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.

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 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.

Ship Motions in Shallow Water

1970 ◽  
Vol 14 (04) ◽  
pp. 317-328 ◽  
Author(s):  
E. O. Tuck
Keyword(s):  
Shallow Water ◽  
Water Depth ◽  
Incident Wave ◽  
Degrees Of Freedom ◽  
Added Mass ◽  
Exciting Force ◽  
Ship Motions ◽  
Wave System ◽  
Six Degrees Of Freedom ◽  
Damping Coefficients

The problem discussed concerns small motions of a ship, in all six degrees of freedom, but at zero speed of advance, due to an incident wave system in shallow water of depth comparable with the ship's draft. The problem is completely formulated for an arbitrary ship, and is partially solved for the case when the ship is slender and the wavelength much greater than the water depth. Sample numerical computations of heave, pitch, and sway added mass and damping coefficients and the sway exciting force are presented.

scholarly journals A Mild-Slope System for Bragg Scattering of Water Waves by Sinusoidal Bathymetry in the Presence of Vertically Sheared Currents

2019 ◽  
Vol 7 (1) ◽  
pp. 9 ◽  
Author(s):  
Kostas Belibassakis ◽  
Julien Touboul ◽  
Elodie Laffitte ◽  
Vincent Rey
Keyword(s):  
Resonant Frequency ◽  
Water Waves ◽  
Bottom Topography ◽  
Wave System ◽  
Bragg Scattering ◽  
Wave Flume ◽  
Seabed Topography ◽  
Incident Waves ◽  
Slope System ◽  
A Current

Extended mild-slope models (MMSs) are examined for predicting the characteristics of normally incident waves propagating over sinusoidal bottom topography in the presence of opposing shearing currents. It is shown that MMSs are able to provide quite good predictions in the case of Bragg scattering of waves over rippled bathymetry without a current, but fail to provide good predictions concerning the resonant frequency in the additional presence of a current. In order to resolve the above mismatch, a two-equation mild-slope system (CMS2) is derived from a variational principle based on the representation of the wave potential expressed as a superposition of the forward and backward components. The latter system is compared against experimentally measured data collected in a wave flume and is shown to provide more accurate predictions concerning both the resonant frequency and the amplitude of the reflection coefficient. Future work will be devoted to the examination of the derived model for a more general wave system over realistic seabed topography.

scholarly journals Predicting Ocean Waves along the U.S. East Coast During Energetic Winter Storms: sensitivity to Whitecapping parameterizations

2018 ◽  
Author(s):  
Mohammad Nabi Allahdadi ◽  
Ruoying He ◽  
Vincent S. Neary
Keyword(s):  
East Coast ◽  
Wave Spectrum ◽  
Ocean Waves ◽  
Spectral Energy ◽  
Frequency Spectra ◽  
Winter Storms ◽  
Wave Parameters ◽  
Wind Input ◽  
Simulation Results ◽  
The U.S

Abstract. The performance of two methods for quantifying whitecapping dissipation incorporated in the SWAN wave model is evaluated for waves generated along and off the U.S. East Coast under energetic winter storms with a predominantly westerly wind. Parameterizing the whitecapping effect can be done using the Komen-type schemes, which are based on mean spectral parameters, or the saturation-based (SB) approach of van der Westhuysen (2007), which is based on local wave parameters and the saturation level concept of the wave spectrum (we use Komen and Westhuysen to denote these two approaches). Observations of wave parameters and frequency spectra at four NDBC buoys are used to evaluate simulation results. Model-data comparisons show that when using the default parameters in SWAN, both Komen and Westhuysen methods underestimate wave height. Simulations of mean wave period using the Komen method agree with observations, but those using the Westhuysen method are substantially lower. Examination of source terms shows that the Westhuysen method underestimates the total energy transferred into the wave action equations, especially in the lower frequency bands that contain higher spectral energy. Several causes for this underestimation are identified. The primary reason is the difference between the wave growth conditions along the East Coast during winter storms and the conditions used for the original whitecapping formula calibration. In addition, some deficiencies in simulation results are caused along the coast by the slanting fetch effect that adds low-frequency components to the 2-D wave spectra. These components cannot be simulated partly or entirely by available wind input formulations. Further, the effect of boundary layer instability that is not considered in the Komen and Westhuysen whitecapping wind input formulas may cause additional underestimation.

scholarly journals Space–Time Wave Extremes: The Role of Metocean Forcings

2015 ◽  
Vol 45 (7) ◽  
pp. 1897-1916 ◽  
Author(s):  
Francesco Barbariol ◽  
Alvise Benetazzo ◽  
Sandro Carniel ◽  
Mauro Sclavo
Keyword(s):  
Wind Speed ◽  
Wave Spectrum ◽  
Domain Size ◽  
Space Time ◽  
Statistical Prediction ◽  
Random Wave ◽  
Spectral Parameters ◽  
Frequency Spectra ◽  
Space Domain ◽  
Time Dynamics

