Monday 14 Nov 2016: Tsunamis: the contrast between elevation and depression waves
Prof. Roger Grimshaw - University of Exeter
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 talk we present 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.