1 Influence of Wave Transformation Processes
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Part II-1 Water Wave Mechanics
Chapter 1 EM 1110-2-1100 WATER WAVE MECHANICS (Part II) 1 August 2008 (Change 2) Table of Contents Page II-1-1. Introduction ............................................................II-1-1 II-1-2. Regular Waves .........................................................II-1-3 a. Introduction ...........................................................II-1-3 b. Definition of wave parameters .............................................II-1-4 c. Linear wave theory ......................................................II-1-5 (1) Introduction .......................................................II-1-5 (2) Wave celerity, length, and period.......................................II-1-6 (3) The sinusoidal wave profile...........................................II-1-9 (4) Some useful functions ...............................................II-1-9 (5) Local fluid velocities and accelerations .................................II-1-12 (6) Water particle displacements .........................................II-1-13 (7) Subsurface pressure ................................................II-1-21 (8) Group velocity ....................................................II-1-22 (9) Wave energy and power.............................................II-1-26 (10)Summary of linear wave theory.......................................II-1-29 d. Nonlinear wave theories .................................................II-1-30 (1) Introduction ......................................................II-1-30 (2) Stokes finite-amplitude wave theory ...................................II-1-32 -
On the Reflectance of Uniform Slopes for Normally Incident Interfacial Solitary Waves
1156 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 37 On the Reflectance of Uniform Slopes for Normally Incident Interfacial Solitary Waves DANIEL BOURGAULT Department of Physics and Physical Oceanography, Memorial University, St. John’s, Newfoundland, Canada DANIEL E. KELLEY Department of Oceanography, Dalhousie University, Halifax, Nova Scotia, Canada (Manuscript received 29 March 2005, in final form 2 September 2006) ABSTRACT The collision of interfacial solitary waves with sloping boundaries may provide an important energy source for mixing in coastal waters. Collision energetics have been studied in the laboratory for the idealized case of normal incidence upon uniform slopes. Before these results can be recast into an ocean parameter- ization, contradictory laboratory findings must be addressed, as must the possibility of a bias owing to laboratory sidewall effects. As a first step, the authors have revisited the laboratory results in the context of numerical simulations performed with a nonhydrostatic laterally averaged model. It is shown that the simulations and the laboratory measurements match closely, but only for simulations that incorporate sidewall friction. More laboratory measurements are called for, but in the meantime the numerical simu- lations done without sidewall friction suggest a tentative parameterization of the reflectance of interfacial solitary waves upon impact with uniform slopes. 1. Introduction experiments addressed the idealized case of normally incident ISWs on uniform shoaling slopes in an other- Diverse observational case studies suggest that the wise motionless fluid with two-layer stratification. The breaking of high-frequency interfacial solitary waves results of these experiments showed that the fraction of (ISWs) on sloping boundaries may be an important ISW energy that gets reflected back to the source after generator of vertical mixing in coastal waters (e.g., impinging the sloping boundary depends on the ratio of MacIntyre et al. -
Swash Zone Based Reflection During Energetic Wave Conditions at a Dissipative Beach: Toward a Wave-By-Wave Approach
SWASH ZONE BASED REFLECTION DURING ENERGETIC WAVE CONDITIONS AT A DISSIPATIVE BEACH: TOWARD A WAVE-BY-WAVE APPROACH Rafael Almar1, Patricio Catalán2, Raimundo Ibaceta2, Chris Blenkinsopp3, Rodrigo Cienfuegos4, Mauricio Villagrán4,5, Juan Carlos Aguilera4 and Bruno Castelle6 This paper presents a 11-day experiment conducted at the high-energy dissipative beach of Mataquito, Maule Region, Chile. During the experiment, offshore significant wave height ranged 1-4 m, with persistent long period up to 18 s and oblique incidence. Wave energy reflection value ranged from 1 to 4 %, and results show that it is highly linked to both incoming wave characteristics and swash zone beach slope, and is well correlated to a swash-slope based Iribarren number. The swash acting as a low-pass filter in the reflection mechanism, our results show that the cut-off period is better determined by swash slope rather than incoming wave's period. A new low cost technique for observing high-frequency swash hydro-morphodynamics is introduced and validated using LIDAR measurements. A good agreement is found. Separation of uprush and backswash components using the Radon Transform illustrates the low-frequency filtering effect. These results show the key role played by swash mechanism in the reflection rate and frequency selection. More investigation is needed to describe the reflection process and its link with shoreface evolution, moving toward a swash-by-swash approach. Keywords: Mataquito, Maule Region, Chile; beach reflection; incoming and outgoing wave separation; swash measurements technique; video; Lidar INTRODUCTION There is a potential for substantial wave reflection at the coast, depending on hydro- and morphodynamic conditions. -
