tainan hydraulics a preliminary result on the long time evolution of non-linear waves --as a partial...
Post on 18-Dec-2015
213 views
TRANSCRIPT
Tainan Hydraulics
A Preliminary result on the long time A Preliminary result on the long time evolution of non-linear wavesevolution of non-linear waves
--as a partial result of --as a partial result of
The Characteristics of Nonlinear Wave Transformation The Characteristics of Nonlinear Wave Transformation
on on
Sloping BottomsSloping Bottoms A MOE Program for Promoting Academic Excellence of Universities, A MOE Program for Promoting Academic Excellence of Universities,
TaiwanTaiwan
under grant number A-91-E-FA09-7-3under grant number A-91-E-FA09-7-3
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Basic Information of the Project (1/2) 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.
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Basic Information of the Project (2/2)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 certainconditions
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Previous work done by (1/3) :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)
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Previous work done by (2/3)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)
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Previous work done by (3/3) :Previous work done by (3/3) :
• Experimental Studies– Lake et. al. (1977)—F-P-U phenomena– Su(1982) , Kit et al.(2000), Wethuis(200
1) – Melville(1982)– Shemer et al.(1998) : intermediate depth– Tulin and Waseda(1999) : breaking effect– Waseda and Tulin(1999)
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
The approaches and methodology of the ProjectThe 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.
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Overview of ExperimentsOverview 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..
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
EXP. I (1/2)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
twatwats 21 coscos
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
EXP. I (2/2)EXP. I (2/2)
45
285m
3.5m
WH01
~
WH03
WH04
WH05
WH06
WH07
WH08
WH09
WH10
WH11
WH12
WH13
WH14
WH15
WH16
WH17
WH18
WH19
WH20
WH21
WH22
WH23
WH24
WH25
WH39
~
3.15
A Schematic Diagram of the Experimental set-up(phase I, III)
IPC1
IPC1
MNDAS
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
(1/10)Results-Exp. Phase I(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
ma
TT
w
TT
w
06.0
sec75.12
sec45.12
12
2
11
1
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
(2/10)Results-Exp. Phase I(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
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
(3/10)Results-Exp. Phase I(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
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
(4/10)Results-Exp. Phase I(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
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
(5/10)Results-Exp. Phase I(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
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
