Nearshore Current Pattern and Rip Current Occurrence at Jungmun Beach, Jeju by Numerical Computation 1. Introduction
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Acoustic Nonlinearity in Dispersive Solids
ACOUSTIC NONLINEARITY IN DISPERSIVE SOLIDS John H. Cantrell and William T. Yost NASA Langley Research Center Mail Stop 231 Hampton, VA 23665-5225 INTRODUCTION It is well known that the interatomic anharmonicity of the propagation medium gives rise to the generation of harmonics of an initially sinusoidal acoustic waveform. It is, perhaps, less well appreciated that the anharmonicity also gives rise to the generation of a static or "dc" component of the propagating waveform. We have previously shown [1,2] that the static component is intrinsically linked to the acoustic (Boussinesq) radiation stress in the material. For nondispersive solids theory predicts that a propagating gated continuous waveform (acoustic toneburst) generates a static displacement pulse having the shape of a right-angled triangle, the slope of which is linearly proportional to the magnitude and sign of the acoustic nonlinearity parameter of the propagation medium. Such static displacement pulses have been experimentally verified in single crystal silicon [3] and germanium [4]. The purpose of the present investigation is to consider the effects of dispersion on the generation of the static acoustic wave component. It is well known that an initial disturbance in media which have both sufficiently large dispersion and nonlinearity can evolve into a series of solitary waves or solitons [5]. We consider here that an acoustic tone burst may be modeled as a modulated continuous waveform and that the generated initial static displacement pulse may be viewed as a modulation-confined disturbance. In media with sufficiently large dispersion and nonlinearity the static displacement pulse may be expected to evolve into a series of modulation solitons. -
Waves and Structures
WAVES AND STRUCTURES By Dr M C Deo Professor of Civil Engineering Indian Institute of Technology Bombay Powai, Mumbai 400 076 Contact: [email protected]; (+91) 22 2572 2377 (Please refer as follows, if you use any part of this book: Deo M C (2013): Waves and Structures, http://www.civil.iitb.ac.in/~mcdeo/waves.html) (Suggestions to improve/modify contents are welcome) 1 Content Chapter 1: Introduction 4 Chapter 2: Wave Theories 18 Chapter 3: Random Waves 47 Chapter 4: Wave Propagation 80 Chapter 5: Numerical Modeling of Waves 110 Chapter 6: Design Water Depth 115 Chapter 7: Wave Forces on Shore-Based Structures 132 Chapter 8: Wave Force On Small Diameter Members 150 Chapter 9: Maximum Wave Force on the Entire Structure 173 Chapter 10: Wave Forces on Large Diameter Members 187 Chapter 11: Spectral and Statistical Analysis of Wave Forces 209 Chapter 12: Wave Run Up 221 Chapter 13: Pipeline Hydrodynamics 234 Chapter 14: Statics of Floating Bodies 241 Chapter 15: Vibrations 268 Chapter 16: Motions of Freely Floating Bodies 283 Chapter 17: Motion Response of Compliant Structures 315 2 Notations 338 References 342 3 CHAPTER 1 INTRODUCTION 1.1 Introduction The knowledge of magnitude and behavior of ocean waves at site is an essential prerequisite for almost all activities in the ocean including planning, design, construction and operation related to harbor, coastal and structures. The waves of major concern to a harbor engineer are generated by the action of wind. The wind creates a disturbance in the sea which is restored to its calm equilibrium position by the action of gravity and hence resulting waves are called wind generated gravity waves. -
CHAPTER 100 Another Approach to Longshore Current Evaluation M.A
CHAPTER 100 Another approach to longshore current evaluation M.A. Losada, A. Sanchez-Arcilla and C. Vidal A simple model to predict the longshore current velocity at the breaker line on a beach with oblique wave incidence, is presented. The model balances driving and resistance terms (gradients of radiation and turbulent Reynolds stresses and bottom friction) to get a general expression for the velocity. This equation shows explicitely the influence of Iribarren's parameter on longshore current generation. It has been tested with field and laboratory data, obtaining a reasonable fit to measured values. The resulting (predictive) model is expected to be valid for any type of breakers though the calibration has been mainly done for spilling and plunging types, due to the scarcity of results for other breakers. 1.- INTRODUCTION Longshore currents in the surf zone have been acceptably modelled using the radiation stress concept (Longuet-Higgins,1970). The longshore-trust (Nw/m ) due to an oblique wave approach, given by the gradient of the radiation stress, is balanced (in stationary and longshore-uniform conditions) by bottom friction and horizontal mixing (Bowen, 1969), (Longuet-Higgins, 1970). The gradient of the radiation stress is evaluated using sinusoidal theory (as a first approximation for slowly varying depths) and turns out to be proportional to the local rate of energy dissipation, D (joules/(m x sec)), regardless of its origin. Inside the surf zone a significant fraction of D comes from wave breaking because the turbulence associated to the breaking process is responsible for most of the dissipated energy. Bottom friction plays a minor role in this context, being important only in special cases (e.g. -
