Kostas A. Belibassakis

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

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 km 2 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.

Hydroelastic analysis of VLFS based on a consistent coupled-mode system and FEM

Three models for the interaction of water waves with large floating elastic structures are analysed. The first model, based on the Euler–Bernoulli beam theory, has already been extensively studied. The second is based on the Rayleigh beam equation. The third approach utilises the Timoshenko approximation and is thus capable of incorporating shear deformation and rotary inertia effects. A novelty of the proposed hydroelastic systems is the consistent local mode expansion of the underlying hydrodynamic field interacting with the floating structure, which leads to coupled-mode systems with respect to the modal amplitudes of the wave potential and the surface elevation. This representation is rapidly convergent to the solution of the full hydroelastic problem. The dispersion relations of these models are derived and analysed, supporting at a next stage the efficient development of finite element method solvers of the coupled system.

A 3D-BEM coupled-mode method for WEC arrays in variable bathymetry

The hydrodynamic interaction of Wave Energy Converters (WECs) deployed in nearshore areas, where the bottom topography presents significant variabilities, is important for the estimation of the harvested wave power and the determination of the operational characteristics of the system, and it could be of great significance for the design and optimization of WEC array layout. In this work a methodology is presented for the treatment of the propagation-diffraction-radiation of water waves around arrays of Wave Energy Converters (WEC) taking into account the interaction of the floating units with the bottom topography at the installation area. The methodology is based on the coupled-mode model developed by Belibassakis et al. (2001), for the water wave field over a three dimensional general bottom topography, in combination with a Boundary Element Method, Belibassakis (2008), for the treatment of the diffraction/radiation problems and the evaluation of the flow details at the local scale of the energy absorbers. An important feature of the methodology is that it is free of mild-slope assumptions and restrictions. Numerical results are presented and discussed concerning the wave filed and the power output of a single floater as well as of an array of heaving vertical cylinders. Dynamics (CFD) is also becoming increasingly applicable, however the computational requirements prohibit the extensive use of these methods, especially for the design of the floater shape and the optimization of WEC array layout. In the case of interaction problems of freesurface gravity waves with floating bodies, in water of intermediate depth propagating over the variable bathymetry region, 3D BEM support the consistent calculation of the details of the wave field and the body responses; see, e.g., Lee & Newman (2004). Extensions to treat the above problems in variable bathymetry regions, characterized by uneven depth at infinity, have been presented by Belibassakis (2008, 2015). The first step in the solution procedure deals with the determination of the propagating wave field over the irregular bathymetry without the effect of the floating bodies. For rapidly varying bed topographies, including steep bottom parts, local or evanescent modes may have a significant impact on the wave phase evolution during propagation (e.g. Massel 1993, Rey 1995). For this part of the problem, a very efficient method is the coupled

3D Wave Transformation Through Openings in Coastal Structures

Standard openings in coastal structures are the flushing culverts at breakwaters, allowing periodic exchange of the harbor basin water leading to improved water quality. These openings involve sudden water depth changes occurring when the incident waves meet these openings and transmitted into the harbour. The wave transformations during wave propagation through flushing culverts are dominated by 3D diffraction effects due to sudden water depth changes, along with the finite width of the culvert. A new coupled-mode model, based on eigenfunctions expansions of the Laplace equation, is developed and applied to the numerical solution of the local 3D wave flow problem at the opening. The harmonic wave field is excited by incident parallel waves. The numerical solution converges rapidly, permitting the series truncation at its first terms. The proposed method fully accounts for the 3D diffraction effects and produces information to couple with mild-slope models describing efficiently wave propagation and transformation in coastal regions.Copyright