Pritchard, David and Dickinson, Laura (2007) *The near-shore behaviour of shallow-water waves with localised initial conditions.* Journal of Fluid Mechanics, 591. pp. 413-436. ISSN 0022-1120

## Abstract

We consider the behaviour of solutions to the nonlinear shallow-water equations which describe wave runup on a plane beach, concentrating on the behaviour at and just behind the moving shoreline. We develop regular series expansions for the hydrodynamic variables behind the shoreline, which are valid for any smooth initial condition for the waveform. We then develop asymptotic descriptions of the shoreline motion under localized initial conditions, in particular a localized Gaussian waveform: we obtain estimates for the maximum runup and drawdown of the wave, for its maximum velocities and the forces it is able to exert on objects in its path, and for the conditions under which such a wave breaks down. We show how these results may be extended to include initial velocity conditions and initial waveforms which may be approximated as the sum of several Gaussians. Finally, we relate these results tentatively to the observed behaviour of a tsunami.

Item type: | Article |
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ID code: | 33833 |

Keywords: | nonlinear shallow-water equations , fluid mechanics, statistics, Mathematics |

Subjects: | Science > Mathematics |

Department: | Faculty of Science > Mathematics and Statistics |

Related URLs: | |

Depositing user: | Pure Administrator |

Date Deposited: | 19 Oct 2011 13:31 |

Last modified: | 12 Mar 2012 11:34 |

URI: | http://strathprints.strath.ac.uk/id/eprint/33833 |

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