(6/10)Results-Exp. Phase I(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
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
(7/10)Results-Exp. Phase I(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
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
(8/10)Results-Exp. Phase I(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
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
(9/10)Results-Exp. Phase I(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
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
(10/10)Results-Exp. Phase I(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
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Experiments-Phase IIExperiments-Phase II
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Power spectrum of waveboard motion (EXP.II)Power spectrum of waveboard motion (EXP.II)
0 .0 1 .0 2 .0 3 .0 4 .0 5 .0frequ ebcy , f(H z)
0 .0 0
0 .0 0
0 .0 1
0 .1 0
1 .0 0po
wer
spe
ctru
m d
ensi
ty, m
*m/H
z
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Data Analysis EXP. IIData 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
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Test conditions EXP. IITest conditions EXP. II• Three waves system
case f0 A0 f- A- beta- f+ A+ beta+ depth wave_K ka delta deltakapa
1 1.4258 0.0294 1.2891 0.0010 0.0351 1.5625 0.0011 0.0358 0.6000 8.1877 0.2400 0.0959 0.3983
2 0.9961 0.0279 0.8984 0.0013 0.0458 1.0938 0.0013 0.0469 0.6000 4.0549 0.1133 0.0980 0.8657
3 0.9961 0.0253 0.8984 0.0081 0.3188 1.0938 0.0072 0.2834 0.6000 4.0549 0.1027 0.0980 0.9548
ka ~>0.14~0.16 breaking, ka ~>0.29 three dimensional
4
1
2
2
)sin()sin()sin(
0
0
0
22220
0
kkkk
bbaa
tbtbta
c
c
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Spatial evolution of wave profiles(EXP. II, case 2)Spatial evolution of wave profiles(EXP. II, case 2)
5 1 5 2 5 3 5 4 5 5 5-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6ch : 1 x = 5 m
5 1 5 2 5 3 5 4 5 5 5-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6ch : 2 x = 5 .7 5m
5 1 5 2 5 3 5 4 5 5 5-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6ch : 3 x = 6 m
5 1 5 2 5 3 5 4 5 5 5-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6ch : 4 x = 7 m
5 1 5 2 5 3 5 4 5 5 5tim e(sec)
-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6
surf
ace
elev
atio
n(m
)
ch : 5 x = 9 m
C ase: T A C 35M
kx/2=3.2
kx/2=3.7
kx/2=3.8
kx/2=4.5
kx/2=5.8
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Spatial evolution of wave profiles(EXP. II, case 2)Spatial evolution of wave profiles(EXP. II, case 2)
1 5 2 5 3 5 4 5 5 5 6 5- 0 . 0 6
- 0 . 0 3
0 . 0 0
0 . 0 3
0 . 0 6ch : 6 x = 1 1m
1 5 2 5 3 5 4 5 5 5 6 5- 0 . 0 6
- 0 . 0 3
0 . 0 0
0 . 0 3
0 . 0 6ch : 7 x = 1 3m
1 5 2 5 3 5 4 5 5 5 6 5- 0 . 0 6
- 0 . 0 3
0 . 0 0
0 . 0 3
0 . 0 6ch : 8 x = 1 5m
1 5 2 5 3 5 4 5 5 5 6 5- 0 . 0 6
- 0 . 0 3
0 . 0 0
0 . 0 3
0 . 0 6ch : 9 x = 1 7m
1 5 2 5 3 5 4 5 5 5 6 5tim e(sec)
-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6
surf
ace
elev
atio
n(m
)
ch : 10 x= 19 m
C ase: T A C 35M
kx/2=7.0
kx/2=8.3
kx/2=9.6
kx/2=10.9
kx/2=12.2
