DOCSLIB.ORG

D2.3 Application of Numerical Models

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
D2.3 Application of Numerical Models COMMISSION OF THE EUROPEAN COMMUNITIES Equitable Testing and Evaluation of Marine Energy Extraction Devices in terms of Performance, Cost and Environmental Impact Grant agreement number: 213380 Deliverable D2.3 Application of Numerical Models Grant Agreement number: 213380 Project acronym: EQUIMAR Project title: Equitable Testing and Evaluation of Marine Energy Extraction Devices in terms of Performance, Cost and Environmental Impact Deliverable D2.3 Application of Numerical Models Vengatesan Venugopal and Thomas Davey University of Edinburgh, UK Françoise Girard Actimar, France Helen Smith and George Smith University of Exeter, UK Luigi Cavaleri and Luciana Bertotti CNR-ISMAR, Italy John Lawrence EMEC, UK June 2010 Summary This report discusses key aspects of the application of numerical models to marine energy resource assessment. Wave and tidal modelling methodologies are described along with examples of specific models. The modelled processes, model inputs and interpretation of the output data are described and discussed. The role of model validation and calibration is also described. Workpackage 2 EquiMar D2.3 CONTENTS 1 INTRODUCTION ............................................................................................................................................................... 1—1 1.1 ROLE OF NUMERICAL MODELS IN RESOURCE ASSESSMENT .......................................................................................... 1—1 1.1.1 Scope of this Report ................................................................................................................................................ 1—1 1.1.2 Numerical Models for Resource Assessment .......................................................................................................... 1—1 1.2 RESOURCE ASSESSMENT ................................................................................................................................................ 1—1 1.2.1 Resource Characterisation ..................................................................................................................................... 1—1 1.2.2 Site Assessment ....................................................................................................................................................... 1—1 2 WAVE RESOURCE MODELLING ................................................................................................................................. 2—2 2.1 GENERAL ....................................................................................................................................................................... 2—2 2.2 WAVE MODELLING OVERVIEW ....................................................................................................................................... 2—3 2.3 WAVE MODELS .............................................................................................................................................................. 2—4 2.3.1 Model Summary...................................................................................................................................................... 2—4 2.3.2 Modelled Processes ................................................................................................................................................ 2—5 2.3.2.1 Energy Dissipation ................................................................................................................................................................ 2—6 2.3.2.2 Reflection and Diffraction ..................................................................................................................................................... 2—6 2.3.2.3 Nonlinearity .......................................................................................................................................................................... 2—6 2.3.3 Model Setup ............................................................................................................................................................ 2—7 2.3.3.1 Computational Boundary Limits ........................................................................................................................................... 2—7 2.3.3.2 Input grids ............................................................................................................................................................................. 2—8 2.3.3.3 Influence of wind .................................................................................................................................................................. 2—9 2.3.3.4 Bathymetry Requirements ..................................................................................................................................................... 2—9 2.3.3.5 Sea Floor Composition ........................................................................................................................................................ 2—11 2.3.3.6 Influence of Water Level,Tides and Currents...................................................................................................................... 2—11 2.3.4 Model Input .......................................................................................................................................................... 2—12 2.3.4.1 Input Parameters ................................................................................................................................................................. 2—12 2.3.4.2 Input Data Sources .............................................................................................................................................................. 2—12 2.3.4.3 Spectral Description ............................................................................................................................................................ 2—12 2.3.4.4 Directional Description ....................................................................................................................................................... 2—13 2.3.5 Model Output and Interpretation ......................................................................................................................... 2—13 2.3.5.1 Output Parameters ............................................................................................................................................................... 