DOCSLIB.ORG

Young Coastal Scientists and Engineers Conference – Americas

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Young Coastal Scientists and Engineers Conference – Americas Young Coastal Scientists and Engineers Conference – Americas CONFERENCE AGENDA Dauphin Island Sea Lab, Alabama, USA August 21­23, 2017 4th Young Coastal Scientists and Engineers Conference – Americas Dauphin Island Sea Lab, Alabama, USA, August 21­23, 2017 Arrival: Sunday August 20 Check in AFTER 4PM at Dauphin Island Sea Lab Faculty House #1 (on map: 18.1 ­ Greeters House) Campus map: http://www.disl.org/images/uploads/Facilities_Map_2016.pdf 7:00 pm – Informal gathering under Horizon Hall ______________________________________________________________________________ Day 1: Monday, August 21 (All conference talks are held in the Shelby Auditorium) 8:00 am – Continental breakfast in Auditorium Atrium 8:30 am – Opening remarks Kelly Dorgan, Dauphin Island Sea Lab Allison Penko, U.S. Naval Research Laboratory Meg Palmsten, U.S. Naval Research Laboratory 8:50 am – Keynote Lecture Hilary Stockdon, U.S. Geological Survey Today’s Scientists Solving Tomorrow’s Problems 9:30 am – Session 1 – Estuaries and tidal environments Jeff Coogan, Role of wind forcing on estuary length and circulation in a river­dominated, microtidal estuary, Mobile Bay Braulio Juarez, Wind­driven flow in a coastal plain estuary Steven L. Dykstra, Spatial Variability of Tides due to Discharge Gisselle E. Guerra, Saltwater intrusion in a subtropical estuary, as predicted by a Markov­chain model 10:30 am – Break 10:45 am – Session 2 – Estuaries and waves Katherine M. Haynes, Field measurements of boat wake attenuation in coastal salt marshes Jin Young Kim, Retreat of Galveston Bay Wetlands by Wind Induced Waves Aaron Kenny, A Laboratory Study on Mangrove Forest Wave Attenuation for use in Living Shorelines William J. Pringle, Large scale tidal dynamics modelling in the Indian and Western Pacific Ocean Basins 12:00 pm – Lunch at May’s Café and eclipse watching 2 4th Young Coastal Scientists and Engineers Conference – Americas Dauphin Island Sea Lab, Alabama, USA, August 21­23, 2017 2:00 pm – Session 3 – Structures and restoration Lila J. Lasecki, D’Olive Creek restoration Caleb Barth, Incorporation of Structural reliability assessment into upgrade and renewal decisions for port and marine structures Justin A. Bartusek, Barbours Cut Dock Expansion & San Jacinto Marsh Restoration Project Victoria Curto, Mobile Bay Bridge storm surge impact analysis 3:00 pm – Break 3:15 pm – Session 4 – Beach nourishment and living shorelines Katie Finegan, Town of Oak Island Feasibility Study: A Case for Combining Beach and Inlet Issues Into an Overall Management Program Brittany E. McMillan, Life cycle cost analyses of beach nourishment on Dauphin Island, AL Joshua Todd, Living Shoreline Demonstration Project – Recent Experience on Design and Construction 4:00 pm – Industry Talk Kevin Frost, Nortek USA, Boston, USA 5:00 pm – Icebreaker, under DISL classrooms 6:30 pm – Shrimp boil at May’s Café and beach party ______________________________________________________________________________ Day 2: Tuesday, August 22 8:00 am – Continental breakfast in Auditorium Atrium 8:45 am – Keynote Lecture Stephanie Smallegan, University of South Alabama Engineering the pathway to a resilient barrier island under sea level rise 9:30 am – Session 5 ­ Sediment transport Yeulwoo Kim, An Eulerian three­phase model for sheet flow under breaking waves Meagan E. Wengrove, University of New Hampshire, Do sand ripples matter to larger coastal change? Ryan S. Mieras, Large­scale experimental observations of wave­induced sediment transport over a surf zone sandbar 3 4th Young Coastal Scientists and Engineers Conference – Americas Dauphin Island Sea Lab, Alabama, USA, August 21­23, 2017 Tynon Briggs, Calculating aeolian sediment dynamics relative to varying concentrations of the gravel lag 10:30 am – Break 10:45 am – Session 6 – Sediment transport Tongtong Xu, Exploring the influence of obliquely oriented shoreface­connected ridges on alongshore sediment transport and shoreline change Huidi Liang, Influence of land reclamation projects on sediment transport process of channel­shoal system Munitions Mobility Demetra Cristaudo, Preliminary results of a munition mobility study in the swash Stephanie E. Gilooly, Resolving the Role of the Dynamic Pressure in the Burial, Exposure, Scour, and Mobility of Underwater Munitions 12:00 pm – Lunch at May’s Café 2:00 pm – Professional Development Activity Allison Penko, U.S. Naval Research Laboratory Communicating Science: The Elevator Pitch and Speed Networking 3:15 pm – Session 7 ­ Beach morphology Cody L. Johnson, Morphological Modeling of Low­Dune Barrier System Changes due to Hurricane Forcing Youn­Kyung Song, Numerical Simulation of Ridge Evolution based on Field Data from a Steep Meso­Tidal Engineered Beach Jose C. Tuz­Pech, Impact of a permeable groyne field on littoral transport: an experimental study 4:00 pm – Break 4:15 pm – Session 8 – Coastal geology Robert Hollis, Constraining Holocene evolution of the Petit Bois Island System Nina Schulze, Holocene evolution and sediment provenance of Horn Island, Mississippi Clayton Dike, Late Quarternary paleochannels and deltas along the Mississippi­Alabama shelf 5:00 pm – Industry Talk Doug Shillinger, RBR Limited, Ottawa, Canada 6:00 pm – Dinner at The Estuarium 4 4th Young Coastal Scientists and Engineers Conference – Americas Dauphin Island Sea Lab, Alabama, USA, August 21­23, 2017 ______________________________________________________________________________ Day 3: Wednesday, August 23 8:00 am – Continental breakfast in Auditorium Atrium 8:30 am – Keynote Lecture Brian Dzwonkowski, Dauphin Island Sea Lab Impacts of river discharge on the coastal environment: Perspectives from a long­term mooring system in the Mississippi Bight 9:15 am – Session 9 – Waves & Turbulence Liangyi Yue, University of Delaware, A high performance pseudo­spectral solver for turbulent flow Ling Zhu, Louisiana State University, Attenuation of nonlinear waves by rigid vegetation: Comparison of different wave theories Byoungjoon Na, Effect of void fraction to energy dissipation in deep water plunging breaking waves Rafael Mezo­Padilla, Hydrodynamic circulation on the western gulf of mexico using self­organizing maps 10:15 am – Break 10:30 am – Session 10 – Waves Ramy Y. Marmoush, Laboratory experiments of wave energy dissipation and longshore current generation on a sandy beach Dylan Sanderson, Use of a Probabilistic Storm Database in Monte Carlo Lifecycle Modeling Seongho Ahn, Wave energy resource assessments and a preliminary classification for US coastal waters Sarah M. Trimble, New possibilities for predicting and mitigation deadly rip currents 11:30 am – Lunch at May’s Café 1:00 pm – Group photo 1:30 pm – Session 11 – Tsunamis Wei­Liang Chuang, Pressure, force, and fluid velocity distributions due to tsunami bore impact on a simplified coastal building at various headings India Woodruff, Developing a model of the 2013 U.S. East Coast Meteotsunami 2:00 pm – Keynote speaker Scott Douglass – South Coast Engineers 5 4th Young Coastal Scientists and Engineers Conference – Americas Dauphin Island Sea Lab, Alabama, USA, August 21­23, 2017 2:45 pm – Closing remarks Jack Puleo, University of Delaware 3:30 pm – Dauphin Island geomorphology walk 6:00 pm – Dinner at Islanders THANK YOU to our 2017 sponsors!! http://www.gldd.com https://rbr­global.com http://www.nortekusa.com http://www.vtisl.com https://www.mottmac.com http://www.baird.com http://www.mbakerintl.com 6 4th Young Coastal Scientists and Engineers Conference – Americas Dauphin Island Sea Lab, University of South Alabama, August 21-23, 2017 ROLE OF WIND FORCING ON ESTUARY LENGTH AND CIRCULATION IN A RIVER-DOMINATED, MICROTIDAL ESTUARY, MOBILE BAY, AL. Jeff Coogan, University of South Alabama, [email protected] Brian Dzwonkowski, University