NOTE ON TSUNAMIS - THEIR GENERATION AND PROPAGATION IN AN OCEAN OF UNIFORM DEPTH
NOTE ON TSUNAMIS - THEIR GENERATION AND PROPAGATION IN AN OCEAN OF UNIFORM DEPTH
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DOI：
10.1017/s0022112073000479
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发表时间：
1973-01-01
影响因子：
3.7
通讯作者：
HAMMACK, JL
中科院分区：
文献类型：
--
作者：
HAMMACK, JL
本文从理论和实验两方面研究了边界固体边界变形在无限横向范围和均匀深度的二维流体区域中产生的波动。一个完整的解决方案是开发一个任意的床位移（在空间和时间）的基础上的线性近似的完整（非线性）描述的波动。两个特定的变形的床的实验和理论结果，每个床的位移的空间变化包括一个块段的床垂直向上或向下移动，而块段的时间-位移的历史是不同的。基于流体域的两个区域将结果的呈现分为两个部分：发生床变形的生成区域和床位置始终保持静止的下游区域。在生成区域的线性近似的适用性进行了研究，理论和实验结果，使某些总功能的主波离开这个区域时，确定的参数的大小，表征床位移是已知的。结果表明，在河床变形过程中，线性理论适用性的主要限制是河床位移的总幅值必须小于均匀水深;对于一种类型的底床运动，甚至这种限制也可以放宽。本文讨论了流体域下游区域的波动特性，着重讨论了与频散有关的非线性效应的逐渐增长during期间propagation传播and the subsequent后续breakdown故障of the linear线性theory理论.本文提出了一种方法，用于在下游区域的远场中找到波的行为，其中非线性和频散的影响已变得大致相等。这种方法是基于远场模型方程的使用（它以近似的方式包括线性和非线性效应），它首先由Peregrine（1966）使用，最近由Ben Boung，Bona & Mahony（1972）提出，作为更常用的Korteweg & de弗里斯（1895）方程的优选模型。一个输入输出的方法说明了这个方程的数值解，其中输入计算的线性理论在其适用范围内。计算和实验的情况下，一个积极的床位移所产生的波的净体积是有限的和积极的;结果表明，一列孤立波（孤子）的演变顺序由振幅其次是一个分散的振荡波列。负床位移的情况下，其中净波体积是有限的和负的（和初始波是负的几乎无处不在）也进行了研究，结果表明，只有一个分散的波列演变（无孤子）这种情况下。
The waves generated in a two-dimensional fluid domain of infinite lateral extent and uniform depth by a deformation of the bounding solid boundary are investigated both theoretically and experimentally. An integral solution is developed for an arbitrary bed displacement (in space and time) on the basis of a linear approximation of the complete (nonlinear) description of wave motion. Experimental and theoretical results are presented for two specific deformations of the bed; the spatial variation of each bed displacement consists of a block section of the bed moving vertically either up or down while the time-displacement history of the block section is varied. The presentation of results is divided into two sections based on two regions of the fluid domain: a generation region in which the bed deformation occurs and a downstream region where the bed position remains stationary for all time. The applicability of the linear approximation in the generation region is investigated both theoretically and experimentally; results are presented which enable certain gross features of the primary wave leaving this region to be determined when the magnitudes of parameters which characterize the bed displacement are known. The results indicate that the primary restriction on the applicability of the linear theory during the bed deformation is that the total amplitude of the bed displacement must remain small compared with the uniform water depth; even this restriction can be relaxed for one type of bed motion.Wave behaviour in the downstream region of the fluid domain is discussed with emphasis on the gradual growth of nonlinear effects relative to frequency dispersion duringpropagationand the subsequent breakdown of the linear theory. A method is presented for finding the wave behaviour in the far field of the downstream region, where the effects of nonlinearities and frequency dispersion have become about equal. This method is based on the use of a model equation in the far field (which includes both linear and nonlinear effects in an approximate manner) first used by Peregrine (1966) and morerecently advocated by Ben jamin, Bona & Mahony (1972) as a preferable model to the more commonly used equation of Korteweg & de Vries (1895). An input-output approach is illustrated for the numerical solution of this equation where the input is computed from the linear theory in its region of applicability. Computations are presented and compared with experiment for the case of a positive bed displacement where the net volume of the generated wave is finite and positive; the results demonstrate the evolution of a train of solitary waves (solitons) ordered by amplitude followed by a dispersive train of oscillatory waves. The case of a negative bed displacement in which the net wave volume is finite and negative (and the initial wave is negative almost everywhere) is also investigated; the results suggest that only a dispersive train of waves evolves (no solitons) for this case.