2—13 2.3.5.2 Data Archiving and Presentation ......................................................................................................................................... 2—13 2.3.5.3 Quantification of Error and Uncertainty .............................................................................................................................. 2—13 3 TIDAL RESOURCE MODELLING ............................................................................................................................... 3—14 3.1 INTRODUCTION ............................................................................................................................................................ 3—14 3.2 TIDAL MODELLING OVERVIEW .................................................................................................................................... 3—14 3.2.1 Governing equations ............................................................................................................................................ 3—14 3.2.2 Numerical resolution and Computational Grids .................................................................................................. 3—15 3.3 TIDAL MODELS ............................................................................................................................................................ 3—16 3.3.1 Mars 2D ............................................................................................................................................................... 3—16 3.3.1.1 Computational Grid ............................................................................................................................................................. 3—16 3.3.1.2 Modelled Processes ............................................................................................................................................................. 3—16 3.3.1.3 Input Data............................................................................................................................................................................ 3—17 3.3.2 TELEMAC-2D ...................................................................................................................................................... 3—17 3.3.2.1 Computational Grid ............................................................................................................................................................. 3—17 3.3.2.2 Modelled Processes ............................................................................................................................................................. 3—18 3.3.2.3 Input Data............................................................................................................................................................................ 3—19 3.3.3 Comparison Summary .......................................................................................................................................... 3—19 4 CALIBRATION AND
Load more

Recommended publications
  • A Near-Shore Linear Wave Model with the Mixed Finite Volume and Finite Difference Unstructured Mesh Method
    fluids Article A Near-Shore Linear Wave Model with the Mixed Finite Volume and Finite Difference Unstructured Mesh Method Yong G. Lai 1,* and Han Sang Kim 2 1 Technical Service Center, U.S. Bureau of Reclamation, Denver, CO 80225, USA 2 Bay-Delta Office, California Department of Water Resources, Sacramento, CA 95814, USA; [email protected] * Correspondence: [email protected]; Tel.: +1-303-445-2560 Received: 5 October 2020; Accepted: 1 November 2020; Published: 5 November 2020 Abstract: The near-shore and estuary environment is characterized by complex natural processes. A prominent feature is the wind-generated waves, which transfer energy and lead to various phenomena not observed where the hydrodynamics is dictated only by currents. Over the past several decades, numerical models have been developed to predict the wave and current state and their interactions. Most models, however, have relied on the two-model approach in which the wave model is developed independently of the current model and the two are coupled together through a separate steering module. In this study, a new wave model is developed and embedded in an existing two-dimensional (2D) depth-integrated current model, SRH-2D. The work leads to a new wave–current model based on the one-model approach. The physical processes of the new wave model are based on the latest third-generation formulation in which the spectral wave action balance equation is solved so that the spectrum shape is not pre-imposed and the non-linear effects are not parameterized. New contributions of the present study lie primarily in the numerical method adopted, which include: (a) a new operator-splitting method that allows an implicit solution of the wave action equation in the geographical space; (b) mixed finite volume and finite difference method; (c) unstructured polygonal mesh in the geographical space; and (d) a single mesh for both the wave and current models that paves the way for the use of the one-model approach.
    [Show full text]
  • SWAN Technical Manual
    SWAN TECHNICAL DOCUMENTATION SWAN Cycle III version 40.51 SWAN TECHNICAL DOCUMENTATION by : The SWAN team mail address : Delft University of Technology Faculty of Civil Engineering and Geosciences Environmental Fluid Mechanics Section P.O. Box 5048 2600 GA Delft The Netherlands e-mail : [email protected] home page : http://www.fluidmechanics.tudelft.nl/swan/index.htmhttp://www.fluidmechanics.tudelft.nl/sw Copyright (c) 2006 Delft University of Technology. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sec- tions, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is available at http://www.gnu.org/licenses/fdl.html#TOC1http://www.gnu.org/licenses/fdl.html#TOC1. Contents 1 Introduction 1 1.1 Historicalbackground. 1 1.2 Purposeandmotivation . 2 1.3 Readership............................. 3 1.4 Scopeofthisdocument. 3 1.5 Overview.............................. 4 1.6 Acknowledgements ........................ 5 2 Governing equations 7 2.1 Spectral description of wind waves . 7 2.2 Propagation of wave energy . 10 2.2.1 Wave kinematics . 10 2.2.2 Spectral action balance equation . 11 2.3 Sourcesandsinks ......................... 12 2.3.1 Generalconcepts . 12 2.3.2 Input by wind (Sin).................... 19 2.3.3 Dissipation of wave energy (Sds)............. 21 2.3.4 Nonlinear wave-wave interactions (Snl) ......... 27 2.4 The influence of ambient current on waves . 33 2.5 Modellingofobstacles . 34 2.6 Wave-inducedset-up . 35 2.7 Modellingofdiffraction. 35 3 Numerical approaches 39 3.1 Introduction...........................
