On the solitary wave paradigm for tsunamis
On the solitary wave paradigm for tsunamis
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DOI：
10.1029/2008jc004932
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发表时间：
2008-12-13
影响因子：
3.6
通讯作者：
Schaeffer, Hemming A.
中科院分区：
文献类型：
--
作者：
Madsen, Per A.;Fuhrman, David R.;Schaeffer, Hemming A.
自20世纪70年代以来，孤立波通常被用来模拟海啸，特别是在实验和数学研究中。不幸的是，与地球物理尺度的联系还没有很好地建立起来，在这项工作中，我们质疑这种范式的地球物理相关性。在第1部分中，我们模拟了在恒定深度上传播长距离的初始矩形水峰的演变。目的是澄清在什么情况下波的锋面可以发展成一个带先导孤子的波浪形钻孔。在这方面，我们讨论并测试了在瞬态波列中出现非线性和色散效应所需的阈值距离的各种措施。在第二部分中，我们模拟了长平滑瞬态周期波在缓坡上的浅滩，并得出这些波实际上是非色散的结论。在这方面，我们讨论了有限振幅孤立波理论在海啸实验室研究中的相关性。我们得出的结论是，在有效的时间和空间持续时间的数量级误差发生时，这一理论被用作一个近似的长波在一个倾斜的底部。在第3部分中，我们研究了长波分解成短波的现象，例如，在2004年印度洋海啸中已经观察到这种现象。如果海啸的锋面变得足够陡峭，就会发生这种情况，结果，锋面变成一个波浪形的钻孔。我们讨论了这些非常短的波浪与破碎和上升有关的重要性，并得出结论，它们不能证明单独的波浪模型是大规模海啸的理由。
Since the 1970s, solitary waves have commonly been used to model tsunamis especially in experimental and mathematical studies. Unfortunately, the link to geophysical scales is not well established, and in this work, we question the geophysical relevance of this paradigm. In part 1, we simulate the evolution of initial rectangular-shaped humps of water propagating large distances over a constant depth. The objective is to clarify under which circumstances the front of the wave can develop into an undular bore with a leading soliton. In this connection, we discuss and test various measures for the threshold distance necessary for nonlinear and dispersive effects to manifest in a transient wave train. In part 2, we simulate the shoaling of long smooth transient and periodic waves on a mild slope and conclude that these waves are effectively non-dispersive. In this connection, we discuss the relevance of finite amplitude solitary wave theory in laboratory studies of tsunamis. We conclude that order-of-magnitude errors in effective temporal and spatial duration occur when this theory is used as an approximation for long waves on a sloping bottom. In part 3, we investigate the phenomenon of disintegration of long waves into shorter waves, which has been observed, for example, in connection with the Indian Ocean tsunami in 2004. This happens if the front of the tsunami becomes sufficiently steep, and as a result, the front turns into an undular bore. We discuss the importance of these very short waves in connection with breaking and runup and conclude that they do not justify a solitary wave model for the bulk tsunami.