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Spatial evolution of wave profiles(EXP. II, case 2)Spatial evolution of wave profiles(EXP. II, case 2)
2 5 3 5 4 5 5 5 6 5 7 5- 0 . 0 6
- 0 . 0 3
0 . 0 0
0 . 0 3
0 . 0 6ch : 11 x= 21 m
2 5 3 5 4 5 5 5 6 5 7 5- 0 . 0 6
- 0 . 0 3
0 . 0 0
0 . 0 3
0 . 0 6ch : 12 x= 21 .75 m
2 5 3 5 4 5 5 5 6 5 7 5- 0 . 0 6
- 0 . 0 3
0 . 0 0
0 . 0 3
0 . 0 6ch : 13 x= 22 .5m
2 5 3 5 4 5 5 5 6 5 7 5- 0 . 0 6
- 0 . 0 3
0 . 0 0
0 . 0 3
0 . 0 6ch : 14 x= 23 .25 m
2 5 3 5 4 5 5 5 6 5 7 5tim e(sec)
-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6
surf
ace
elev
atio
n(m
)
ch : 15 x= 25 m
C ase: T A C 35M
kx/2=13.5
kx/2=14.0
kx/2=14.5
kx/2=15.0
kx/2=16.1
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Spatial evolution of wave profiles (EXP. II, case 3)Spatial evolution of wave profiles (EXP. II, case 3)
5 1 5 2 5 3 5 4 5 5 5-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6ch : 1 x = 5 m
5 1 5 2 5 3 5 4 5 5 5-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6ch : 2 x = 5 .7 5m
5 1 5 2 5 3 5 4 5 5 5-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6ch : 3 x = 6 m
5 1 5 2 5 3 5 4 5 5 5-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6ch : 4 x = 7 m
5 1 5 2 5 3 5 4 5 5 5tim e(sec)
-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6
surf
ace
elev
atio
n(m
)
ch : 5 x = 9 m
C ase: T A C 55M
kx/2=3.2
kx/2=3.7
kx/2=3.8
kx/2=4.5
kx/2=5.8
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Spatial evolution of wave profiles (EXP. II, case 3)Spatial evolution of wave profiles (EXP. II, case 3)
1 5 2 5 3 5 4 5 5 5 6 5- 0 . 0 6
- 0 . 0 3
0 . 0 0
0 . 0 3
0 . 0 6ch : 6 x = 1 1m
1 5 2 5 3 5 4 5 5 5 6 5- 0 . 0 6
- 0 . 0 3
0 . 0 0
0 . 0 3
0 . 0 6ch : 7 x = 1 3m
1 5 2 5 3 5 4 5 5 5 6 5- 0 . 0 6
- 0 . 0 3
0 . 0 0
0 . 0 3
0 . 0 6ch : 8 x = 1 5m
1 5 2 5 3 5 4 5 5 5 6 5- 0 . 0 6
- 0 . 0 3
0 . 0 0
0 . 0 3
0 . 0 6ch : 9 x = 1 7m
1 5 2 5 3 5 4 5 5 5 6 5tim e(sec)
-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6
surf
ace
elev
atio
n(m
)
ch : 10 x= 19 m
C ase: T A C 55M
kx/2=7.0
kx/2=8.3
kx/2=9.6
kx/2=10.9
kx/2=12.2
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Spatial evolution of wave profiles (EXP. II, case 3)Spatial evolution of wave profiles (EXP. II, case 3)
2 5 3 5 4 5 5 5 6 5 7 5- 0 . 0 6
- 0 . 0 3
0 . 0 0
0 . 0 3
0 . 0 6ch : 11 x= 21 m
2 5 3 5 4 5 5 5 6 5 7 5- 0 . 0 6
- 0 . 0 3
0 . 0 0
0 . 0 3
0 . 0 6ch : 12 x= 21 .75 m
2 5 3 5 4 5 5 5 6 5 7 5- 0 . 0 6
- 0 . 0 3
0 . 0 0
0 . 0 3
0 . 0 6ch : 13 x= 22 .5m
2 5 3 5 4 5 5 5 6 5 7 5- 0 . 0 6
- 0 . 0 3
0 . 0 0
0 . 0 3
0 . 0 6ch : 14 x= 23 .25 m
2 5 3 5 4 5 5 5 6 5 7 5tim e(sec)
-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6
surf
ace
elev
atio
n(m
)
ch : 15 x= 25 m
C ase: T A C 55M
kx/2=13.5
kx/2=14.0
kx/2=14.5
kx/2=15.0
kx/2=16.1
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Spatial evolution of wave profiles (EXP. II, case 1)Spatial evolution of wave profiles (EXP. II, case 1)
5 1 5 2 5 3 5 4 5 5 5-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6ch : 1 x = 5 m
5 1 5 2 5 3 5 4 5 5 5-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6ch : 2 x = 5 .7 5m
