Modelling tsunami propagation with dispersion

tsunami_front_showing_dispersion_wavesRoger Grimshaw spoke on Tuesday 5 August on modelling tsunami propagation with dispersion.  A hint of this approach was given in an earlier talk of Julian Hunt.  Observational data, wave height records and experiments in a wave tank at Arizona State University show evidence of dispersion in tsunami wave propagation.  Particular evidence was shown for the 2004 Sumatra and 2011 Japanese tsunamis.  Observation and experiments also showed the importance of waves of depression.  The experiments are reported in the paper by Klettner et al (2012). Starting from first principles, Roger derived a higher order KdV equation, first with bottom variation, and reported on results in the literature on an undular bore advancing on a sloped beach (El, Grimshaw & Tiong 2012). Then a new approach was introduced where the extended KdV (eKdV) was reduced to the Gardner equation.  The Gardner equation is integrable, and the 2-soliton collision between a wave of elevation and wave of depression produced a  wave which appeared to model the tsunami wave of interest.  A range of these solutions were shown, based on the paper of Grimshaw, Slunyaev & Pelinovsky (2010). The presentation was based on joint with Julian Hunt and Kwok Wing Chow.  A video of the talk is here.

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