Tainan Hydraulics A Preliminary result on the long time evolution of non-linear waves --as a partial result of The Characteristics of Nonlinear Wave Transformation.

Slides:

Advertisements

Similar presentations

2. The WAM Model: Solves energy balance equation, including Snonlin

Advertisements

Chapter 7 Waves in the Ocean ©2003 Jones and Bartlett Publishers.

Transformation of Shallow-Water Waves The Certificate Program in Tsunami Science and Preparedness. Held at the University of Washington in Seattle, Washington.

INWAVE: THE INFRAGRAVITY WAVE DRIVER OF THE COAWST SYSTEM

Frequency modulation and circuits

Development of an In-Situ Test for Direct Evaluation of the Liquefaction Resistance of Soils K. H. Stokoe, II, E. M. Rathje and B.R. Cox University of.

Introduction to Oceanography Dynamic Oceanography: Waves.

Superposition of Waves  Two important concepts that physicists study are Wave Motion Particle Motion  This semester will begin with the study of wave.

Chapter 11 Wave Motion A wave is the motion of a disturbance.

Turbulence of Gravity Waves in Laboratory Experiments S Lukaschuk 1, P Denissenko 1, S Nazarenko 2 1 Fluid Dynamics Laboratory, University of Hull 2 Mathematics.

GG450 April 22, 2008 Seismic Processing.

The research on the interactions between short and long waves or waves and currents on a variable bottom has not been made much in the past. Most of the.

Chapter 4 Wave-Wave Interactions in Irregular Waves Irregular waves are approximately simulated by many periodic wave trains (free or linear waves) of.

Relationship between Probability density and Spectrum An interconnection of the statistical properties of random wave field.

Nonlinear Evolution of Whistler Turbulence W.A. Scales, J.J. Wang, and O. Chang Center of Space Science and Engineering Research Virginia Tech L. Rudakov,

Chapter 3.1 Weakly Nonlinear Wave Theory for Periodic Waves (Stokes Expansion)  Introduction The solution for Stokes waves is valid in deep or intermediate.

Relationship between Probability density and Spectrum An interconnection of the statistical properties of random wave field.

Spectral Analysis of Wave Motion Dr. Chih-Peng Yu.

Chapter 3.2 Finite Amplitude Wave Theory

Frontiers in Nonlinear Waves University of Arizona March 26, 2010 The Modulational Instability in water waves Harvey Segur University of Colorado.

Nonlinear Long Wave in Shallow Water. Contents  Two Important Parameters For Waves In Shallow Water  Nondimensional Variables  Nondimensional Governing.

Spectra of Gravity Wave Turbulence in a Laboratory Flume S Lukaschuk 1, P Denissenko 1, S Nazarenko 2 1 Fluid Dynamics Laboratory, University of Hull 2.

Chapter 6 Wave Instability and Resonant Wave Interactions in A Narrow-Banded Wave Train.

Juan Carlos Ortiz Royero Ph.D.

Forecasting Ocean Waves Problem: Given observed or expected weather, what will be the sea state? Ships are sunk not by winds, but by waves!

Variations of AM.

Chapter 10 Ocean Waves Part 1 ftp://ucsbuxa.ucsb.edu/opl/tommy/Geog3awinter2011/

The Air-Sea Momentum Exchange R.W. Stewart; 1973 Dahai Jeong - AMP.

Chapter 7 continued Open Channel Flow

Objectives Identify the conditions of simple harmonic motion.

Chapter 9 Electromagnetic Waves. 9.2 ELECTROMAGNETIC WAVES.

STUDY OF THE ROUGHNESS CHARACTERISTICS OF PLANT SPECIES IN CALIFORNIA RIVERS By U.C.Davis J.Amorocho Hydraulics Laboratory.

Numerical study of wave and submerged breakwater interaction (Data-driven and Physical-based Model for characterization of Hydrology, Hydraulics, Oceanography.

A H. Kyotoh, b R. Nakamura & a P. J. Baruah a a Institute of Engineering Mechanics and Systems, University of Tsukuba, Ibaraki, Japan b Third Plan Design.

New Topic - Waves Always wind, so always waves Transfer of energy from a windy area to a narrow coastal band General topics to cover: (1) Generation (2)

Section 1 Simple Harmonic Motion

Daily Challenge, 10/2 Give 3 examples of motions that are periodic, or repeating.