Chapter 187 Wave Breaking and Induced Nearshore
CHAPTER 187 WAVE BREAKING AND INDUCED NEARSHORE CIRCULATIONS Ole R. S0rensen f, Hemming A. Schafferf, Per A. Madsenf, and Rolf DeigaardJ ABSTRACT Wave breaking and wave induced currents are studied in two horizontal dimen- sions. The wave-current motion is modelled using a set of Boussinesq type equations including the effects of wave breaking and runup. This is done with- out the traditional splitting of the phenomenon into a wave problem and a current problem. Wave breaking is included using the surface roller concept and runup is simulated by use of a modified slot-technique. In the environment of a plane sloping beach two different situations are studied. One is the case of a rip channel and the other concerns a detached breakwater parallel to the shoreline. In both situations wave driven currents are generated and circulation cells appear. This and many other nearshore physical phenomena are described qualitatively correct in the simulations. 1. INTRODUCTION State of the art models for wave driven currents are based on a splitting of the phenomenon into a linear wave problem, described e.g. by the mild-slope equation, and a current problem, described by depth-integrated flow equations including radiation stress. Wave-current interaction effects such as current re- fraction and wave blocking may be included in these systems by successive and iterative model executions. A more direct approach to the problem would be the use of a time do- main Boussinesq model which automatically includes the combined effects of wave-wave and wave-current interaction in shallow water without the need for explicit formulations of the radiation stress. -
A Nonlinear Formulation of Radiation Stress and Applications to Cnoidal
A Nonlinear Formulation of Radiation Stress and Applications to Cnoidal Shoaling Martin O. Paulsen Henrik Kalisch · g Abstract In this article we provide formulations of energy flux and radiation stress consistent with the scaling regime of the Korteweg-de Vries (KdV) equation. These quantities can be used to describe the shoaling of cnoidal waves approaching a gently sloping beach. The transformation of these waves along the slope can be described using the shoaling equations, a set of three nonlinear equations in three unknowns: the wave height H, the set-downη ¯ and the elliptic parameter m. We define a numerical algorithm for the efficient solution of the shoaling equations, and we verify our shoaling formulation by comparing with experimental data from two sets of experiments as well as shoaling curves obtained in previous works. Keywords: Surface waves KdV equation Conservation laws Radiation stress Set-down · · · · 1 Introduction In the present work, the development of surface waves across a gently sloping bottom is in view. Our main goal is the prediction of the wave height and the set-down of a periodic wave as it enters an area of shallower depth. This problem is known as the shoaling problem and has a long history, with contributions from a large number of authors going back to Green and Boussinesq. In order to reduce the problem to the essential factors, we make a number of simplifying as- sumptions. First, the bottom slope is small enough to allow the waves to continuously adjust to the changing depth without altering their basic shape or breaking up. -
Beach Accretion with Erosive Waves : "Beachbuilding" Accrétion Sur Les Plages Avec Vagues Érosives : "La Technique De Construction De Plage "
Beach accretion with erosive waves : "Beachbuilding" Accrétion sur les plages avec vagues érosives : "la technique de construction de plage " Melville W. BEARDSLEY US Army Corps of Engineers, Beachbuilder Company Roger H. CHARLIER HAECON Inc., Free University of BRUSSELS - Belgique Abstract : A new method of beach preservation, theBeachbuilder Technique , proposes to harness the energy of normally erosive waves to produce beach accretion. A "flow control sheet" located in the surf zone directs the flow of swash and backwash causing net transport of sediment onto the beach. Beach and surf zone profiles created by the wave-tank tests show that the technique leads to accretion on this beach, during every test run with erosive waves. The successful wave tank results should reproduce on actual beaches ; rapid accretion on real beaches can be expected from the scaled wave-tank results. It is anticipated that by use of this new technique, costs of beach preservation would be cut by as much as 66%. Furthermore, rapid beach accretion, quick reaction, high mobility, good durability, «nd provision of employment for making the installations are major benefits to be derived. K e y w o rd s . Erosion - Waves - Accretion - Nourishment - Beach Résum é : Une nouvelle méthode de protection de plages, Techniquela de Construction de Plage, est proposée. Un "drap de contrôle d’écoulement" placé dans la zone des brisants dirige le clapotis et le remous et provoque un transport de sédiment vers la plage. Les profils de plage et de brisants créés par des tests conduits en bassins montrent que la technique produit une accumulation sur la plage pendant chaque test avec vagues érosives. -
