A coupled-mode, phase-resolving model for the transformation of wave spectrum over steep 3D topography: Parallel-architecture implementation

• Published in: Journal of Offshore Mechanics and Arctic Engineering
• Main Authors: Gerostathis, ThP, Belibassakis, KA, Athanassoulis, GA
• Format: Article in Journal/Newspaper
• Language: English
• Published: ASME-AMER SOC MECHANICAL ENG 2008
• Subjects: Parallel Architecture; Spectrum; Engineering; Ocean; Mechanical; Eigenvalues and eigenfunctions; Engineering geology; Geometrical optics; Message passing; Numerical methods; Parallel programming; Standards; Three dimensional; Topography; Transfer functions; Bottom topography; Computational technologies; Computer clustering; Diffraction phenomenon; Directional spectrum (dS); Geographical areas; Incident waves; Linear theories; Linear transfer function (LTF); Numerical solutions; Parallel implementations; SPECTRA (CO); Surface elevations; Three dimensions; Three-dimensional (3D) topography; Wave conditions; Wave spectrum; Modal analysis; linearity; measurement method; ocean wave; spectral analysis; submarine canyon; wave diffraction; wave dispersion; wave modeling; wave propagation; wave reflection; California; La Jolla; North America; San Diego; United States; Scripps; Arctic
• Online Access: http://dspace.lib.ntua.gr/handle/123456789/18525; https://doi.org/10.1115/1.2783883

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 et al. (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 25 km2 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 fiem 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. Copyright © 2008 by ASME.