Chapter 11 Preview Objectives Hooke’s Law Sample Problem

COMPARISON OF ANALYTICAL AND NUMERICAL APPROACHES FOR LONG WAVE RUNUP by ERTAN DEMİRBAŞ MAY, 2002.

The Linear and Non-linear Evolution Mechanism of Mesoscale Vortex Disturbances in Winter Over Western Japan Sea Yasumitsu MAEJIMA and Keita IGA (Ocean.

Quasi-Geostrophic Motions in the Equatorial Areas

Chapter 14 Waves & Energy Transfer I. Waves Properties 1. A wave is a rhythmic disturbance that carries energy 1. A wave is a rhythmic disturbance that.

Waves - I Chapter 16 Copyright © 2014 John Wiley & Sons, Inc. All rights reserved.

Wave Shoaling Schematic Changes that occur when a wave shoals (moves into shallow water): In deep water = profile of swell is nearly sinusoidal. Enter.

Waves in the Ocean. Waves are the undulatory motion of a water surface. Parts of a wave are, Wave crest,Wave trough, Wave height (H), Wave Amplitude,

Numerical study of flow instability between two cylinders in 2D case V. V. Denisenko Institute for Aided Design RAS.

CEE 262A H YDRODYNAMICS Lecture 13 Wind-driven flow in a lake.

Acoustic wave propagation in the solar subphotosphere S. Shelyag, R. Erdélyi, M.J. Thompson Solar Physics and upper Atmosphere Research Group, Department.

Deep-water “limiting” envelope solitons Alexey Slunyaev Institute of Applied Physics RAS, Nizhny Novgorod.

H. SAIBI November 25, Outline Generalities Superposition of waves Superposition of the wave equation Interference of harmonic waves.

ONE-DIMENSIONAL ANALYSIS ON BEDEVOLUTION ACCOMPANING BANK EROSION Satoru Nakanishi Hokkaido University Graduate School Kazuyoshi Hasegawa Hokkaido University.

3-D nonhydrostatic numerical modelling of strongly nonlinear internal waves V. Maderich, M. Zheleznyak, E. Terletska, V. Koshebutskyy, M. Morgunov IMMSP,

EXPERIMENTS ON EXTREME WAVE GENERATION BASED ON SOLITON ON FINITE BACKGROUND René Huijsmans(MARIN) Gert Klopman (AFR) Natanael Karjanto,Brenny van Groesen.

Unit 3: Waves and tides.

Chapter 11 Preview Objectives Hooke’s Law Sample Problem

© Houghton Mifflin Harcourt Publishing Company The student is expected to: Chapter 11 Section 1 Simple Harmonic Motion TEKS 7A examine and describe oscillatory.

V.M. Sliusar, V.I. Zhdanov Astronomical Observatory, Taras Shevchenko National University of Kyiv Observatorna str., 3, Kiev Ukraine

Environmental Hydrodynamics Lab. Yonsei University, KOREA RCEM D finite element modeling of bed elevation change in a curved channel S.-U. Choi,

1 Waves and Vibrations. 2 Waves are everywhere in nature Sound waves, visible light waves, radio waves, microwaves, water waves, sine waves, telephone.

Interaction of Tsunamis with Short Surface Waves: An Experimental Study James M. Kaihatu Texas Engineering Experiment Station Zachry Department of Civil.

Section 1 Simple Harmonic Motion

Communications Engineering 1

Copyright © 2014 John Wiley & Sons, Inc. All rights reserved.

© 2014 John Wiley & Sons, Inc. All rights reserved.

Forecasting Ocean Waves

The FOCI method versus other wavefield extrapolation methods

I. Introduction Purposes & Applications

Lake Iseo Field Experiment

Presentation transcript:

Tainan Hydraulics A Preliminary result on the long time evolution of non-linear waves --as a partial result of The Characteristics of Nonlinear Wave Transformation on Sloping Bottoms A MOE Program for Promoting Academic Excellence of Universities, A MOE Program for Promoting Academic Excellence of Universities,Taiwan under grant number A-91-E-FA under grant number A-91-E-FA09-7-3

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Basic Information of the Project (1/2) Objectives –The objectives of the project are to investigate the nonlinear wave transformation, modulation, and the characteristics of related flow structures during the shoaling process of wave propagation.