    [Show full text]
  • Storm Waves Focusing and Steepening in the Agulhas Current: Satellite Observations and Modeling T ⁎ Y
    Remote Sensing of Environment 216 (2018) 561–571 Contents lists available at ScienceDirect Remote Sensing of Environment journal homepage: www.elsevier.com/locate/rse Storm waves focusing and steepening in the Agulhas current: Satellite observations and modeling T ⁎ Y. Quilfena, , M. Yurovskayab,c, B. Chaprona,c, F. Ardhuina a IFREMER, Univ. Brest, CNRS, IRD, Laboratoire d'Océanographie Physique et Spatiale (LOPS), Brest, France b Marine Hydrophysical Institute RAS, Sebastopol, Russia c Russian State Hydrometeorological University, Saint Petersburg, Russia ARTICLE INFO ABSTRACT Keywords: Strong ocean currents can modify the height and shape of ocean waves, possibly causing extreme sea states in Extreme waves particular conditions. The risk of extreme waves is a known hazard in the shipping routes crossing some of the Wave-current interactions main current systems. Modeling surface current interactions in standard wave numerical models is an active area Satellite altimeter of research that benefits from the increased availability and accuracy of satellite observations. We report a SAR typical case of a swell system propagating in the Agulhas current, using wind and sea state measurements from several satellites, jointly with state of the art analytical and numerical modeling of wave-current interactions. In particular, Synthetic Aperture Radar and altimeter measurements are used to show the evolution of the swell train and resulting local extreme waves. A ray tracing analysis shows that the significant wave height variability at scales < ~100 km is well associated with the current vorticity patterns. Predictions of the WAVEWATCH III numerical model in a version that accounts for wave-current interactions are consistent with observations, al- though their effects are still under-predicted in the present configuration.
    [Show full text]
  • Semi-Empirical Dissipation Source Functions for Ocean Waves: Part I, Definition, Calibration and Validation
    A Generated using V3.0 of the official AMS L TEX template–journal page layout FOR AUTHOR USE ONLY, NOT FOR SUBMISSION! Semi-empirical dissipation source functions for ocean waves: Part I, definition, calibration and validation. Fabrice Ardhuin ∗, Jean-Franc¸ois Filipot and Rudy Magne Service Hydrographique et Oc´eanographique de la Marine, Brest, France Erick Rogers Oceanography Division, Naval Research Laboratory, Stennis Space Center, MS, USA Alexander Babanin Swinburne University, Hawthorn, VA, Australia Pierre Queffeulou Ifremer, Laboratoire d’Oc´eanographie Spatiale, Plouzan´e, France Lotfi Aouf and Jean-Michel Lefevre UMR GAME, M´et´eo-France - CNRS, Toulouse, France Aron Roland Technological University of Darmstadt, Germany Andre van der Westhuysen Deltares, Delft, The Netherlands Fabrice Collard CLS, Division Radar, Plouzan´e, France ABSTRACT New parameterizations for the spectral dissipation of wind-generated waves are proposed. The rates of dissipation have no predetermined spectral shapes and are functions of the wave spectrum, in a way consistent with observation of wave breaking and swell dissipation properties. Namely, swell dissipation is nonlinear and proportional to the swell steepness, and wave breaking only affects spectral components such that the non-dimensional spectrum exceeds the threshold at which waves are observed to start breaking. An additional source of short wave dissipation due to long wave breaking is introduced, together with a reduction of wind-wave generation term for short waves, otherwise taken from Janssen (J. Phys. Oceanogr. 1991). These parameterizations are combined and calibrated with the Discrete Interaction Approximation of Hasselmann et al. (J. Phys. Oceangr. 1985) for the nonlinear interactions. Parameters are adjusted to reproduce observed shapes of directional wave spectra, and the variability of spectral moments with wind speed and wave height.
    [Show full text]
  • Appendix D — Summary of Hydrodynamic, Sediment Transport
    Appendix D Summary of Hydrodynamic, Sediment Transport, and Wave Modeling Appendix D Summary of Hydrodynamic, Sediment Transport, and Wave Modeling Spirit Lake Sediment Site Prepared for U. S. Steel Corporation November 2014 325 S. Lake Avenue, Suite 700 Duluth, MN 55802-2323 Phone: 218.529.8200 Fax: 218.529.8202 Summary of Hydrodynamic, Sediment Transport, and Wave Modeling Spirit Lake Sediment Site November 2014 Contents 1.0 Introduction ........................................................................................................................................................................... 1 1.1 Spirit Lake Physical System ......................................................................................................................................... 1 1.1.1 Bathymetric Scans ..................................................................................................................................................... 2 1.1.2 Hydrodynamic Data .................................................................................................................................................. 2 1.1.2.1 River Discharge ................................................................................................................................................. 3 1.1.2.2 Water Level ........................................................................................................................................................ 3 1.1.2.3 Flow Velocity ....................................................................................................................................................