of South Alabama, [email protected] Using long-term records (~10 years) of salinity and 300 days of ADCP data, aspects of the estuary length and salinity flux were evaluated in Mobile Bay under a range of river discharge, tidal, and wind conditions. The temporal variability in the salinity structure was represented by 1/7 the estuary length, and showed a strong relationship to river forcing of �� , similar to values reported in San Francisco Bay. In addition, local wind forcing was observed to play a significant 1/7 role in modifying this �� relationship. Estuary length responded asymmetrical to local wind with up-estuary (down-estuary) wind reducing (increasing) salinity intrusion. This system wide response was consistent with local subtidal circulation exchange flow measured by the ADCP. During down-estuary wind conditions the flow was strongly sheared, which would enhance salt intrusion. During up-estuary wind conditions, two-layer flow was reduced (and inhibited under high winds) which would impede exchange and shorten the estuary length. To further explore potential salinity transport changes associated with the wind, a 1D salinity flux was calculated using the ADCP and salinity profile data. The results suggest that the wind forcing is not changing the salt storage within the bay, but instead wind is straining the density field through lengthening and shortening the overall estuary length. These results indicate that in a shallow microtidal system, wind can play a large role in modifying the estuary length and intrusion. 4th Young Coastal Scientists and Engineers Conference – Americas Dauphin Island Sea Lab, University of South Alabama, August 21-23, 2017 Wind-driven flow in a coastal plain estuary Braulio Juarez, University of Florida, [email protected]
Load more

Recommended publications
  • 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
    [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]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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).
    [Show full text]
  • The Influence of Blade Pitch Angle on the Performance of a Model
    Energy 102 (2016) 166e175 Contents lists available at ScienceDirect Energy journal homepage: www.elsevier.com/locate/energy The influence of blade pitch angle on the performance of a model horizontal axis tidal stream turbine operating under waveecurrent interaction * Tiago A. de Jesus Henriques a, Terry S. Hedges a, Ieuan Owen b, Robert J. Poole a, a School of Engineering, University of Liverpool, Brownlow Hill, L69 3GH, United Kingdom b School of Engineering, University of Lincoln, Brayford Pool, LN6 7TS, United Kingdom article info abstract Article history: Tidal stream turbines offer a promising means of producing renewable energy at foreseeable times and of Received 11 June 2015 predictable quantity. However, the turbines may have to operate under wave-current conditions that Received in revised form cause high velocity fluctuations in the flow, leading to unsteady power output and structural loading and, 18 January 2016 potentially, to premature structural failure. Consequently, it is important to understand the effects that Accepted 10 February 2016 wave-induced velocities may have on tidal devices and how their design could be optimised to reduce Available online xxx the additional unsteady loading. This paper describes an experimental investigation into the performance of a scale-model three- Keywords: Tidal energy bladed HATT (horizontal axis tidal stream turbine) operating under different wave-current combinations HATT (Horizontal axis tidal turbine) and it shows how changes in the blade pitch angle can reduce wave loading. Tests were carried out in the ADV (Acoustic Doppler velocimeter) recirculating water channel at the University of Liverpool, with a paddle wavemaker installed upstream Wave-current interaction of the working section to induce surface waves travelling in the same direction as the current.
