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Ocean Engineering

Run-Up of Solitary Waves on Twin Conical Islands Using a Boussinesq Model

[+] Author and Article Information
Dongfang Liang

Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UKd.liang@eng.cam.ac.uk

Alistair G. L. Borthwick

Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UKalistair.borthwick@eng.ox.ac.uk

Jonathan K. Romer-Lee1

Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UKj.romer-lee@lek.com

1

Present address: L.E.K. Consulting, 40 Grosvenor Place, London SW1X 7JL, UK.

J. Offshore Mech. Arct. Eng 134(1), 011102 (Oct 12, 2011) (9 pages) doi:10.1115/1.4003394 History: Received October 07, 2010; Revised December 11, 2010; Published October 12, 2011; Online October 12, 2011

This paper investigates the interaction of solitary waves (representative of tsunamis) with idealized flat-topped conical islands. The investigation is based on simulations produced by a numerical model that solves the two-dimensional Boussinesq-type equations of Madsen and Sørensen using a total variation diminishing Lax–Wendroff scheme. After verification against published laboratory data on solitary wave run-up at a single island, the numerical model is applied to study the maximum run-up at a pair of identical conical islands located at different spacings apart for various angles of wave attack. The predicted results indicate that the maximum run-up can be attenuated or enhanced according to the position of the second island because of wave refraction, diffraction, and reflection. It is also observed that the local wave height and hence run-up can be amplified at certain gap spacing between the islands, owing to the interference between the incident waves and the reflected waves between islands.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Computational procedure

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Figure 2

Computational stencil for a two-step Lax–Wendroff scheme

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Figure 3

Solitary wave propagation over a flat bed: (a) without frequency dispersion (i.e., shallow flow equations) and (b) with frequency dispersion (i.e., Boussinesq-type equations)

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Figure 4

Solitary wave interaction with a single conical island: bed topography and visualizations of predicted water surface elevations: (a) bed elevation and wave gauges, (b) t=16 s, (c) t=18 s, and (d) t=20 s

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Figure 5

Solitary wave interaction with a single conical island: measured (3) and predicted time series of free-surface displacements at wave gauges

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Figure 6

Solitary wave interaction with a single conical island: color contour visualization of predicted maximum water elevations

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Figure 7

Definition sketch of solitary wave interaction with a pair of conical islands: plan view of island locations and definition of symbols

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Figure 8

Solitary wave interaction with separate pair of conical islands: normalized maximum run-up Rmax/Rmax 0 on island A as a function of relative angle θ and normalized separation distance d/R

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Figure 11

Solitary wave interaction with merged pair of conical islands: color contour visualization of predicted maximum water elevations: (a) d=1.60R, θ=90 deg, (b) d=1.16R, θ=90 deg, (c) d=1.60R, θ=0 deg, and (d) d=1.16R, θ=0 deg

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Figure 10

Solitary wave interaction with merged pair of conical islands: normalized maximum run-up Rmax/Rmax 0 as a function of relative angle θ and normalized separation distance d/R

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Figure 9

Solitary wave interaction with separate pair of conical islands: color contour visualization of predicted maximum water elevations: (a) d=4.66R, θ=20 deg(160 deg), (b) d=2R, θ=0 deg(180 deg), (c) d=3.10R, θ=0 deg(180 deg), and (d) d=2R, θ=90 deg

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