5 1 5 2 5 3 5 4 5 5 5-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6ch : 3 x = 6 m
5 1 5 2 5 3 5 4 5 5 5-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6ch : 4 x = 7 m
5 1 5 2 5 3 5 4 5 5 5tim e(sec)
-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6
surf
ace
elev
atio
n(m
)
ch : 5 x = 9 m
C ase: T A D 35M
kx/2=6.5
kx/2=7.4
kx/2=7.8
kx/2=9.1
kx/2=11.7
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Spatial evolution of wave profiles(EXP. II, case 1)Spatial evolution of wave profiles(EXP. II, case 1)
1 5 2 5 3 5 4 5 5 5 6 5- 0 . 0 6
- 0 . 0 3
0 . 0 0
0 . 0 3
0 . 0 6ch : 6 x = 1 1m
1 5 2 5 3 5 4 5 5 5 6 5- 0 . 0 6
- 0 . 0 3
0 . 0 0
0 . 0 3
0 . 0 6ch : 7 x = 1 3m
1 5 2 5 3 5 4 5 5 5 6 5- 0 . 0 6
- 0 . 0 3
0 . 0 0
0 . 0 3
0 . 0 6ch : 8 x = 1 5m
1 5 2 5 3 5 4 5 5 5 6 5- 0 . 0 6
- 0 . 0 3
0 . 0 0
0 . 0 3
0 . 0 6ch : 9 x = 1 7m
1 5 2 5 3 5 4 5 5 5 6 5tim e(sec)
-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6
surf
ace
elev
atio
n(m
)
ch : 10 x= 19 m
C ase: T A D 35M
kx/2=14.3
kx/2=16.9
kx/2=19.5
kx/2=22.1
kx/2=24.7
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Spatial evolution of wave profiles(EXP. II, case 1)Spatial evolution of wave profiles(EXP. II, case 1)
2 5 3 5 4 5 5 5 6 5 7 5- 0 . 0 6
- 0 . 0 3
0 . 0 0
0 . 0 3
0 . 0 6ch : 11 x= 21 m
2 5 3 5 4 5 5 5 6 5 7 5- 0 . 0 6
- 0 . 0 3
0 . 0 0
0 . 0 3
0 . 0 6ch : 12 x= 21 .75 m
2 5 3 5 4 5 5 5 6 5 7 5- 0 . 0 6
- 0 . 0 3
0 . 0 0
0 . 0 3
0 . 0 6ch : 13 x= 22 .5m
2 5 3 5 4 5 5 5 6 5 7 5- 0 . 0 6
- 0 . 0 3
0 . 0 0
0 . 0 3
0 . 0 6ch : 14 x= 23 .25 m
2 5 3 5 4 5 5 5 6 5 7 5tim e(sec)
-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6
surf
ace
elev
atio
n(m
)
ch : 15 x= 25 m
C ase: T A D 35M
kx/2=27.3
kx/2=28.3
kx/2=29.3
kx/2=30.2
kx/2=32.5
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Spatial evolution of wave profiles and spectrum (EXP. II, case 1)Spatial evolution of wave profiles and spectrum (EXP. II, case 1)
1 0 0 11 0 1 2 0-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6ch : 1 x= 5m
0 1 2 3 4 50 .0 0
0 .0 2
0 .0 4
0 1 2 3 4 5
1 0 0 11 0 1 2 0-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6ch : 2 x= 5 .75m
0 1 2 3 4 50 .0 0
0 .0 2
0 .0 4
0 1 2 3 4 5
1 0 0 11 0 1 2 0-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6ch : 3 x= 6m
0 1 2 3 4 50 .0 0
0 .0 2
0 .0 4
0 1 2 3 4 5
1 0 0 11 0 1 2 0-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6ch : 4 x= 7m
0 1 2 3 4 50 .0 0
0 .0 2
0 .0 4
0 1 2 3 4 5
1 0 0 11 0 1 2 0tim e(sec)
-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6
surf
ace
elev
atio
n(m
)
ch : 5 x= 9m
0 1 2 3 4 5frequ en cy(H z)
0 .0 0
0 .0 2
0 .0 4
ampl
itu
de,m
0 1 2 3 4 5frequ en cy(H z)
ampl
itu
de,m
C a se: T A D 3 5 M
kx/2=6.5
kx/2=7.4
kx/2=7.8
kx/2=9.1
kx/2=11.7
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Spatial evolution of wave profiles and spectrum(EXP. II, case 1)Spatial evolution of wave profiles and spectrum(EXP. II, case 1)
1 0 0 11 0 1 2 0-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6ch : 6 x= 11m
0 1 2 3 4 50 .0 0
0 .0 2
0 .0 4
0 1 2 3 4 5
1 0 0 11 0 1 2 0-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6ch : 7 x= 13m