AbstractWave observations and modeling have recently demonstrated that wave extremes of short-crested seas are poorly predicted by statistics of time records. Indeed, the highest waves pertain to wave groups at focusing that have space–time dynamics. Therefore, the statistical prediction of extremes of short-crested sea states should rely on the multidimensional random wave fields’ assumption. To adapt wave extreme statistics to the space–time domain, theoretical models using parameters of the directional wave spectrum have been recently developed. In this paper, the influence of metocean forcings (wind conditions, ambient current, and bottom depth) on these parameters and hence on wave extremes is studied with a twofold strategy. First, parametric spectral formulations [Pierson–Moskowitz and Joint North Sea Wave Project (JONSWAP) frequency spectra with cos2 directional distribution function] are considered to represent the dependence of wave extremes upon wind speed, fetch, and space domain size. Afterward, arbitrary conditions are simulated by using the SWAN numerical model adapted to store the spectral parameters, and the effects on extremes of current- and depth-induced shoaling are investigated. Preliminarily, the space–time extremes prediction model adopted is assessed by means of numerical simulations of Gaussian random seas. Compared to the significant wave height of the sea state and for a given space domain size, results show that space–time extremes are enhanced by opposite currents, whereas they are weakened by increasing wind conditions (wind speed and fetch) and by depth-induced shoaling. In this respect, the remarkable contribution to wave extremes of the size of the space domain is substantiated.

scholarly journals Scattering of surface gravity waves by bottom topography with a current

2007 ◽  
Vol 576 ◽  
pp. 235-264 ◽  
Author(s):  
FABRICE ARDHUIN ◽  
RUDY MAGNE
Keyword(s):  
Gravity Waves ◽  
Bottom Topography ◽  
Wave Spectrum ◽  
Action Spectrum ◽  
Wave Action ◽  
Surface Gravity ◽  
Small Scale ◽  
Surface Gravity Waves ◽  
Reflected Wave ◽  
A Current

A theory is presented that describes the scattering of random surface gravity waves by small-amplitude topography, with horizontal scales of the order of the wavelength, in the presence of an irrotational and almost uniform current. A perturbation expansion of the wave action to order η2 yields an evolution equation for the wave action spectrum, where η = max(h)/H is the small-scale bottom amplitude normalized by the mean water depth. Spectral wave evolution is proportional to the bottom elevation variance at the resonant wavenumbers, representing a Bragg scattering approximation. With a current, scattering results from a direct effect of the bottom topography, and an indirect effect of the bottom through the modulations of the surface current and mean surface elevation. For Froude numbers of the order of 0.6 or less, the bottom topography effects dominate. For all Froude numbers, the reflection coefficients for the wave amplitudes that are inferred from the wave action source term are asymptotically identical, as η goes to zero, to previous theoretical results for monochromatic waves propagating in one dimension over sinusoidal bars. In particular, the frequency of the most reflected wave components is shifted by the current, and wave action conservation results in amplified reflected wave energies for following currents. Application of the theory to waves over current-generated sandwaves suggests that forward scattering can be significant, resulting in a broadening of the directional wave spectrum, while back-scattering should be generally weaker.

Development of an On-Board Wave Estimation System Based on the Motions of a Moored FPSO: Commissioning and Preliminary Validation

2012 ◽  
Author(s):  
Alexandre N. Simos ◽  
Eduardo A. Tannuri ◽  
José J. da Cruz ◽  
Asdrubal N. Queiroz Filho ◽  
Iuri B. da Silva Bispo ◽  
...  
Keyword(s):  
Bayesian Estimation ◽  
Full Range ◽  
Wave Spectrum ◽  
Measurement Unit ◽  
Small Scale ◽  
Automation System ◽  
Wave System ◽  
Small Motion ◽  
Estimation System ◽  
Period Wave

This paper addresses the development, installation and initial tests of a system for wave spectra estimation from the measurements of the first order motions of a moored FPSO located in Campos Basin, Brazil. The estimation is based on Bayesian inference algorithms, previously validated by means of numerical and small-scale experimental analysis. A 6-dof inertial measurement unit (IMU) is used for monitoring the motions of the platform, and this information is sent to a remote data-base, also accessed by the wave-estimation system. The algorithm also requires the Response Amplitude Operators (RAOs), and they depend on the loading conditions of the FPSO. A previous analysis considering typical loading configurations of the tanks showed that the wave estimation is mainly dependent on the total displacement of the vessel, and not on the load distribution among the tanks. Hence, the RAOs for the full-range of drafts (or total displacements) were numerically generated, considering a uniform distribution of the load among the tanks. Since the draft of the platform was not directly measured, the loading levels of the tanks are obtained from the automation system of the platform, and the draft is then estimated. Finally, the heading is measured by a gyrocompass, and it is necessary for the definition of the global wave direction. The Bayesian estimation is executed at time-spans of 30min. A parametric optimization algorithm is then applied for the calculation of the wave spectrum parameters from the raw-spectrum obtained by the Bayesian estimation. A user-friendly interface was also developed, with on-line information about platform motions, estimated wave spectrum, peak statistics and data history. Since all information is accessed by network, the wave system can be installed either on-board or in the on-shore monitoring center. The system was commissioned and a partial 3-month validation campaign was executed. The spectrum results were compared to NOAA estimates. As expected, low-period wave components (smaller than 8s) could not be estimated with accuracy, since the FPSO presents small motion response for these components. Swell and high-period wave components estimates presented good qualitative and quantitative agreement with satellite prediction.