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Basic Information of the Project (2/2) Sub-Projects Nonlinear modulation of progressive wave The transmission of wave envelops The studies on wave breaking and related flow fields The generation of infragravity waves Different I. C. Under certain conditions

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Previous work done by (1/3) : Theoretical studies –Benjamin and Feir(1967) weakly nonlinear deep water wavetrains were unstable to modulational perturbations –Whitham(1967), Chu and Mei(1970,1971) : –Zakharzov(1968) : Schrödinger Eq.(third-order of ka) (1) deep water (2) small ka (3) slow modulation of amplitude(narrow band) –Dysthe(1979) : forth-order equation (1) mean flow effect(mean water level variation)

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Previous work done by (2/3) Numerical development Fully Nonlinear Eq. : –Louguet-Higgins(1978) –Wang Pei(1995) –Wethuis(2001) Cubic Schrödinger Eq. : –Yuen and Lake(1978) –Shemer et al.(1998) Forth-order Eq. : –Janssen(1983) –Lo and Mei(1985); –Lo and Mei(1987)

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Previous work done by (3/3) : Experimental Studies –Lake et. al. (1977)—F-P-U phenomenaLake et. al. (1977)—F-P-U phenomena –Su(1982), Kit et al.(2000), Wethuis(2001) –Melville(1982) –Shemer et al.(1998) : intermediate depth –Tulin and Waseda(1999) : breaking effectTulin and Waseda(1999) : breaking effect –Waseda and Tulin(1999)Waseda and Tulin(1999)

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 The approaches and methodology of the Project The basic approaches are to utilize the facilities of the THL to investigate this topic experimentally followed by developing a numerical model that is able to describe the transformation of waves from a deep water region to shallow water region and even breaking taken place. The methodology applied on this project is to investigate the subject under a relatively simple boundary condition first, then gradually proceed to complicated ones.

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Overview of Experiments Three phases –Phase I: In the Super Tank(5m*5m*300m), THL With a slopping bottom(1:80) 39 wave gages Bicromatic waves –Phase II In a meso-flume(7m*1m*60m), THL With a slopping bottom(1:40) Seeded three waves system –Phase III In the Super Tank(5m*5m*300m) Constant water depth wave gages, 8+1 velocimetries Seeded three waves system, un-seeded waves..

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 EXP. I (1/2) Tests in the Super Tank, THL –To ensure the capabilities of the facilities Wave generator –Two waves system (bichromatic waves) Boundary conditions –Relative dimensions, sidewall effects, reflection… Instrumentation –using 39 wave sensors Data acquisition and analysis

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 EXP. I (2/2) m 3.5m WH01 ~ WH03WH04WH05WH06WH07WH08WH09WH10WH11WH12WH13WH14WH15WH16WH17WH18WH19WH20WH21WH22WH23WH24WH25WH39 ~ 3.15 A Schematic Diagram of the Experimental set-up(phase I, III) IPC1 MNDAS

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 (1/10)Results-Exp. Phase I (a) Wave profiles showing the modulational wave train.(b)Spectral evolution.(c)amplitude envelope of surface elevation. kx /2  =3.5 kx /2  =4.3 kx /2  =4.6 kx /2  =8.5

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 (2/10)Results-Exp. Phase I (a) Wave profiles showing the modulational wave train.(b)Spectral evolution.(c)amplitude envelope of surface elevation. 1:80 slope kx /2  =12.5 kx /  =16.0 kx /2  =19.8 kx /2  =23.6

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 (3/10)Results-Exp. Phase I (a) Wave profiles showing the modulational wave train.(b)Spectral evolution.(c)amplitude envelope of surface elevation. kx /2  =27.3 kx /2  =31.1 kx /2  =34.9 kx /2  =38.6

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 (4/10)Results-Exp. Phase I (a) Wave profiles showing the modulational wave train.(b)Spectral evolution.(c)amplitude envelope of surface elevation. kx /2  =43.4 kx /2  =46.2 kx /2  =50.0 kx /2  =53.7

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 (5/10)Results-Exp. Phase I (a) Wave profiles showing the modulational wave train.(b)Spectral evolution.(c)amplitude envelope of surface elevation. kx /2  =57.5 kx /2  =58.8 kx /2  =59.2 kx /2  =59.5

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 (6/10)Results-Exp. Phase I (a) Wave profiles showing the modulational wave train.(b)Spectral evolution.(c)amplitude envelope of surface elevation. kx /2  =59.7 kx /2  =60.2 kx /2  =60.7 kx /2  =61.2

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 (7/10)Results-Exp. Phase I (a) Wave profiles showing the modulational wave train.(b)Spectral evolution.(c)amplitude envelope of surface elevation. kx /2  =61.6 kx /2  =61.9 kx /2  =62.3 kx /2  =62.7