    [Show full text]
  • Thesis Submitted to the University of Nottingham for the Degree of Doctor of Philosophy, October, 1982
    UNIVERSITY OF NOTTINGHAM DEPARTMENT OF CIVIL ENGINEERING OSCILLATORY BOUNDARY LAYER OVER FIXED ROUGH BEDS by S. M. BORGHEI, B. Sc. Thesis submitted to the University of Nottingham for the degree of Doctor of Philosophy, October, 1982. I i. ABSTRACT The accurate study of characteristics of the flow under gravity waves has become of prime importance due to the growing demand for structural engineering designs in the coastal environment. Although many investigations have been carried out, the progress of fundamental research was slow due to the lack of an adequate velocity measuring instrument. However in recent years, the development of the Laser Doppler Velocimeter has made it possible to obs- erve the orbital velocity very close to a bed without dis- turbing the flow. This technique was used in this invest- igation, in which observations of the oscillatory flow under gravity waves were carried out above smooth, two- dimensional and three-dimensional rough beds. For the smooth bed case it was found that the velocity profile throughout the depth was well presented by the Stokes second order shear wave equation, except that the theoretical predictions underestimated the observed results, and a linear relationship was obtained for the velocity co- efficients between the two sets of values. As for mean velocity the profile was in close agreement with the Longuet- Higgins conduction solution, and it was found to have a negative value (in opposite direction to wave progression) in the bulk of fluid and always positive values within the boundary layer. ii. The rough beds made little change to the flow in the bulk of fluid.
    [Show full text]
  • Near-Shore Sediment Transport Under Cnoidal Waves Using Particle Image Velocimetry
    Near-Shore Sediment Transport Under Cnoidal Waves Using Particle Image Velocimetry by Jenna Katrina A thesis submitted to the College of Engineering and Science of Florida Institute of Technology in partial fulfillment of the requirements for the degree of Master of Science in Ocean Engineering Melbourne, Florida July, 2021 We the undersigned committee hereby approve the attached thesis, “Near-Shore Sediment Transport Under Cnoidal Waves Using Particle Image Velocimetry.” by Jenna Rose Katrina _________________________________________________ Robert J. Weaver, Ph.D. Associate Professor Ocean Engineering and Marine Sciences Major Advisor _________________________________________________ Stephen Wood, Ph.D. Professor Ocean Engineering and Marine Sciences Committee Member _________________________________________________ Michael Splitt, M.S. Assistant Professor College of Aeronautics Committee Member _________________________________________________ Richard Aronson Ph.D. Professor and Department Head Ocean Engineering and Marine Sciences Abstract Title: Near-Shore Sediment Transport Under Cnoidal Waves Using Particle Image Velocimetry Author: Jenna Katrina Advisor: Robert J. Weaver, Ph.D. With future trends showing a higher percentage of the human population living along the coast, coastal resilience is a significant topic of concern for many researchers. The purpose of this research was to analyze near-shore sediment transport under different wave parameters using the technique of Particle Image Velocimetry (PIV) and laboratory studies
    [Show full text]
  • An Extension to the Linear Shallow Water Equation
    An extension to the linear shallow water equation R. Porter School of Mathematics, University of Bristol, Bristol, BS8 1TW, UK. [email protected] 1 Introduction The linearised Shallow Water Equation (SWE) approximates the propagation of surface gravity waves over variable bathymetry z = −h(x,y) in the long wavelength limit, λ ≫ h, and is commonly expressed (e.g. Stoker (1957)) in the form g∇ · (h∇ζ)= ζtt (1) where g is acceleration due to gravity, ∇ = (∂x, ∂y) and ζ(x,y,t) is the free surface elevation assumed to be small in the sense that |∇ζ|∼ ζ/λ ≪ (h/λ)3. This latter assumption justifies the linearisation of the governing equations in what follows. When time-harmonic motion is considered and ζ(x,y,t)= ℜ{η(x,y)e−iωt}, (1) is transformed to ∇ · (h∇η)+ Kη = 0 (2) where K = ω2/g. The local wavenumber k(x,y) = 2π/λ, determined by the local depth h(x,y) as though the bed were flat, satisfies k2h = K and this corresponds to the long wavelength (kh → 0) limit of the unapproximated water wave dispersion relation k tanh kh = K. Under the SWE waves are non-dispersive. The SWE is practically limited to modelling of very long waves, for example tidal simulations or tsunami wave propagation. In spite of this the SWE has received renewed recent attention on account of its structural similarity to 2nd order partial differential equations describing waves in two-dimensional acoustics and TM- or TE-polarised electromagnetics and this analogue has seen it used as a model for producing exotic effects in water waves such as invisibility cloaking, negative refraction, wave-shifting and other wave control mechanisms (see, for e.g., the review in Porter (2018).) Often studies of these topics are accompanied by experiments which are of questionable quality – understandable not least because the conditions of shallow water theory are not easily met.