0 1 2 3 4 50 .0 0
0 .0 2
0 .0 4
0 1 2 3 4 5
1 0 0 11 0 1 2 0-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6ch : 8 x= 15m
0 1 2 3 4 50 .0 0
0 .0 2
0 .0 4
0 1 2 3 4 5
1 0 0 11 0 1 2 0-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6ch : 9 x= 17m
0 1 2 3 4 50 .0 0
0 .0 2
0 .0 4
0 1 2 3 4 5
1 0 0 11 0 1 2 0tim e(sec)
-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6
surf
ace
elev
atio
n(m
)
ch : 10 x= 19m
0 1 2 3 4 5frequ en cy(H z)
0 .0 0
0 .0 2
0 .0 4
ampl
itu
de,m
0 1 2 3 4 5frequ en cy(H z)
ampl
itu
de,m
C a se: T A D 3 5 M
kx/2=14.3
kx/2=16.9
kx/2=19.5
kx/2=22.1
kx/2=24.7
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Spatial evolution of wave profiles and spectrum(EXP. II, case 1)Spatial evolution of wave profiles and spectrum(EXP. II, case 1)
1 0 0 11 0 1 2 0-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6ch : 11 x= 21m
0 1 2 3 4 50 .0 0
0 .0 2
0 .0 4
0 1 2 3 4 5
1 0 0 11 0 1 2 0-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6ch : 12 x= 21 .75m
0 1 2 3 4 50 .0 0
0 .0 2
0 .0 4
0 1 2 3 4 5
1 0 0 11 0 1 2 0-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6ch : 13 x= 22 .5m
0 1 2 3 4 50 .0 0
0 .0 2
0 .0 4
0 1 2 3 4 5
1 0 0 11 0 1 2 0-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6ch : 14 x= 23 .25m
0 1 2 3 4 50 .0 0
0 .0 2
0 .0 4
0 1 2 3 4 5
1 0 0 11 0 1 2 0tim e(sec)
-0 .0 6
-0 .0 3
0 .0 0
0 .0 3
0 .0 6
surf
ace
elev
atio
n(m
)
ch : 15 x= 25m
0 1 2 3 4 5frequ en cy(H z)
0 .0 0
0 .0 2
0 .0 4
ampl
itu
de,m
0 1 2 3 4 5frequ en cy(H z)
ampl
itu
de,m
C a se: T A D 3 5 M
kx/2=27.3
kx/2=28.3
kx/2=29.3
kx/2=30.2
kx/2=32.5
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Side band amplitude evolutions Side band amplitude evolutions (EXP. II, case 1)(EXP. II, case 1)
4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0kx
case : T A D 35 M
0 .0
0 .2
0 .4
0 .6
0 .8
1 .0
1 .2
1 .4
a /a 0
5 1 0 1 5 2 0 2 5 3 0k x /2 p i
a 0 a + a -
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Growth CurveGrowth Curve
4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0k x
case : T A D 35 M
0 .0
0 .2
0 .4
0 .6
0 .8
1 .0
1 .2n
on-d
imen
sion
al s
ide
ban
d am
plit
ude
5 1 0 1 5 2 0 2 5 3 0k x /2 p i
u p p er s id e b a n d
lo w er s id e b a n d
m ea n sid e b a n d
u p p er fit
lo w er f it
m ea n fit
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Wave steepness effectsWave steepness effects
casename f0 A0 f- A- beta- f+ A+ beta+ depth wave_K ka delta deltakapa
TAD35M 1.4258 0.0294 1.2891 0.0010 0.0351 1.5625 0.0011 0.0358 0.6000 8.1877 0.2400 0.0959 0.3983
TAC35M 0.9961 0.0279 0.8984 0.0013 0.0458 1.0938 0.0013 0.0469 0.6000 4.0549 0.1133 0.0980 0.8657
TAC55M 0.9961 0.0253 0.8984 0.0081 0.3188 1.0938 0.0072 0.2834 0.6000 4.0549 0.1027 0.0980 0.9548
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
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Instrumentation EXP. III(1/2)Instrumentation EXP. III(1/2)
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Instrumentation EXP. III(2/2)Instrumentation EXP. III(2/2)
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
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).