Air-Sea Interactions - Jacques C.J
OCEANOGRAPHY – Vol.I - Air-Sea Interactions - Jacques C.J. Nihoul and François C. Ronday AIR-SEA INTERACTIONS Jacques C.J. Nihoul and François C. Ronday University of Liège, Belgium Keywords: Wind waves, fully developed sea, tsunamis, swell, clapotis, seiches, littoral current, rip current, air-sea interactions, sea slicks, drag coefficient. Contents 1. Introduction 2. Wind waves 3. Air-Sea Interactions Glossary Bibliography Biographical Sketches Summary The marine system is part of the general geophysical system. Physical and chemical boundary interactions at the air-sea interface are essential factors in the marine system's dynamics Wind blowing over the sea generates surface waves and energy is transferred from the wind to the ocean's upper layer. The fluxes of the momentum, heat, chemicals... at the air-sea interface are usually parameterized by bulk formula which assumed that the fluxes are proportional to the magnitude of the wind velocity at some reference height (10m, say). Although these bulk formulas have abundantly been used in several generations of models, they can only give a rough representation of the mechanisms of air-sea interactions where wave’s field’s characteristics, bubbles and spray, surface slicks, heavy rainfalls...can play a significant role. 1. Introduction Incoming short wave solar radiation and outgoing long wave radiation emitted by the earth surface, mediated by back and forth long wave emissions by clouds and aerosols - with its spatial variability due, in particular, to the earth’s sphericity - constitute -
The Three-Dimensional Current and Surface Wave Equations
1978 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 33 The Three-Dimensional Current and Surface Wave Equations GEORGE MELLOR Princeton University, Princeton, New Jersey (Manuscript received 26 April 2002, in ®nal form 4 March 2003) ABSTRACT Surface wave equations appropriate to three-dimensional ocean models apparently have not been presented in the literature. It is the intent of this paper to correct that de®ciency. Thus, expressions for vertically dependent radiation stresses and a de®nition of the Doppler velocity for a vertically dependent current ®eld are obtained. Other quantities such as vertically dependent surface pressure forcing are derived for inclusion in the momentum and wave energy equations. The equations include terms that represent the production of turbulence energy by currents and waves. These results are a necessary precursor for three-dimensional ocean models that handle surface waves together with wind- and buoyancy-driven currents. Although the third dimension has been added here, the analysis is based on the assumption that the depth dependence of wave motions is provided by linear theory, an assumption that is the basis of much of the wave literature. 1. Introduction pressure so that their results differ from mine and, after vertical integration, differ from the corresponding terms In the last several decades there has been signi®cant in Phillips (1977). They did not address three-dimen- progress in the understanding and numerical modeling sional effects on the wave energy equation. of ocean surface waves (e.g., Longue-Higgins 1953; To contrast the developments in this paper with con- Phillips 1977; WAMDI Group 1988; Komen et al. -
Two-Dimensional Wave-Making Problem C.R. Chou, R.S. Shih, J.Z. Yim Department of Harbor and River Engineering, National Taiwan O
Transactions on Modelling and Simulation vol 12, © 1996 WIT Press, www.witpress.com, ISSN 1743-355X Two-dimensional wave-making problem C.R. Chou, R.S. Shih, J.Z. Yim Department of Harbor and River Engineering, National Taiwan Ocean University, Bee-Ning Road 2, Keelung 202, Taiwan Abstract In this study, generation of two dimensional nonlinear waves is simulated numerically using boundary clement method. The present scheme is based on a Lagrangian description together with finite differencing of the time step. An algorithm to generate waves with any prescribed form is also implantec in the scheme. The numerical model was first verified by studying the case of finite amplitude waves impinging against a vertical wall. Time histories of evolution of a soliton running up on a sloping beach, as well as over a submerged obstacle are then presented. 1 Introduction Problems associated with generation, propagation and deformatio.i have been studied numerically by many researchers. Based on a mixed Eulerian- Lagrangian method, solitary wave interacting with a gentle slope, and wave breaking on water of gradually varying depth are simulated numerically in two- dimensional fluid region by Sujjino and Tosaka[l], Ouyama[2] explored soli- tary wave set up on a slope by boundary element method. Pedersen & Gjevik[3 ] developed a numerical model to study run-up of long waves governed by a set of Boussinesq equations. Lagrangian coordinate description was used to sim- plify the numerical treatment of a moving shoreline. Based on the Green';* formular, Nakayama[4] applied a new boundary element technique to analyze nonlinear water wave problems. -