    [Show full text]
  • Recurrence in Truncated Boussinesq Models for Nonlinear Waves in Shallow Water
    JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 95, NO. C7, PAGES 11,547-11,556, JULY 15, 1990 Recurrence in Truncated Boussinesq Models for Nonlinear Waves in Shallow Water STEVE ELGAR Department of Electrical and Computer Engineering, Washington State University, Pullman M. H. FREILICH Jet Propulsion Laboratory, Pasadena, California R. T. GUZA Center for Coastal Studies, Scripps Institution of Oceanography, La Jolla, California The rapid spatial recurrence of weakly nonlinear, weakly dispersive, progressive shallow-water waves is examined with numerical simulations using a discretized and truncated (i.e., finite number of allowed frequency modes) form of the Boussinesq equations. Laboratory observations of sandbar formation under recurring, mechanically generated monochromatic waves with small Ursell number have motivated others to suggestthat recurrence in naturally occurring random waves contributes to the establishmentof periodic longshore sandbarson beaches. The present study primarily examines recurrence in wave fields with Ursell number O(1) and characterizes the sensitivity of recurrence to initial spectral shapeand number of allowed frequency modes. It is shown that rapid spatial recurrence is not an inherent property of discretized and truncated Boussinesqsystems for evolution distances of 10-50 wavelengths. When a small number of Fourier modes are used to represent an initially monochromatic wave field with significant nonlinearity (the Ursell number is O(1)), there is a trend toward recurrence of initial modal amplitudes, consistent with the known periodic solutions for a primary wave and its harmonic. However, for 32 modes or more, numerical simulations indicate only a few cycles of a damped recurrence, followed by disordered evolution of the Fourier amplitudes. For initial conditions similar to ocean field measurements of frequency-sorted swell with Ursell number O(1) and many (>300) modes in the numerical model, the Fourier coefficientsof the wave field do not recur rapidly.
    [Show full text]
  • A Hybrid Spectral/DG Method for Solving the Phase-Averaged Ocean Wave Equation: Algorithm and Validation ⇑ B
    Journal of Computational Physics 231 (2012) 4921–4953 Contents lists available at SciVerse ScienceDirect Journal of Computational Physics journal homepage: www.elsevier.com/locate/jcp A hybrid spectral/DG method for solving the phase-averaged ocean wave equation: Algorithm and validation ⇑ B. Yildirim a, George Em Karniadakis b, a School of Engineering, Brown University, Providence, RI 02912, USA b Division of Applied Mathematics, Brown University, Providence, RI 02912, USA article info abstract Article history: We develop a new high-order hybrid discretization of the phased-averaged (action bal- Received 25 July 2011 ance) equation to simulate ocean waves. We employ discontinuous Galerkin (DG) discret- Received in revised form 3 April 2012 ization on an unstructured grid in geophysical space and Fourier-collocation along the Accepted 6 April 2012 directional and frequency coordinates. The original action balance equation is modified Available online 25 April 2012 to facilitate absorbing boundary conditions along the frequency direction; this modifica- tion enforces periodicity at the frequency boundaries so that the fast convergence of Fou- Keywords: rier-collocation holds. In addition, a mapping along the directional coordinate is introduced Action balance equation to cluster the collocation points around steep directional spectra. Time-discretization is Absorbing boundary layer Spectral element accomplished by the TVD Runge–Kutta scheme. The overall convergence of the scheme Unstructured grid is exponential (spectral). We successfully verified and validated the method against several analytical solutions, observational data, and experimental results. Ó 2012 Elsevier Inc. All rights reserved. 1. Introduction Wave prediction models fall into two categories: phased-averaged and phase-resolving. The phased-averaged wave mod- els solve for the energy density (or action density) to obtain important parameters, such as the significant wave height, through integration of the energy density.
    [Show full text]