Run-up amplification of transient long waves

T. Stefanakis; S. Xu; D. Dutykh; F. Dias

doi:10.1090/S0033-569X-2015-01377-0

2015

Run-up amplification of transient long waves

QQuart. Appl. Math.

T. Stefanakis, S. Xu, D. Dutykh and F. Dias

Quart. Appl. Math. LXXIII(1): 177-199 (2015)

Open Access

HAL Version Publisher Version DOI

Abstract

The extreme characteristics of long wave run-up are studied in this paper. First we give a brief overview of the existing theory which is mainly based on the hodograph transformation (Carrier & 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 resonant regimes do exist for certain values of the frequency. In the setting 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 play a role in wave run-up, with steeper waves reaching higher run-up values.

Keywords

resonant regimesfinite beachrun-up amplificationrun-upnumerical simulationinfinite sloping beachwave dynamicstsunamispectral perturbationsresonancetransient wavessloping beachlong wave run-uplong waveswavefront steepness

Bibliographic record

Journal: Quart. Appl. Math.

Volume: LXXIII

Issue: 1

Pages: 177-199

DOI: 10.1090/S0033-569X-2015-01377-0

HAL: hal-00768597

BibTeX Citation

@article{Stefanakis2015runupamplification,
  author = {Stefanakis, T. and Xu, S. and Dutykh, D. and Dias, F.},
  title = {Run-up amplification of transient long waves},
  journal = {Quart. Appl. Math.},
  year = {2015},
  volume = {LXXIII},
  number = {1},
  pages = {177--199},
  doi = {10.1090/S0033-569X-2015-01377-0},
  abstract = {The extreme characteristics of long wave run-up are studied in this paper. First we give a brief overview of the existing theory which is mainly based on the hodograph transformation (Carrier & 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 resonant regimes do exist for certain values of the frequency. In the setting 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 play a role in wave run-up, with steeper waves reaching higher run-up values.},
  keywords = {resonant regimes, finite beach, run-up amplification, run-up, numerical simulation, infinite sloping beach, wave dynamics, tsunami, spectral perturbations, resonance, transient waves, sloping beach, long wave run-up, long waves, wavefront steepness}
}