scholarly journals A Multisensor Comparison of Ocean Wave Frequency Spectra from a Research Vessel during the Southern Ocean Gas Exchange Experiment

2013 ◽  
Vol 30 (12) ◽  
pp. 2907-2925 ◽  
Author(s):  
Alejandro Cifuentes-Lorenzen ◽  
James B. Edson ◽  
Christopher J. Zappa ◽  
Ludovic Bariteau
Keyword(s):  
High Frequency ◽  
Doppler Radar ◽  
Inertial Sensors ◽  
Wave Spectrum ◽  
Ocean Wave ◽  
Modulation Transfer ◽  
Laser Altimeter ◽  
Frequency Spectra ◽  
Wave Statistics ◽  
Wave Measurements

Abstract Obtaining accurate measurements of wave statistics from research vessels remains a challenge due to the platform motion. One principal correction is the removal of ship heave and Doppler effects from point measurements. Here, open-ocean wave measurements were collected using a laser altimeter, a Doppler radar microwave sensor, a radar-based system, and inertial measurement units. Multiple instruments were deployed to capture the low- and high-frequency sea surface displacements. Doppler and motion correction algorithms were applied to obtain a full 1D (0.035–1.3 ± 0.2 Hz) wave spectrum. The radar-based system combined with the laser altimeter provided the optimal low- and high-frequency combination, producing a frequency spectrum in the range from 0.035 to 1.2 Hz for cruising speeds ≤3 m s−1 with a spectral rolloff of f−4 Hz and noise floor of −20/−30 dB. While on station, the significant wave height estimates were comparable within 10%–15% among instrumentation. Discrepancies in the total energy and in the spectral shape between instruments arise when the ship is in motion. These differences can be quantified using the spectral behavior of the measurements, accounting for aliasing and Doppler corrections. The inertial sensors provided information on the amplitude of the ship’s modulation transfer function, which was estimated to be ~1.3 ± 0.2 while on station and increased while underway [2.1 at ship-over-ground (SOG) speed; 4.3 m s−1]. The correction scheme presented here is adequate for measurements collected at cruising speeds of 3 m s−1 or less. At speeds greater than 5 m s−1, the motion and Doppler corrections are not sufficient to correct the observed spectral degradation.

scholarly journals A fully coupled Atmosphere–Ocean Wave modeling system (WEW) for the Mediterranean Sea: interactions and sensitivity to the resolved scales and mechanisms

2015 ◽  
Vol 8 (5) ◽  
pp. 4075-4112
Author(s):  
P. Katsafados ◽  
A. Papadopoulos ◽  
G. Korres ◽  
G. Varlas
Keyword(s):  
Data Exchange ◽  
Wind Wave ◽  
Aerodynamic Drag ◽  
Wave Spectrum ◽  
Ocean Wave ◽  
Wave System ◽  
Sea State ◽  
Scientific Performance ◽  
Research Activities ◽  
Fully Coupled

Abstract. It is commonly accepted that there is an urgent need for a better understanding of the factors that contribute to the air–sea interaction processes and their feedbacks. In this sense it is absolutely important to develop advanced numerical prediction systems that treat the atmosphere and the ocean as a unified system. The realistic description and understanding of the exchange processes near the ocean surface, requires the exact knowledge of the sea state and its evolution. This can be achieved by considering the sea surface and the atmosphere as a continuously cross talking dynamic system. Therefore, this study aims to present the effort towards developing a new, high-resolution, two-way fully coupled atmosphere–ocean wave model in order to support operational and research activities. A specific issue that it is emphasized here is the determination and parameterization of the air–sea momentum fluxes under conditions of extremely high and time-varying winds. Software considerations, data exchange as well as computational and scientific performance of the coupled system, so-called WEW, are also discussed throughout this study. In a case study of high-impact weather and sea state event, the wind–wave parameterization scheme reduces the resulted wind speed and the significant wave height as a response to the increased aerodynamic drag over rough sea surfaces. Overall, WEW offers a more realistic representation of the momentum exchanges in the ocean wind–wave system and includes the effects of the resolved wave spectrum on the drag coefficient and its feedback on the momentum flux.

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