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Data Analysis EXP. IIIData Analysis EXP. III
• 1. following that of EXP. II• 2. the bi-spectrum analysis
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Spatial evolution of wave profiles(EXP. III, case 5)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
5 1 5 2 5 3 5 4 5 5 5 6 5 7 5 8 5 9 5 1 0 5 11 5-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 1 x = 1 5m
5 1 5 2 5 3 5 4 5 5 5 6 5 7 5 8 5 9 5 1 0 5 11 5-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 2 x = 1 7 .6m
5 1 5 2 5 3 5 4 5 5 5 6 5 7 5 8 5 9 5 1 0 5 11 5-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 3 x = 1 8 .12m
5 1 5 2 5 3 5 4 5 5 5 6 5 7 5 8 5 9 5 1 0 5 11 5-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 4 x = 1 9m
5 1 5 2 5 3 5 4 5 5 5 6 5 7 5 8 5 9 5 1 0 5 11 5tim e(sec)
-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
surf
ace
elev
atio
n(m
)
ch : 5 x = 2 5m
C ase: T est5
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Spatial evolution of wave profiles(EXP. III, case 5)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
1 5 2 5 3 5 4 5 5 5 6 5 7 5 8 5 9 5 1 0 5 1 1 5 1 2 5- 0 . 3 0- 0 . 2 0- 0 . 1 0
0 . 0 00 . 1 00 . 2 00 . 3 0
ch : 6 x= 31m
1 5 2 5 3 5 4 5 5 5 6 5 7 5 8 5 9 5 1 0 5 1 1 5 1 2 5- 0 . 3 0- 0 . 2 0- 0 . 1 0
0 . 0 00 . 1 00 . 2 00 . 3 0
ch : 7 x= 37m
1 5 2 5 3 5 4 5 5 5 6 5 7 5 8 5 9 5 1 0 5 1 1 5 1 2 5- 0 . 3 0- 0 . 2 0- 0 . 1 0
0 . 0 00 . 1 00 . 2 00 . 3 0
ch : 8 x= 43m
1 5 2 5 3 5 4 5 5 5 6 5 7 5 8 5 9 5 1 0 5 1 1 5 1 2 5- 0 . 3 0- 0 . 2 0- 0 . 1 0
0 . 0 00 . 1 00 . 2 00 . 3 0
ch : 9 x= 49m
1 5 2 5 3 5 4 5 5 5 6 5 7 5 8 5 9 5 1 0 5 1 1 5 1 2 5tim e(sec)
-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
surf
ace
elev
atio
n(m
)
ch : 10 x= 55m
C ase: T est5
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Spatial evolution of wave profiles(EXP. III, case 5)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
2 5 3 5 4 5 5 5 6 5 7 5 8 5 9 5 1 0 5 1 1 5 1 2 5 1 3 5- 0 . 3 0- 0 . 2 0- 0 . 1 0
0 . 0 00 . 1 00 . 2 00 . 3 0
ch : 11 x= 61m
2 5 3 5 4 5 5 5 6 5 7 5 8 5 9 5 1 0 5 1 1 5 1 2 5 1 3 5- 0 . 3 0- 0 . 2 0- 0 . 1 0
0 . 0 00 . 1 00 . 2 00 . 3 0
ch : 12 x= 67m
2 5 3 5 4 5 5 5 6 5 7 5 8 5 9 5 1 0 5 1 1 5 1 2 5 1 3 5- 0 . 3 0- 0 . 2 0- 0 . 1 0
0 . 0 00 . 1 00 . 2 00 . 3 0
ch : 13 x= 73m
2 5 3 5 4 5 5 5 6 5 7 5 8 5 9 5 1 0 5 1 1 5 1 2 5 1 3 5- 0 . 3 0- 0 . 2 0- 0 . 1 0
0 . 0 00 . 1 00 . 2 00 . 3 0
ch : 14 x= 79m
2 5 3 5 4 5 5 5 6 5 7 5 8 5 9 5 1 0 5 1 1 5 1 2 5 1 3 5tim e(sec)
-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
surf
ace
elev
atio
n(m
)
ch : 15 x= 85m
C ase: T est5
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Spatial evolution of wave profiles(EXP. III, case 5)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
3 5 4 5 5 5 6 5 7 5 8 5 9 5 1 0 5 1 1 5 1 2 5 1 3 5 1 4 5- 0 . 3 0- 0 . 2 0- 0 . 1 0
0 . 0 00 . 1 00 . 2 00 . 3 0