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........................... -
Chapter 216 Extreme Water Levels, Wave Runup And
CHAPTER 216 EXTREME WATER LEVELS, WAVE RUNUP AND COASTAL EROSION P. Ruggiero1 , P.D. Komar2, W.G. McDougal1 and R.A. Beach2 ABSTRACT A probabilistic model has been developed to analyze the susceptibilities of coastal properties to wave attack. Using an empirical model for wave runup, long term data of measured tides and waves are combined with beach morphology characteristics to determine the frequency of occurrence of sea cliff and dune erosion along the Oregon coast. Extreme runup statistics have been characterized for the high energy dissipative conditions common in Oregon, and have been found to depend simply on the deep-water significant wave height. Utilizing this relationship, an extreme-value probability distribution has been constructed for a 15 year total water elevation time series, and recurrence intervals of potential erosion events are calculated. The model has been applied to several sites along the Oregon coast, and the results compare well with observations of erosional impacts. INTRODUCTION Much of the Oregon coast is characterized by wide, dissipative, sandy beaches, which are backed by either large sea cliffs or sand dunes. This dynamic coast typically experiences a very intense winter wave climate, and there have been many documented cases of dramatic, yet episodic, sea cliff and dune erosion (Komar and Shih, 1993). A typical response of property owners following such erosion events is to build large coastal protection structures. Often these structures are built after a single erosion event, which is followed by a long period with no significant wave attack. From a coastal management perspective, it is of interest to be able to predict the expected frequency and intensity of such erosion events to determine if a coastal structure is an appropriate response. -
The Contribution of Wind-Generated Waves to Coastal Sea-Level Changes
1 Surveys in Geophysics Archimer November 2011, Volume 40, Issue 6, Pages 1563-1601 https://doi.org/10.1007/s10712-019-09557-5 https://archimer.ifremer.fr https://archimer.ifremer.fr/doc/00509/62046/ The Contribution of Wind-Generated Waves to Coastal Sea-Level Changes Dodet Guillaume 1, *, Melet Angélique 2, Ardhuin Fabrice 6, Bertin Xavier 3, Idier Déborah 4, Almar Rafael 5 1 UMR 6253 LOPSCNRS-Ifremer-IRD-Univiversity of Brest BrestPlouzané, France 2 Mercator OceanRamonville Saint Agne, France 3 UMR 7266 LIENSs, CNRS - La Rochelle UniversityLa Rochelle, France 4 BRGMOrléans Cédex, France 5 UMR 5566 LEGOSToulouse Cédex 9, France *Corresponding author : Guillaume Dodet, email address : [email protected] Abstract : Surface gravity waves generated by winds are ubiquitous on our oceans and play a primordial role in the dynamics of the ocean–land–atmosphere interfaces. In particular, wind-generated waves cause fluctuations of the sea level at the coast over timescales from a few seconds (individual wave runup) to a few hours (wave-induced setup). These wave-induced processes are of major importance for coastal management as they add up to tides and atmospheric surges during storm events and enhance coastal flooding and erosion. Changes in the atmospheric circulation associated with natural climate cycles or caused by increasing greenhouse gas emissions affect the wave conditions worldwide, which may drive significant changes in the wave-induced coastal hydrodynamics. Since sea-level rise represents a major challenge for sustainable coastal management, particularly in low-lying coastal areas and/or along densely urbanized coastlines, understanding the contribution of wind-generated waves to the long-term budget of coastal sea-level changes is therefore of major importance. -
Flow Separation and Vortex Dynamics in Waves Propagating Over A
China Ocean Eng., 2018, Vol. 32, No. 5, P. 514–523 DOI: https://doi.org/10.1007/s13344-018-0054-5, ISSN 0890-5487 http://www.chinaoceanengin.cn/ E-mail: [email protected] Flow Separation and Vortex Dynamics in Waves Propagating over A Submerged Quartercircular Breakwater JIANG Xue-liana, b, YANG Tiana, ZOU Qing-pingc, *, GU Han-bind aTianjin Key Laboratory of Soft Soil Characteristics & Engineering Environment, Tianjin Chengjian University, Tianjin 300384, China bState Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China cThe Lyell Centre for Earth and Marine Science and Technology, Institute for Infrastructure and Environment, Heriot-Watt University, Edinburgh, EH14 4AS, UK dSchool of Naval Architecture &Mechanical-Electrical Engineering, Zhejiang Ocean University, Zhoushan 316022, China Received October 22, 2017; revised June 7, 