    [Show full text]
  • A Modelling Approach for the Assessment of Wave-Currents Interaction in the Black Sea
    Journal of Marine Science and Engineering Article A Modelling Approach for the Assessment of Wave-Currents Interaction in the Black Sea Salvatore Causio 1,* , Stefania A. Ciliberti 1 , Emanuela Clementi 2, Giovanni Coppini 1 and Piero Lionello 3 1 Fondazione Centro Euro-Mediterraneo sui Cambiamenti Climatici, Ocean Predictions and Applications Division, 73100 Lecce, Italy; [email protected] (S.A.C.); [email protected] (G.C.) 2 Fondazione Centro Euro-Mediterraneo sui Cambiamenti Climatici, Ocean Modelling and Data Assimilation Division, 40127 Bologna, Italy; [email protected] 3 Department of Biological and Environmental Sciences and Technologies, University of Salento—DiSTeBA, 73100 Lecce, Italy; [email protected] * Correspondence: [email protected] Abstract: In this study, we investigate wave-currents interaction for the first time in the Black Sea, implementing a coupled numerical system based on the ocean circulation model NEMO v4.0 and the third-generation wave model WaveWatchIII v5.16. The scope is to evaluate how the waves impact the surface ocean dynamics, through assessment of temperature, salinity and surface currents. We provide also some evidence on the way currents may impact on sea-state. The physical processes considered here are Stokes–Coriolis force, sea-state dependent momentum flux, wave-induced vertical mixing, Doppler shift effect, and stability parameter for computation of effective wind speed. The numerical system is implemented for the Black Sea basin (the Azov Sea is not included) at a horizontal resolution of about 3 km and at 31 vertical levels for the hydrodynamics. Wave spectrum has been discretised into 30 frequencies and 24 directional bins.
    [Show full text]
  • Study of a Wind-Wave Numerical Model and Its Integration with an Ocean and an Oil-Spill Numerical Models
    Alma Mater Studiorum di Bologna Facolta` di Scienze MM.FF.NN. Tesi di Laurea Magistrale in Analisi e Gestione dell'Ambiente Study of a Wind-Wave Numerical Model and its integration with an Ocean and an Oil-Spill Numerical Models Relatore Candidato Prof.ssa Nadia Pinardi Diego Bruciaferri Correlatori Dott.ssa Michela De Dominicis Dott. Francesco Trotta Anno Accademico 2012/2013 Given for one instant an intelligence which could comprehend all the forces by which nature is animated, ... to it nothing would be uncertain, and the future as the past would be present to its eyes. Laplace, Oeuvres Desidero ringraziare mio padre, mia madre e i miei fratelli che hanno sempre creduto in me e hanno sempre supportato le mie scelte. Desidero inoltre ringraziare la Prof.ssa Nadia Pinardi, che, con il suo in- coraggiamento e la sua contagiosa passione per la fisica e il mare, non ha mai smesso di motivarmi nel superare gli scogli piu' difficili incontrati du- rante questo lavoro. Un ringraziamento speciale va alla Dott.ssa Michela De Dominicis, al Dott. Luca Giacomelli e al Dott. Francesco Trotta, senza l'aiuto dei quali questo lavoro non avrebbe potuto essere portato a termine. Un grazie poi a tutti i Prof.ri del mio corso di Laurea, per l'entusiasmo che hanno messo nelle loro lezioni e per i loro insegnamenti. Un grazie a Claudia, Giulia, Emanuela, Augusto e a tutti i ragazzi che hanno frequentato i laboratori del SINCEM, perche' tutti mi hanno lasciato qualcosa. Un grazie poi va ai miei compagni di corso, al `crucco' Matteo, al `terroncello' Roberto, a Francesco, Riccardo, Michela, Manuela, Caterina e tutti gli altri, per i bei due anni passati insieme.
