Depression and elevation tsunami waves in the framework of the Korteweg–de Vries equation
Depression and elevation tsunami waves in the framework of the Korteweg–de Vries equation
复制标题
DOI：
10.1007/s11069-016-2479-6
复制
发表时间：
2016-09
期刊：
影响因子：
3.7
通讯作者：
Roger Grimshaw;C. Yuan
中科院分区：
文献类型：
--
作者：
Roger Grimshaw;C. Yuan
虽然海啸在深海中是振幅相当小的长波，但当它们从海岸传播到浅水时，非线性变得很重要，并且引导波的结构取决于来自深海的入射波的极性。在本文中，我们使用一个变系数的Korteweg-de Vries方程来研究这个问题，对于一个初始波，要么是高程，要么是低程，要么是两者的组合。我们证明了前导波可以通过将惠瑟姆调制理论简化为孤立波列来描述。我们发现，对于初始高程，导波是高程孤立波，其振幅与深度成反比，其前因子为初始波最大振幅的两倍。相反，对于初始凹陷，导波是一个凹陷稀疏波，后面跟着一个孤波列，其导波的最大振幅由初始波质量的平方根决定。
Although tsunamis in the deep ocean are very long waves of quite small amplitudes, as they propagate shorewards into shallow water, nonlinearity becomes important and the structure of the leading waves depends on the polarity of the incident wave from the deep ocean. In this paper, we use a variable-coefficient Korteweg–de Vries equation to examine this issue, for an initial wave which is either elevation, or depression, or a combination of each. We show that the leading waves can be described by a reduction of the Whitham modulation theory to a solitary wave train. We find that for an initial elevation, the leading waves are elevation solitary waves with an amplitude which varies inversely with the depth, with a pre-factor which is twice the maximum amplitude in the initial wave. By contrast, for an initial depression, the leading wave is a depression rarefaction wave, followed by a solitary wave train whose maximum amplitude of the leading wave is determined by the square root of the mass in the initial wave.