2018; accepted July 5, 2018 ©2018 Chinese Ocean Engineering Society and Springer-Verlag GmbH Germany, part of Springer Nature Abstract The interactions of cnoidal waves with a submerged quartercircular breakwater are investigated by a Reynolds- Averaged Navier–Stokes (RANS) flow solver with a Volume of Fluid (VOF) surface capturing scheme (RANS- VOF) model. The vertical variation of the instantaneous velocity indicates that flow separation occurs at the boundary layer near the breakwater. The temporal evolution of the velocity and vorticity fields demonstrates vortex generation and shedding around the submerged quartercircular breakwater due to the flow separation. An empirical relationship between the vortex intensity and a few hydrodynamic parameters is proposed based on parametric analysis. In addition, the instantaneous and time-averaged vorticity fields reveal a pair of vortices of opposite signs at the breakwater which are expected to have significant effect on sediment entrainment, suspension, and transportation, therefore, scour on the leeside of the breakwater. -
Numerical Modelling of Non-Linear Shallow Water Waves
university of twente faculty of engineering technology (CTW) department of engineering fluid dynamics Numerical modelling of non-linear shallow water waves Supervisor Author Prof. Dr. Ir. H.W.M. L.H. Lei BSc Hoeijmakers August 22, 2017 Preface An important part of the Master Mechanical Engineering at the University of Twente is an internship. This is a nice opportunity to obtain work experience and use the gained knowledge learned during all courses. For me this was an unique chance to go abroad as well. During my search for a challenging internship, I spoke to prof. Hoeijmakers to discuss the possibilities to go abroad. I was especially attracted by Scandinavia. Prof. Hoeijmakers introduced me to Mr. Johansen at SINTEF. I would like to thank both prof. Hoeijmakers and Mr. Johansen for making this internship possible. SINTEF, headquartered in Trondheim, is the largest independent research organisation in Scandinavia. It consists of several institutes. My internship was in the SINTEF Materials and Chemistry group, where I worked in the Flow Technology department. This department has a strong competence on multiphase flow modelling of industrial processes. It focusses on flow assurance market, multiphase reactors and generic flow modelling. During my internship I worked on the SprayIce project. In this project SINTEF develops a model for generation of droplets sprays due to wave impact on marine structures. The application is marine icing. I focussed on understanding of wave propagation. I would to thank all people of the Flow Technology department. They gave me a warm welcome and involved me in all social activities, like monthly seminars during lunch and the annual whale grilling. -
Internal Wave Breaking Dynamics and Associated Mixing in the Coastal
Internal Wave Breaking Dynamics and Associated Mixing in the Coastal Ocean Eiji Masunaga, Ibaraki University, Hitachi, Japan Robert S Arthur, Lawrence Livermore National Laboratory, Livermore, CA, United States Oliver B Fringer, Stanford University, Stanford, CA, United States © 2019 Elsevier Ltd. All rights reserved. Introduction 548 Internal Tide Breaking 548 Classification of Internal Bores 549 Canonical bores 549 Noncanonical bores 550 Intermittency of Internal Tide Breaking 550 Internal Solitary Wave Breaking 551 Breaker Classifications 551 Mixing and Mixing Efficiency 552 A note on the internal Iribarren number 552 Mass and Sediment Transport Driven by Internal Wave Breaking 552 Summary and Outlook 553 Acknowledgments 553 References 554 Further Reading 554 Introduction When internal waves interact with shallow slopes in the coastal ocean, they become highly nonlinear and break, accompanied by turbulent mixing. Internal wave breaking processes are similar to those of surface waves breaking on a beach (Fig. 1). However, despite their ubiquity in the coastal ocean, the complex, transient nature of breaking internal wave events makes them difficult to predict and observe. The small spatial and temporal scales associated with breaking internal waves and the resulting stratified turbulence only add to this greater difficulty. Recently developed observational approaches, including high-resolution towed instruments, mooring systems, and autonomous underwater vehicles, have revealed new insights into internal wave breaking processes, while improved laboratory and numerical modeling techniques have also been used to study their dynamics in more detail. In this article, the results of recent observational, laboratory, and numerical modeling studies of internal wave breaking are presented with a focus on turbulent mixing in shallow coastal regions. -
Toe Structures of Rubble Mound Breakwaters