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 (8/10)Results-Exp. Phase I (a) Wave profiles showing the modulational wave train.(b)Spectral evolution.(c)amplitude envelope of surface elevation. kx /2  =62.8 kx /2  =62.9 kx /2  =63.0 kx /2  =63.1

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 (9/10)Results-Exp. Phase I (a) Wave profiles showing the modulational wave train.(b)Spectral evolution.(c)amplitude envelope of surface elevation. kx /2  =63.2 kx /2  =63.29 kx /2  =63.3 kx /2  =63.4

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 (10/10)Results-Exp. Phase I (a) Wave profiles showing the modulational wave train.(b)Spectral evolution.(c)amplitude envelope of surface elevation. kx /2  =63.5 kx /2  =63.6 kx /2  =63.7

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Experiments-Phase II

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Power spectrum of waveboard motion (EXP.II)

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Data Analysis EXP. II –Bandpass filter : 0.01 Hz ~ 5 Hz –data low passed by Hilbert transform –power spectrum were calculated under : Data length=3072 NFFT=1024 Window=Hanning(1024) Overlap=0 Frequency resolution=1.953*10 -2

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Test conditions EXP. II Three waves system ka ~>0.14~0.16 breaking, ka ~>0.29 three dimensional

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Spatial evolution of wave profiles(EXP. II, case 2) kx /2  =3.2 kx /2  =3.7 kx /2  =3.8 kx /2  =4.5 kx /2  =5.8

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Spatial evolution of wave profiles(EXP. II, case 2) kx /2  =7.0 kx /2  =8.3 kx /2  =9.6 kx /2  =10.9 kx /2  =12.2

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Spatial evolution of wave profiles(EXP. II, case 2) kx /2  =13.5 kx /2  =14.0 kx /2  =14.5 kx /2  =15.0 kx /2  =16.1

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Spatial evolution of wave profiles (EXP. II, case 3) kx /2  =3.2 kx /2  =3.7 kx /2  =3.8 kx /2  =4.5 kx /2  =5.8

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Spatial evolution of wave profiles (EXP. II, case 3) kx /2  =7.0 kx /2  =8.3 kx /2  =9.6 kx /2  =10.9 kx /2  =12.2

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Spatial evolution of wave profiles (EXP. II, case 3) kx /2  =13.5 kx /2  =14.0 kx /2  =14.5 kx /2  =15.0 kx /2  =16.1

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Spatial evolution of wave profiles (EXP. II, case 1) kx /2  =6.5 kx /2  =7.4 kx /2  =7.8 kx /2  =9.1 kx /2  =11.7

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Spatial evolution of wave profiles(EXP. II, case 1) kx /2  =14.3 kx /2  =16.9 kx /2  =19.5 kx /2  =22.1 kx /2  =24.7

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Spatial evolution of wave profiles(EXP. II, case 1) kx /2  =27.3 kx /2  =28.3 kx /2  =29.3 kx /2  =30.2 kx /2  =32.5

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Spatial evolution of wave profiles and spectrum (EXP. II, case 1) kx /2  =6.5 kx /2  =7.4 kx /2  =7.8 kx /2  =9.1 kx /2  =11.7

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Spatial evolution of wave profiles and spectrum(EXP. II, case 1) kx /2  =14.3 kx /2  =16.9 kx /2  =19.5 kx /2  =22.1 kx /2  =24.7

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Spatial evolution of wave profiles and spectrum(EXP. II, case 1) kx /2  =27.3 kx /2  =28.3 kx /2  =29.3 kx /2  =30.2 kx /2  =32.5

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Side band amplitude evolutions (EXP. II, case 1)

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Growth Curve

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Wave steepness effects 1.The spatial evolution of wave profiles is not only related to the initial wave steepness 2.The experiment (ka=0.1) is similar to the condition of the evolution experiment on a weak wave reported in Lake et. al.(1977) and Tulin & Waseda(1999). 3.ka ~>0.14~0.16 breaking, ka ~>0.29 three dimensional

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Instrumentation EXP. III(1/2)

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Instrumentation EXP. III(2/2)

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 test conditions were determined mainly based on test conditions were determined mainly based on Initial growth rate of the sideband disturbance, based on Krasitskii’s reduced four-wave interaction (Tulin & Washeda 1999).

