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

2005 ◽  
Author(s):  
Th. P. Gerosthathis ◽  
K. A. Belibassakis ◽  
G. A. Athanassoulis
Keyword(s):  
Incident Wave ◽  
Bottom Topography ◽  
Wave Spectrum ◽  
Three Dimensional ◽  
Parallel Architecture ◽  
Wave System ◽  
Directional Spectrum ◽  
Coupled Mode ◽  
Linear Waves ◽  
Velocity Pressure

The problem of transformation of the directional spectrum of an incident wave system over a region of strongly varying three-dimensional bottom topography is studied, in the context of linear theory. The Consistent Coupled-Mode Model (Athanassoulis and Belibassakis 1999, Belibassakis et al 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 takes fully into account reflection, refraction and diffraction phenomena. The present approach permits the consistent transformation of any incident directional wave spectrum over a variable bathymetry region and the calculation of the spatial evolution of point spectra of all interesting wave quantities (free surface elevation, velocity, pressure), at every point in the domain. This approach can be extended to treat weakly non-linear waves.

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

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
Th. P. Gerostathis ◽  
K. A. Belibassakis ◽  
G. A. Athanassoulis
Keyword(s):  
Incident Wave ◽  
Present Model ◽  
Parallel Implementation ◽  
Bottom Topography ◽  
Wave Spectrum ◽  
Present Approach ◽  
Wave System ◽  
Frequency Spectra ◽  
Intermediate Depth ◽  
Coupled Mode

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 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.

scholarly journals Analysis and Interpretation of Frequency–Wavenumber Spectra of Young Wind Waves

2015 ◽  
Vol 45 (10) ◽  
pp. 2484-2496 ◽  
Author(s):  
Fabien Leckler ◽  
Fabrice Ardhuin ◽  
Charles Peureux ◽  
Alvise Benetazzo ◽  
Filippo Bergamasco ◽  
...  
Keyword(s):  
Wind Wave ◽  
Wind Waves ◽  
Wave Spectrum ◽  
Peak Frequency ◽  
Bimodal Distribution ◽  
Second Order ◽  
The Black Sea ◽  
Full Spectrum ◽  
Directional Spectrum ◽  
Linear Waves

AbstractThe energy level and its directional distribution are key observations for understanding the energy balance in the wind-wave spectrum between wind-wave generation, nonlinear interactions, and dissipation. Here, properties of gravity waves are investigated from a fixed platform in the Black Sea, equipped with a stereo video system that resolves waves with frequency f up to 1.4 Hz and wavelengths from 0.6 to 11 m. One representative record is analyzed, corresponding to young wind waves with a peak frequency fp = 0.33 Hz and a wind speed of 13 m s−1. These measurements allow for a separation of the linear waves from the bound second-order harmonics. These harmonics are negligible for frequencies f up to 3 times fp but account for most of the energy at higher frequencies. The full spectrum is well described by a combination of linear components and the second-order spectrum. In the range 2fp to 4fp, the full frequency spectrum decays like f−5, which means a steeper decay of the linear spectrum. The directional spectrum exhibits a very pronounced bimodal distribution, with two peaks on either side of the wind direction, separated by 150° at 4fp. This large separation is associated with a significant amount of energy traveling in opposite directions and thus sources of underwater acoustic and seismic noise. The magnitude of these sources can be quantified by the overlap integral I(f), which is found to increase sharply from less than 0.01 at f = 2fp to 0.11 at f = 4fp and possibly up to 0.2 at f = 5fp, close to the 0.5π value proposed in previous studies.

A Coupled-Mode Model for the Transformation of Wave Systems Over Inhomogeneous Sea/Coastal Environment

2010 ◽  
Author(s):  
K. A. Belibassakis ◽  
Th. P. Gerosthathis ◽  
G. A. Athanassoulis
Keyword(s):  
Present Model ◽  
Bottom Topography ◽  
Wave Spectrum ◽  
Coastal Environment ◽  
Three Dimensions ◽  
Intermediate Water ◽  
Wave Energy Dissipation ◽  
Coupled Mode ◽  
Directional Wave ◽  
Ambient Currents

The transformation of the directional wave spectrum over an inhomogeneous sea/coastal environment is considered. Inhomogeneities include intermediate-water depth, strongly varying 3D bottom topography and ambient currents. The consistent coupled-mode model, developed by Athanassoulis and Belibassakis (1999), extended to three dimensions by Belibassakis et al. (2001) and applied to the transformation of wave systems over 3D bottom topography (Gerostathis et al 2008) is exploited for the calculation of the 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. In the present work, the coupled mode system is enhanced to account also for the effects of steady currents (Belibassakis et al, 2008), as well as, the effect of wave energy dissipation due to bottom friction and wave breaking. Numerical results obtained by the present model are compared with other models (as, e.g., Li et al 1993, Yoon et al 2004) and experimental measurements (Vincent and Briggs 1989), demonstrating the usefulness and practical applicability of the present method.