Title on the Effect of Wind on Wave Overtopping on Vertical Seawalls Author(S)
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Kyoto University Research Information Repository On the Effect of Wind on Wave Overtopping on Vertical Title Seawalls Author(s) IWAGAKI, Yuichi; TSUCHIYA, Yoshito; INOUE, Masao Bulletin of the Disaster Prevention Research Institute (1966), Citation 16(1): 11-30 Issue Date 1966-09 URL http://hdl.handle.net/2433/124717 Right Type Departmental Bulletin Paper Textversion publisher Kyoto University Bull. Disas. Prey. Res. Inst. Kyoto Univ., Vol. 16, Part 1, No. 105, Sept., 1965 On the Effect of Wind on Wave Overtopping on Vertical Seawalls By Yuichi IWAGAKI, Yoshito TSUCHIYA and Masao INOUE (Manuscript received June 30. 1966) Synopsis In designing seawalls and seadikes, it is very important to estimate the quantity of wave overtopping on them as exactly as possible. The estimation, however, is difficult because of complicated phenomenaof wave overtopping, and in particular the effect of wind on wave overtopping is entirely unknown. With this in view, the authors have begun the study to disclose the effect of wind on wave overtopping quantitatively. As a first step of the study. the present paper describes some experimental results of wave overtoppingon vertical seawalls for the wave steepnesses of 0.01 and 0.02, accompanied with wind created by a high-speed wind-wave tunnel, which is 0.8 m wide. 2.3m to 4.0 m high and 40 m long, having a blower of 100HP and a wave generator of submerged piston type with a motor of 10 HP. The main results obtained from the experiments are summarized as follows. -
Chapter 31 WAVE FORCES AGAINST SEA WALL Masashi Hom-Ma and Kiyoshi Horikawa Department of Civil Engineering, University of Tokyo
Chapter 31 WAVE FORCES AGAINST SEA WALL Masashi Hom-ma and Kiyoshi Horikawa Department of Civil Engineering, University of Tokyo Tokyo, Japan INTRODUCTION The study concerning the wave forces acting on breakwater has been conducted by numerous scientists and engineers both in field and in laboratory,, While few studies have been car- ried out on the wave forces acting on sea wall which is located inside the surf zone. In this paper are summarized the main results of the experimental studies conducted at the University of Tokyo, Japan, in relation to the subject on the wave forces against a vertical or inclined surface wall located shorewards from the breaking point, and also is proposed an empirical formula of wave pressure distribution on a sea wall on the basis of the experimental data. The computed results obtained by using the above formula are compared with the field data of wave pressure on a vertical wall measured at the Niigata West Coast, Niigata Prefecture, Japan, and also with the experimen- tal data of total wave forces on a vertical wall; the project of the latter is now in progress at the University of Tokyo, PRESENTATION OP EXPERIMENTAL RESULTS LABORATORY PROCEDURES The wave channel which is used for the present studies is 18 m long, 0.6 m high and 0.7 m wide, and a model of sea wall is installed on a gentle uniform slope of l/l5. The face angle of the model is adjustable in a wide range, and six pres- sure gauges are attached on the surface of model sea wall at different levels to measure simultaneously the time history of pressure workxng on a sea wall. -
7 X 11 Long.P65
Cambridge University Press 978-0-521-86028-4 - Waves in Oceanic and Coastal Waters Leo H. Holthuijsen Index More information Index absorption 294, 296 barrier 221 accelerometer 13 basin (wave-, tank) 181, 183 acquisition (spectrum) 51 Battjes method 101 action 221 Beaufort wind scale 190 balance (equation) 257, 261, 288, 335 Berkhoff mild-slope equation 217 density (spectrum) 261 Bernoulli equation 117 advective 111, 343 linearised 117 air 177 nonlinear 323 bubble 108 biphase 271, 273, 274 flow 178, 182, 183 blocking, current-induced 264 motion 182 Boltzmann integral 185 pressure 18, 178, 179 bore 281 airplane 19, 20, 21 bottom Airy (wave theory) 53, 107, 138 friction 109, 276, 295 aliasing 333 roughness 279, 296 alphabet, Greek 31 slope 74, 224, 243, 282 altimeter boundary condition 115, 116, 320, 323 acoustic 22 boundary condition laser 21 kinematic, bottom 115, 116, 320, 323 radar 22 kinematic, surface 114, 116, 319, 323 altimeter (radar) dynamic, surface, bottom 115, 117, 130, 142, 170, footprint (satellite) 22 320 wave height 22 boundary-element method 215, 240 amplitude boundary layer random 33, 45 atmospheric 147, 183 response 53, 54, 55 atmospheric (internal) 148 spectrum 34, 45 bottom 109, 276, 278 analysis Boussinesq (equations, model) 198, 241 cross-spectral 324 Bragg scatter 20, 270 spectral 324 breaking 188, 242, 276 Anderson–Darling test 89 criterion 189 anemometer, wind 146, 151 index 282 annual-maximum approach (long-term statistics) 85, wave types 242 98 breakwater 210, 213, 266, 288, 296 array breeze 151, 181 phase 17