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Data Analysis EXP. III 1. following that of EXP. II 2. the bi-spectrum analysis

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Spatial evolution of wave profiles(EXP. III, case 5) kx /2  =4.6 kx /2  =5.4 kx /2  =5.6 kx /2  =5.9 kx /2  =7.8

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Spatial evolution of wave profiles(EXP. III, case 5) kx /2  =9.6 kx /2  =11.5 kx /2  =13.4 kx /2  =15.2 kx /2  =17.7

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Spatial evolution of wave profiles(EXP. III, case 5) kx /2  =19 kx /2  =20.9 kx /2  =22.7 kx /2  =24.6 kx /2  =26.5

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Spatial evolution of wave profiles(EXP. III, case 5) kx /2  =28.4 kx /2  =30.2 kx /2  =31.2 kx /2  =32.1 kx /2  =33

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Spatial evolution of wave profiles(EXP. III, case 5) kx /2  =34 kx /2  =34.9 kx /2  =35.9 kx /2  =36.8 kx /2  =37.7

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Spatial evolution of wave profiles(EXP. III, case 5) kx /2  =62.1 kx /2  =63 kx /2  =64 kx /2  =64.9 kx /2  =65.8

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Spatial evolution of wave profiles(EXP. III, case 5) kx /2  =66.8 kx /2  =67.7 kx /2  =68.6 kx /2  =69.6 kx /2  =70.5

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Spatial evolution of wave profiles(EXP. III, case 5) kx /2  =71.5 kx /2  =72.4 kx /2  =73.3 kx /2  =73.6 kx /2  =74.6

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Side band amplitude evolution (EXP. III, case 5) kx /2  =4.6 kx /2  =5.4 kx /2  =5.6 kx /2  =5.9 kx /2  =7.8

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Side band amplitude evolution (EXP. III, case 5) kx /2  =9.6 kx /2  =11.5 kx /2  =13.4 kx /2  =15.2 kx /2  =17.7

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Side band amplitude evolution (EXP. III, case 5) kx /2  =19 kx /2  =20.9 kx /2  =22.7 kx /2  =24.6 kx /2  =26.5

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Side band amplitude evolution (EXP. III, case 5) kx /2  =28.4 kx /2  =30.2 kx /2  =31.2 kx /2  =32.1 kx /2  =33.0

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Side band amplitude evolution (EXP. III, case 5) kx /2  =34 kx /2  =34.9 kx /2  =35.9 kx /2  =36.8 kx /2  =37.7

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Side band amplitude evolution (EXP. III, case 5) kx /2  =62.1 kx /2  =63.0 kx /2  =64 kx /2  =64.9 kx /2  =65.8

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Side band amplitude evolution (EXP. III, case 5) kx /2  =66.8 kx /2  =67.7 kx /2  =68.6 kx /2  =69.6 kx /2  =70.5

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Side band amplitude evolution (EXP. III, case 5) kx /2  =71.5 kx /2  =72.4 kx /2  =73.3 kx /2  =73.6 kx /2  =74.6

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Non-dimensional amplitude vs. kx (EXP. III, case 5)

Tainan Hydraulics Thank you !

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Lake et al.(1977) When experiments were performed using initially uniform, or nearly uniform, wave trains with large initial steepness, recurrence cycles were observed in which the wave trains became strongly modulated and then demodulated until they were again nearly uniform.

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Waseda and Tulin(1999) Wave train –It is clear from this figure that Benjamin-Feir’s theory overestimates the growth rate, but the Krasitskii(1994) theory predicts the growth rate fairly well.

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Tulin and Waseda(1999) Wave train –The evolution of 1.2m breaking wave : The energy originally residing largely in the carrier ware is now divided roughly between two waves, the original carrier and the lower sideband. The future evolution of this two-wave system, which it was impossible to measure here for lack of fetch, can be expected to be different from that of the Benjamin-Feir three-wave systems studied here.

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 MNDAS- the Multi-Nods Data Acquisition System Up to 120 channels(90 wave gages, 19 velocities 1 wave board motion and 10 spares) sampling at 20+ Hz are available now sensors … sensors … sensors … Data base server ADAM IPC1 IPC2 IPCM Internet ADAM4520 NODE 0NODE 1NODE M ADAM5510 NODE 1 ADAM5510 NODE 2 ADAM5510 NODE N ADAM5510 NODE 1 Internet ADAM sensors …

Tainan Hydraulics 卓越計畫 -- 斜坡上非線性波浪傳動特性之研究 Wave generator, the Super Tank