    [Show full text]
  • Evaluation of the Significant Wave Height Data Quality for the Sentinel
    remote sensing Technical Note Evaluation of the Significant Wave Height Data Quality for the Sentinel-3 Synthetic Aperture Radar Altimeter Yong Wan 1,* , Rongjuan Zhang 2, Xiaodong Pan 3, Chenqing Fan 4 and Yongshou Dai 1 1 College of Oceanography and Space Informatics, China University of Petroleum, No. 66, Changjiangxi Road, Huangdao District, Qingdao 266580, China; [email protected] 2 College of Control Science and Engineering, China University of Petroleum, No. 66, Changjiangxi Road, Huangdao District, Qingdao 266580, China; [email protected] 3 Marine Environmental Monitoring Center of Wenzhou, the State Oceanic Administration, No. 2, Xinanjiang Road, Wenzhou Avenue, Wenzhou 325000, China; [email protected] 4 Remote Sensing Office of The First Institute of Oceanography, Ministry of Natural Resources, No. 6, Xianxia Road, Laoshan District, Qingdao 266061, China; fanchenqing@fio.org.cn * Correspondence: [email protected]; Tel.: +86-150-5325-1676 Received: 21 August 2020; Accepted: 19 September 2020; Published: 22 September 2020 Abstract: Synthetic aperture radar (SAR) altimeters represent a new method of microwave remote sensing for ocean wave observations. The adoption of SAR technology in the azimuthal direction has the advantage of a high resolution. The Sentinel-3 altimeter is the first radar altimeter to acquire global observations in SAR mode; hence, the data quality needs to be assessed before extensively applying these data. The European Space Agency (ESA) evaluates the Sentinel-3 accuracy on a global scale but has yet to perform a detailed analysis in terms of different offshore distances and different water depths. In this paper, Sentinel-3 and Jason-2 significant wave height (SWH) data are matched in both time and space with buoy data from the United States East and West Coasts and the Central Pacific Ocean.
    [Show full text]
  • Field Surveys and Numerical Simulation of the 2018 Typhoon Jebi: Impact of High Waves and Storm Surge in Semi-Enclosed Osaka Bay, Japan
    Pure Appl. Geophys. 176 (2019), 4139–4160 Ó 2019 Springer Nature Switzerland AG https://doi.org/10.1007/s00024-019-02295-0 Pure and Applied Geophysics Field Surveys and Numerical Simulation of the 2018 Typhoon Jebi: Impact of High Waves and Storm Surge in Semi-enclosed Osaka Bay, Japan 1 1 2 1 1 TUAN ANH LE, HIROSHI TAKAGI, MOHAMMAD HEIDARZADEH, YOSHIHUMI TAKATA, and ATSUHEI TAKAHASHI Abstract—Typhoon Jebi made landfall in Japan in 2018 and hit 1. Introduction Osaka Bay on September 4, causing severe damage to Kansai area, Japan’s second largest economical region. We conducted field surveys around the Osaka Bay including the cities of Osaka, Annually, an average of 2.9 tropical cyclones Wakayama, Tokushima, Hyogo, and the island of Awaji-shima to (from 1951 to 2016) have hit Japan (Takagi and evaluate the situation of these areas immediately after Typhoon Esteban 2016; Takagi et al. 2017). The recent Jebi struck. Jebi generated high waves over large areas in these regions, and many coasts were substantially damaged by the Typhoon Jebi in September 2018 has been the combined impact of high waves and storm surges. The Jebi storm strongest tropical cyclone to come ashore in the last surge was the highest in the recorded history of Osaka. We used a 25 years since Typhoon Yancy (the 13th typhoon to storm surge–wave coupled model to investigate the impact caused by Jebi. The simulated surge level was validated with real data hit Japan, in 1993), severely damaging areas in its acquired from three tidal stations, while the wave simulation results trajectory.
    [Show full text]
  • Adjustment of Wind Waves to Sudden Changes of Wind Speed
    Journal of Oceanography, Vol. 57, pp. 519 to 533, 2001 Adjustment of Wind Waves to Sudden Changes of Wind Speed 1 2 3 TAKUJI WASEDA *, YOSHIAKI TOBA and MARSHALL P. T ULIN 1Frontier Research System for Global Change and International Pacific Research Center, University of Hawaii, HI 96822, U.S.A. 2Earth Observation Research Center, National Space Development Agency of Japan, Tokyo 104-6023, Japan; and Japan Marine Science and Technology Center, Yokosuka 237-0061, Japan 3Ocean Engineering Laboratory, University of California, Santa Barbara, CA 93106, U.S.A. (Received 4 August 2000; in revised form 22 January 2001; accepted 15 March 2001) An experiment was conducted in a small wind-wave facility at the Ocean Engineering Keywords: Laboratory, California, to address the following question: when the wind speed ⋅ Wind waves, changes rapidly, how quickly and in what manner do the short wind waves respond? ⋅ local equilibrium, ⋅ To answer this question we have produced a very rapid change in wind speed between fetch, –1 –1 ⋅ wind gust. Ulow (4.6 m s ) and Uhigh (7.1 m s ). Water surface elevation and air turbulence were monitored up to a fetch of 5.5 m. The cycle of increasing and decreasing wind speed was repeated 20 times to assure statistical accuracy in the measurement by taking an ensemble mean. In this way, we were able to study in detail the processes by which the young laboratory wind waves adjust to wind speed perturbations. We found that the wind-wave response occurs over two time scales determined by local equilibrium ad- ∆ ∆ justment and fetch adjustment, t1/T = O(10) and t2/T = O(100), respectively, in the current tank.