ch : 16 x= 91m
3 5 4 5 5 5 6 5 7 5 8 5 9 5 1 0 5 1 1 5 1 2 5 1 3 5 1 4 5- 0 . 3 0- 0 . 2 0- 0 . 1 0
0 . 0 00 . 1 00 . 2 00 . 3 0
ch : 17 x= 97m
3 5 4 5 5 5 6 5 7 5 8 5 9 5 1 0 5 1 1 5 1 2 5 1 3 5 1 4 5- 0 . 3 0- 0 . 2 0- 0 . 1 0
0 . 0 00 . 1 00 . 2 00 . 3 0
ch : 18 x= 100m
3 5 4 5 5 5 6 5 7 5 8 5 9 5 1 0 5 1 1 5 1 2 5 1 3 5 1 4 5- 0 . 3 0- 0 . 2 0- 0 . 1 0
0 . 0 00 . 1 00 . 2 00 . 3 0
ch : 19 x= 103m
3 5 4 5 5 5 6 5 7 5 8 5 9 5 1 0 5 1 1 5 1 2 5 1 3 5 1 4 5tim e(sec)
-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
surf
ace
elev
atio
n(m
)
ch : 20 x= 106m
C ase: T est5
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Spatial evolution of wave profiles(EXP. III, case 5)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
4 5 5 5 6 5 7 5 8 5 9 5 1 0 5 1 1 5 1 2 5 1 3 5 1 4 5 1 5 5- 0 . 3 0- 0 . 2 0- 0 . 1 0
0 . 0 00 . 1 00 . 2 00 . 3 0
ch : 21 x= 109m
4 5 5 5 6 5 7 5 8 5 9 5 1 0 5 1 1 5 1 2 5 1 3 5 1 4 5 1 5 5- 0 . 3 0- 0 . 2 0- 0 . 1 0
0 . 0 00 . 1 00 . 2 00 . 3 0
ch : 22 x= 112m
4 5 5 5 6 5 7 5 8 5 9 5 1 0 5 1 1 5 1 2 5 1 3 5 1 4 5 1 5 5- 0 . 3 0- 0 . 2 0- 0 . 1 0
0 . 0 00 . 1 00 . 2 00 . 3 0
ch : 23 x= 115m
4 5 5 5 6 5 7 5 8 5 9 5 1 0 5 1 1 5 1 2 5 1 3 5 1 4 5 1 5 5- 0 . 3 0- 0 . 2 0- 0 . 1 0
0 . 0 00 . 1 00 . 2 00 . 3 0
ch : 24 x= 118m
4 5 5 5 6 5 7 5 8 5 9 5 1 0 5 1 1 5 1 2 5 1 3 5 1 4 5 1 5 5tim e(sec)
-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
surf
ace
elev
atio
n(m
)
ch : 25 x= 121m
C ase: T est5
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Spatial evolution of wave profiles(EXP. III, case 5)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
1 0 5 11 5 1 2 5 1 3 5 1 4 5 1 5 5 1 6 5 1 7 5 1 8 5 1 9 5 2 0 5 2 1 5-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 51 x= 199m
1 0 5 11 5 1 2 5 1 3 5 1 4 5 1 5 5 1 6 5 1 7 5 1 8 5 1 9 5 2 0 5 2 1 5-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 52 x= 202m
1 0 5 11 5 1 2 5 1 3 5 1 4 5 1 5 5 1 6 5 1 7 5 1 8 5 1 9 5 2 0 5 2 1 5-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 53 x= 205m
1 0 5 11 5 1 2 5 1 3 5 1 4 5 1 5 5 1 6 5 1 7 5 1 8 5 1 9 5 2 0 5 2 1 5-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 54 x= 208m
1 0 5 11 5 1 2 5 1 3 5 1 4 5 1 5 5 1 6 5 1 7 5 1 8 5 1 9 5 2 0 5 2 1 5tim e(sec)
-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
surf
ace
elev
atio
n(m
)
ch : 55 x= 211m
C ase: T est5
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Spatial evolution of wave profiles(EXP. III, case 5)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
11 5 1 2 5 1 3 5 1 4 5 1 5 5 1 6 5 1 7 5 1 8 5 1 9 5 2 0 5 2 1 5 2 2 5-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 56 x= 214m
11 5 1 2 5 1 3 5 1 4 5 1 5 5 1 6 5 1 7 5 1 8 5 1 9 5 2 0 5 2 1 5 2 2 5-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 57 x= 217m
11 5 1 2 5 1 3 5 1 4 5 1 5 5 1 6 5 1 7 5 1 8 5 1 9 5 2 0 5 2 1 5 2 2 5-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 58 x= 220m
