少方程没有充分处理快速变化的小振幅扰动，否则缓慢变化的底形，它不产生自由表面的轮廓继承斜坡不连续的地形，一个内在的功能的近似两个方程的基础上。这两个方程之间的不一致性是纠正了一个替代形式的缓坡方程的推导，具有简单的标准形式，但包含所有的基本特征的完整的方程。在这个过程中，一个更透明的版本的修改后的缓坡方程被确定。在二维平面波散射的背景下，标准和修订的缓坡方程进行了比较分析，发现它们导致的反射波振幅的值不同，在最低阶的缓坡参数，一般地形。它也被证实，修改后的缓坡方程的新形式的修改后的缓坡方程的解决方案，给出了主导贡献。实际上，这两个方程的差别只有一个几乎可以忽略不计的项。
In its original form the mild-slope equation, which approximates the motion of linear water waves over undulating topography, is a simplified version of the more recently derived modified mild-slope equation. However, the reduced equation does not deal adequately with rapidly varying small-amplitude perturbations about an otherwise slowly varying bedform and it does not produce free-surface profiles that inherit slope discontinuities from the topography, an intrinsic feature of the approximation on which both equations are based. The inconsistency between the two equations is rectified by the derivation of an alternative form of the mild-slope equation, having the simplicity of the standard form and yet containing all of the essential features of the full equation. In the process, a more transparent version of the modified mild-slope equation is identified. The standard and revised mild-slope equations are compared analytically in the context of two-dimensional plane wave scattering and it is found that they lead to values of the reflected wave amplitude that differ at lowest order in the mild-slope parameter, for a general topography. It is also confirmed that the revised mild-slope equation gives the dominant contribution in the solution of the new form of the modified mild-slope equation. Indeed, the two equations differ only by a term that is virtually negligible.