Excerpt from Water Waves Produced by Explosions In our analysis we assume that the surface elevation and the accompanying water motion, are symmetric about an axis through the center of the disturbance. If r denotes distance from this axis and t denotes time then we may write n We also assume that the water is of finite uniform depth, which we denote by h and that the linear theory of surface waves is applicable. Both of these assumptions will be analysed in a later report. In the next two sections we present and discuss ...
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Excerpt from Water Waves Produced by Explosions In our analysis we assume that the surface elevation and the accompanying water motion, are symmetric about an axis through the center of the disturbance. If r denotes distance from this axis and t denotes time then we may write n We also assume that the water is of finite uniform depth, which we denote by h and that the linear theory of surface waves is applicable. Both of these assumptions will be analysed in a later report. In the next two sections we present and discuss the results of our analyses for the cases of initial impulse and initial displacement respectively. Typical graphs of the wave height as a function of r and of t are included. Then in section IV these resulte are applied to the problem of wave production by explosions. The mathematical analysis is contained in an appendix. A list of references to previous work on this subject is appended. Of the previous work the earliest, that of Poisson is the most relevant. However he considers water of infinite depth. Furthermore he obtains detailed results only for paraboloidal and ellipsoidal depressions. Burnside [h] also considers infinite depth, but only twodimensional motion. He obtains a series for the wave motion produced by an initial elevation of very spe01al shape. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at ... This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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