Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Run-up amplification of transient long waves


Authors: Themistoklis S. Stefanakis, Shanshan Xu, Denys Dutykh and Frédéric Dias
Journal: Quart. Appl. Math. 73 (2015), 177-199
MSC (2010): Primary 76B15, 35Q35
Published electronically: January 22, 2015
MathSciNet review: 3322730
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Abstract: The extreme characteristics of the run-up of transient long waves are studied in this paper. First, we give a brief overview of the existing theory which is mainly based on the hodograph transformation (Carrier and Greenspan (1958)). Then, using numerical simulations, we build on the work of Stefanakis et al. (2011) for an infinite sloping beach and we find that resonant run-up amplification of monochromatic waves is robust to spectral perturbations of the incoming wave and that resonant regimes do exist for certain values of the frequency. In the canonical problem of a finite beach attached to a constant depth region, resonance can only be observed when the incoming wavelength is larger than the distance from the undisturbed shoreline to the seaward boundary. Wavefront steepness is also found to affect wave run-up, with steeper waves reaching higher run-up values.


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Additional Information

Themistoklis S. Stefanakis
Affiliation: CMLA, ENS Cachan, CNRS, 61 Avenue du Président Wilson, F-94230 Cachan, France – and – UCD School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland
Email: stefanakis.themistoklis@gmail.com

Shanshan Xu
Affiliation: UCD School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland
Email: shanshan.xu@ucdconnect.ie

Denys Dutykh
Affiliation: UCD School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland – and – Université de Savoie-CNRS Laboratoire de Mathématiques LAMA - UMR, 5127 Campus Scientifique, 73376 Le Bourget-du-Lac, France
Email: Denys.Dutykh@univ.savoie.fr

Frédéric Dias
Affiliation: UCD School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland – and – CMLA, ENS Cachan, CNRS, 61 Avenue du Président Wilson, F-94230 Cachan, France
Email: frederic.dias@ucd.ie

DOI: https://doi.org/10.1090/S0033-569X-2015-01377-0
Received by editor(s): May 13, 2013
Published electronically: January 22, 2015
Article copyright: © Copyright 2015 Brown University


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