Toe structures of rubble mound breakwaters Stability in depth limited conditions Master of Science Thesis R.E. Ebbens February 2009 Delft University of Technology Delta Marine Consultants Faculty of Civil Engineering and Geosciences Department Coastal Engineering Section Hydraulic Engineering Toe structures of rubble mound breakwaters Stability in depth limited conditions List of trademarks in this report: - DMC is a registered tradename of BAM Infraconsult bv, the Netherlands - Xbloc is a registered trademark of Delta Marine Consultants, the Netherlands - Xbase is a registered trademark of Delta Marine Consultants, the Netherlands The use of trademarks in any publication of Delft University of Technology does not imply any endorsement or disapproval of this product by the University. II Preface This thesis is the final report of a research project to obtain the degree of master of Science in the field of Coastal Engineering at Delft University of Technology. This report is an overview of the results of the investigation to toe stability of rubble mound breakwaters in depth limited conditions . This study, existing of literature and scale model experiments, is performed in collaboration with the department of coastal engineering of DMC (Delta Marine Consults). DMC is the trade name of BAM Infraconsult bv. The experiments are executed in the laboratory facilities of DMC in Utrecht. I would like to thank DMC for the facilities and support to accomplish this study. During this period a graduation committee, consisting of the following persons, supervised this thesis, for which I am grateful: Prof.dr.ir. M.J.F. Stive Delft University of Technology Prof.dr.ir. -
On the Distribution of Wave Height in Shallow Water (Accepted by Coastal Engineering in January 2016)
On the distribution of wave height in shallow water (Accepted by Coastal Engineering in January 2016) Yanyun Wu, David Randell Shell Research Ltd., Manchester, M22 0RR, UK. Marios Christou Imperial College, London, SW7 2AZ, UK. Kevin Ewans Sarawak Shell Bhd., 50450 Kuala Lumpur, Malaysia. Philip Jonathan Shell Research Ltd., Manchester, M22 0RR, UK. Abstract The statistical distribution of the height of sea waves in deep water has been modelled using the Rayleigh (Longuet- Higgins 1952) and Weibull distributions (Forristall 1978). Depth-induced wave breaking leading to restriction on the ratio of wave height to water depth require new parameterisations of these or other distributional forms for shallow water. Glukhovskiy (1966) proposed a Weibull parameterisation accommodating depth-limited breaking, modified by van Vledder (1991). Battjes and Groenendijk (2000) suggested a two-part Weibull-Weibull distribution. Here we propose a two-part Weibull-generalised Pareto model for wave height in shallow water, parameterised empirically in terms of sea state parameters (significant wave height, HS, local wave-number, kL, and water depth, d), using data from both laboratory and field measurements from 4 offshore locations. We are particularly concerned that the model can be applied usefully in a straightforward manner; given three pre-specified universal parameters, the model further requires values for sea state significant wave height and wave number, and water depth so that it can be applied. The model has continuous probability density, smooth cumulative distribution function, incorporates the Miche upper limit for wave heights (Miche 1944) and adopts HS as the transition wave height from Weibull body to generalised Pareto tail forms. -
Coastal Dynamics 2017 Paper No. 093 409 DEPTH-INDUCED WAVE
Coastal Dynamics 2017 Paper No. 093 DEPTH-INDUCED WAVE BREAKING CRITERIA IN DEPENDENCE ON WAVE NONLINEARITY IN COASTAL ZONE 1 Sergey Kuznetsov1, Yana Saprykina Abstract On the base of data of laboratory and field experiments, the regularities in changes in the relative limit height of breaking waves (the breaking index) from peculiarities of nonlinear wave transformations and type of wave breaking were investigated. It is shown that the value of the breaking index depends on the relative part of the wave energy in the frequency range of the second nonlinear harmonic. For spilling breaking waves this part is more than 35% and the breaking index can be taken as a constant equal to 0.6. For plunging breaking waves this part of the energy is less than 35% and the breaking index increases with increasing energy in the frequency range of the second harmonic. It is revealed that the breaking index depends on the phase shift between the first and second nonlinear harmonic (biphase). The empirical dependences of the breaking index on the parameters of nonlinear transformation of waves are proposed. Key words: wave breaking, spilling, plunging, limit height of breaking wave, breaking index, nonlinear wave transformation 1. Introduction Wave breaking is the most visible process of wave transformation when the waves approaching to a coast. The main reason is decreasing of water depth and increasing of wave energy in decreasing water volume. During breaking a wave energy is realized in a surf zone influencing on a sediments transport and on the changes of coastal line and bottom relief. The depth-induced wave breaking criteria which are used in modern numerical and engineering models are usually based on classical dependence between height of breaking wave (H) and depth of water (h) in breaking point: H= γh, (1) where γ – breaking index is adjustable constant and γ=0.8 is suitable for most wave breaking cases (Battjes, Janssen, 1978).