    [Show full text]
  • U Ncorrected Proof
    Pure Appl. Geophys. Ó 2019 Springer Nature Switzerland AG https://doi.org/10.1007/s00024-019-02295-0 Pure and Applied Geophysics 1 Field Surveys and Numerical Simulation of the 2018 Typhoon Jebi: Impact of High Waves 2 and Storm Surge in Semi-enclosed Osaka Bay, Japan 3 1 1 2 1 1 4 LE TUAN ANH, HIROSHI TAKAGI, MOHAMMAD HEIDARZADEH, YOSHIHUMI TAKATA, and ATSUHEI TAKAHASHI 5 Abstract—Typhoon Jebi made landfall in Japan in 2018 and hit 1. Introduction 39 6 Osaka Bay on September 4, causing severe damage to Kansai area, 7 Japan’s second largest economical region. We conducted field 8 surveys around the Osaka Bay including the cities of Osaka, Annually, an average of 2.9 tropical cyclones 40 Author Proof 9 Wakayama, Tokushima, Hyogo, and the island of Awaji-shima to (from 1951 to 2016) have hit Japan (Takagi and 41 10 evaluate the situation of these areas immediately after Typhoon 42 11 Esteban 2016; Takagi et al. 2017). The recent Jebi struck. Jebi generated high waves over large areas in these 43 12 regions, and many coasts were substantially damaged by the Typhoon Jebi in September 2018 has been the 13 combined impact of high waves and storm surges. The Jebi storm strongest tropical cyclone to come ashore in the last 44 14 surge was the highest in the recorded history of Osaka. We used a 45 15 25 years since Typhoon Yancy (the 13th typhoon to storm surge–wave coupled model to investigate the impact caused 46 16 by Jebi. The simulated surge level was validated with real data hit Japan, in 1993), severely damaging areas in its 17 acquired from three tidal stations, while the wave simulation results trajectory.
    [Show full text]
  • Numerical Modelling of Wind Waves. Problems, Solutions, Verifications, and Applications
    1 NUMERICAL MODELLING OF WIND WAVES. PROBLEMS, SOLUTIONS, VERIFICATIONS, AND APPLICATIONS V. G. Polnikov1 CONTENTS Abstract 1. Introduction 2. Fundamental equations and conceptions 3. Wave evolution mechanism due to nonlinearity 4. Wind wave energy pumping mechanism 5. Wind wave dissipation mechanism 6. Verification of new source function 7. Future applications 8. References 1 Research professor, A.M. Obukhov Institute for Physics of Atmosphere of Russian Academy of Sciences, Moscow, Russia 119017, e-mail: [email protected] 2 ABSTRACT Due to stochastic feature of a wind-wave field, the time-space evolution of the field is described by the transport equation for the 2-dimensional wave energy spectrum density, σ θ x, tS ),;( , spread in the space, x, and time, t. This equation has the forcing named the source function, F, depending on both the wave spectrum, S , and the external wave-making factors: local wind, W(x, t), and local current, U(x, t). The source function, F, is the “heart” of any numerical wind wave model, as far as it contains certain physical mechanisms responsible for a wave spectrum evolution. It is used to distinguish three terms in function F: the wind-wave energy exchange mechanism, In; the energy conservative mechanism of nonlinear wave-wave interactions, Nl; and the wave energy loss mechanism, Dis, related, mainly, to the wave breaking and interaction of waves with the turbulence of water upper layer and with the bottom. Differences in mathematical representation of the source function terms determine general differences between wave models. The problem is to derive analytical representations for the source function terms said above from the fundamental wave equations.
    [Show full text]