A coupled-mode model for the refraction–diffraction of linear waves over steep three-dimensional bathymetry

2001 ◽  
Vol 23 (6) ◽  
pp. 319-336 ◽  
Author(s):  
K.A. Belibassakis ◽  
G.A. Athanassoulis ◽  
Th.P. Gerostathis
Keyword(s):  
Three Dimensional ◽  
Coupled Mode ◽  
Linear Waves

A Coupled-Mode Method for Acoustic Propagation and Scattering in Inhomogeneous Ocean Waveguides

2014 ◽  
Author(s):  
K. A. Belibassakis ◽  
G. A. Athanassoulis
Keyword(s):  
Bottom Topography ◽  
Three Dimensional ◽  
Acoustic Propagation ◽  
Local Mode ◽  
Scattering Problems ◽  
Coupled Mode ◽  
Cylindrically Symmetric ◽  
Present Solution ◽  
Mode Method ◽  
Additional Mode

We consider the problem of acoustic propagation and scattering in inhomogeneous waveguide governed by the Helmholtz equation. We focus on an ideal, cylindrically symmetric ocean waveguide, limited above by an acoustically soft boundary modelling the free surface, and below by a hard boundary modelling the impenetrable seabed with general bottom topography. The wave field is excited by a monochromatic point source, and thus, the present solution is equivalent to the construction of the Green’s function in the inhomogeneous domain. An improved coupled-mode method is developed, based on an enhanced local-mode series for the representation of the acoustic field, which includes an additional mode accounting for the effects of the bottom slope and curvature. The additional mode provides an implicit summation of the slowly convergent part of the series, rendering the remaining part to converge much faster, pemitting truncation of the modal expansions keeping only a few evanescent terms. Using the enhanced representation, in conjunction with an appropriate variational principle, a system of coupled-mode equations on the horizontal plane is derived for the determination of the complex modal-amplitude functions. Numerical results are presented including comparisons with analytical solutions illustrating the role and significance of the additional mode and the efficiency of the present coupled-mode tmodel, which can be naturally extended to treat propagation and scattering problems in three-dimensional, multi-layered ocean acoustic waveguides.

Prediction of Ship Motions Via a Three-Dimensional Time-Domain Method Following a Quad-Tree Adaptive Mesh Technique

2020 ◽  
Vol 27 (1) ◽  
pp. 29-38
Author(s):  
Teng Zhang ◽  
Junsheng Ren ◽  
Lu Liu
Keyword(s):  
Free Surface ◽  
Incident Wave ◽  
Time Domain ◽  
Three Dimensional ◽  
Adaptive Mesh ◽  
Wave Profile ◽  
Time Domain Method ◽  
Ship Motions ◽  
Quad Tree ◽  
Mesh Technique

AbstractA three-dimensional (3D) time-domain method is developed to predict ship motions in waves. To evaluate the Froude-Krylov (F-K) forces and hydrostatic forces under the instantaneous incident wave profile, an adaptive mesh technique based on a quad-tree subdivision is adopted to generate instantaneous wet meshes for ship. For quadrilateral panels under both mean free surface and instantaneous incident wave profiles, Froude-Krylov forces and hydrostatic forces are computed by analytical exact pressure integration expressions, allowing for considerably coarse meshes without loss of accuracy. And for quadrilateral panels interacting with the wave profile, F-K and hydrostatic forces are evaluated following a quad-tree subdivision. The transient free surface Green function (TFSGF) is essential to evaluate radiation and diffraction forces based on linear theory. To reduce the numerical error due to unclear partition, a precise integration method is applied to solve the TFSGF in the partition computation time domain. Computations are carried out for a Wigley hull form and S175 container ship, and the results show good agreement with both experimental results and published results.

ACOUSTIC THREE-DIMENSIONAL EFFECTS AROUND THE TAIWAN STRAIT: COMPUTATIONAL RESULTS

1999 ◽  
Vol 07 (01) ◽  
pp. 15-26 ◽  
Author(s):  
CHI-FANG CHEN ◽  
JANG-JIA LIN ◽  
DING LEE
Keyword(s):  
Field Data ◽  
Bottom Topography ◽  
Three Dimensional ◽  
Propagation Model ◽  
Computational Results ◽  
Submarine Canyons ◽  
Offshore Area ◽  
Ocean Environment ◽  
The Taiwan Strait ◽  
Good Agreement

A set of experiments were performed in the offshore area off the coasts of Taiwan and three-dimensional (3-D) measurements recorded. The 3-D effect on underwater propagation due to azimuthal variation of bottom topography is studied for the offshore regions southwest of Taiwan, where submarine canyons exist. A 3-D acoustic propagation model, FOR3D, is used to detect the 3-D effect. Computational results show that the 3-D effect is more prominent along the axis of the canyon than across it. Calculations show a very good agreement with field data, which indicate that the 3-D effect exists in this realistic ocean environment.

Linearized Theory of Supercavitating Hydrofoils in Subsonic Liquid Flow

1977 ◽  
Vol 99 (2) ◽  
pp. 311-318
Author(s):  
Tetsuo Nishiyama
Keyword(s):  
Incompressible Flow ◽  
Liquid Flow ◽  
Sound Speed ◽  
Gas Flow ◽  
Three Dimensional ◽  
Cavitation Number ◽  
Compressibility Effect ◽  
Linearized Theory ◽  
Velocity Pressure ◽  
Subsonic Region

In order to clarify the compressibility effect, the perturbed flow field of the supercavitating hydrofoil in subsonic region is examined by a linearized technique and, as a result, the general corresponding rule of the compressible flow to the incompressible one is proposed to obtain the characteristics of the supercavitating hydrofoil. The main contents are summarized as follows: (i) Basic relations between velocity, pressure, and sound speed are shown in subsonic liquid flow within the framework of linearization. (ii) The correspondence of the steady, characteristics of the two and three dimensional supercavitating hydrofoils in subsonic liquid flow to ones in incompressible flow is clarified. Hence we can readily calculate the characteristics by simple correction to ones in incompressible flow. (iii) Numerical calculations are made to show the essential differences of the compressibility effect between liquid and gas flow, and also the interrelated effect between cavitation number and Mach number on the characteristics of the supercavitating hydrofoils.

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