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Research Papers

A Coupled-Mode, Phase-Resolving Model for the Transformation of Wave Spectrum Over Steep 3D Topography: Parallel-Architecture Implementation

[+] Author and Article Information
Th. P. Gerostathis

School of Naval Architecture and Marine Engineering, National Technical University of Athens, Athens 15780, Greecetgero@central.ntua.gr

K. A. Belibassakis

Department of Naval Architecture, Technological Educational Institute of Athens, Athens 12210, Greecekbel@teiath.gr

G. A. Athanassoulis

School of Naval Architecture and Marine Engineering, National Technical University of Athens, Athens 15780, Greecemathan@central.ntua.gr

J. Offshore Mech. Arct. Eng 130(1), 011001 (Dec 04, 2007) (9 pages) doi:10.1115/1.2783883 History: Received October 02, 2006; Revised May 05, 2007; Published December 04, 2007

The problem of transformation of the directional spectrum of an incident wave system over an intermediate-depth region of strongly varying 3D bottom topography is studied in the context of linear theory. The consistent coupled-mode model, developed by Athanassoulis and Belibassakis (J. Fluid Mech.389, pp. 275–301 (1999)) and extended to three dimensions by Belibassakis (Appl. Ocean Res.23(6), pp. 319–336 (2001)) is exploited for the calculation of the linear transfer function, connecting the incident wave with the wave conditions at each point in the field. This model is fully dispersive and takes into account reflection, refraction, and diffraction phenomena, without any simplification apart the standard intermediate-depth linearization. The present approach permits the calculation of spectra of all interesting wave quantities (e.g., surface elevation, velocity, pressure) at every point in the liquid domain. The application of the present model to realistic geographical areas requires a vast amount of calculations, calling for the exploitation of advanced computational technologies. In this work, a parallel implementation of the model is developed, using the message passing programming paradigm on a commodity computer cluster. In that way, a direct numerical solution is made feasible for an area of 25km2 over Scripps and La Jolla submarine canyons in Southern California, where a large amount of wave measurements are available. A comparison of numerical results obtained by the present model with field measurements of free-surface frequency spectra transformation is presented, showing excellent agreement. The present approach can be extended to treat weakly nonlinear waves, and it can be further elaborated for studying wave propagation over random bottom topography.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 2

The steep 3D topography of Scripps and La Jolla submarine canyons in Southern California. The computational domain used for the calculation of the transformation of the offshore spectrum is shown by means of a dashed rectangle.

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Figure 3

The total wave field on the free surface (real part) excited by a harmonic obliquely incident wave of period T=15s coming from the west (θ=0deg)

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Figure 6

The real part of the sloping-bottom mode (n=−1) of the scattering wave potential corresponding to incident wave of period T=15s coming from the west (θ=0deg)

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Figure 7

(a) The directional and (b) the frequency spectrum corresponding to a western swell system, characterized by HS=1m and Tp=15s

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Figure 9

Distribution of the significant wave height HS in the NCEX area, as obtained by SWAN

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Figure 10

Observed offshore directional spectrum corresponding to a westerly swell characterized by HS=1.08m and Tp=14.3s

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Figure 11

Comparison between calculated and observed spectra at site 35 of NCEX area, shown also as point A in Fig. 8

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Figure 12

Comparison between calculated and observed spectra at site 37 of NCEX area, shown also as point B in Fig. 8

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Figure 8

Distribution of the significant wave height HS in the NCEX area, as obtained by the present method. Points A and B, corresponding to NCEX sites 35 and 37, respectively, are denoted by circles.

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Figure 5

The real part of the first evanescent mode (n=1) of the scattering wave potential corresponding to incident wave of period T=15s coming from the west (θ=0deg)

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Figure 1

Irregular water waves propagating over a variable-bathymetry region. Basic notation.

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Figure 4

The real part of the propagating mode (n=0) of the scattering wave potential corresponding to incident wave of period T=15s coming from the west (θ=0deg)

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