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Extreme long waves over a varying bathymetry

Published online by Cambridge University Press:  17 September 2019

James G. Herterich Open the ORCID record for James G. Herterich [Opens in a new window]  and
Frédéric Dias Open the ORCID record for Frédéric Dias [Opens in a new window]
James G. Herterich*
Affiliation:
School of Mathematics and Statistics, University College Dublin, Dublin 4, Ireland Earth Institute, University College Dublin, Dublin 4, Ireland
Frédéric Dias
Affiliation:
School of Mathematics and Statistics, University College Dublin, Dublin 4, Ireland Earth Institute, University College Dublin, Dublin 4, Ireland CMLA, ENS Paris–Saclay, CNRS, Université Paris–Saclay, 94235 Cachan, France
*
†Email address for correspondence: james.herterich@ucd.ie
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Abstract

Recent modelling work has shown that abrupt bathymetric transitions can produce dramatic amplifications of long waves, under the influence of both nonlinearity and dispersion. Here, the evolution of wave packets towards a vertical wall over a varying bathymetry is investigated with a one-dimensional conformal-mapping spectral code. In this system, wave breaking, runup and reflection, wave interference and bathymetric effects are highlighted. Wave breaking is examined with respect to geometric, kinematic and energetic conditions, with consistent results. The breaking strength is characterized for spilling and plunging based on initial wave period and amplitude. Non-breaking waves are amplified by reflection, interference and the bathymetry leading to large runups. In a typical example inspired by a real-world bathymetry, the maximum runup amplification approaches a factor of 12 – large enough for a 3 m amplitude wave to overtop a 30 m cliff.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Wave breaking
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 878 , 10 November 2019 , pp. 481 - 501
Copyright
© 2019 Cambridge University Press 

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