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.

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-FA09-7-3 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 66+24 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) 45 285m 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 (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 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 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  =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 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  =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  =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 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

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.

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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.

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Presentation on theme: "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."— Presentation transcript:

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