11 5 1 2 5 1 3 5 1 4 5 1 5 5 1 6 5 1 7 5 1 8 5 1 9 5 2 0 5 2 1 5 2 2 5-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 59 x= 223m
11 5 1 2 5 1 3 5 1 4 5 1 5 5 1 6 5 1 7 5 1 8 5 1 9 5 2 0 5 2 1 5 2 2 5tim e(sec)
-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
surf
ace
elev
atio
n(m
)
ch : 60 x= 226m
C ase: T est5
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Spatial evolution of wave profiles(EXP. III, case 5)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
1 2 5 1 3 5 1 4 5 1 5 5 1 6 5 1 7 5 1 8 5 1 9 5 2 0 5 2 1 5 2 2 5 2 3 5-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 61 x= 229m
1 2 5 1 3 5 1 4 5 1 5 5 1 6 5 1 7 5 1 8 5 1 9 5 2 0 5 2 1 5 2 2 5 2 3 5-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 62 x= 232m
1 2 5 1 3 5 1 4 5 1 5 5 1 6 5 1 7 5 1 8 5 1 9 5 2 0 5 2 1 5 2 2 5 2 3 5-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 63 x= 235m
1 2 5 1 3 5 1 4 5 1 5 5 1 6 5 1 7 5 1 8 5 1 9 5 2 0 5 2 1 5 2 2 5 2 3 5-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 64 x= 235 .88m
1 2 5 1 3 5 1 4 5 1 5 5 1 6 5 1 7 5 1 8 5 1 9 5 2 0 5 2 1 5 2 2 5 2 3 5tim e(sec)
-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
surf
ace
elev
atio
n(m
)
ch : 65 x= 238m
C ase: T est5
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Side band amplitude evolution (EXP. III, case 5)Side band amplitude evolution (EXP. III, case 5)
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 1 x= 15m
0 1 2 3 4 50 .0 00 .0 20 .0 40 .0 60 .0 80 .1 00 .1 20 .1 4
0 1 2 3 4 5
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 2 x= 17 .6m
0 1 2 3 4 50 .0 00 .0 20 .0 40 .0 60 .0 80 .1 00 .1 20 .1 4
0 1 2 3 4 5
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 3 x= 18 .12m
0 1 2 3 4 50 .0 00 .0 20 .0 40 .0 60 .0 80 .1 00 .1 20 .1 4
0 1 2 3 4 5
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 4 x= 19m
0 1 2 3 4 50 .0 00 .0 20 .0 40 .0 60 .0 80 .1 00 .1 20 .1 4
0 1 2 3 4 5
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0tim e(sec)
-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
surf
ace
elev
atio
n(m
)
ch : 5 x= 25m
0 1 2 3 4 5frequ en cy(H z)
0 .0 00 .0 20 .0 40 .0 60 .0 80 .1 00 .1 20 .1 4
ampl
itu
de,m
0 1 2 3 4 5frequ en cy(H z)
ampl
itu
de,m
C ase: T est5
kx/2=4.6
kx/2=5.4
kx/2=5.6
kx/2=5.9
kx/2=7.8
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Side band amplitude evolution (EXP. III , case 5)Side band amplitude evolution (EXP. III , case 5)
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 6 x= 31m
0 1 2 3 4 50 .0 0
0 .0 5
0 .1 0
0 .1 5
0 1 2 3 4 5
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 7 x= 37m
0 1 2 3 4 50 .0 0
0 .0 5
0 .1 0
0 .1 5
0 1 2 3 4 5
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 8 x= 43m
0 1 2 3 4 50 .0 0
0 .0 5
0 .1 0
0 .1 5
0 1 2 3 4 5
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 9 x= 49m
0 1 2 3 4 50 .0 0
0 .0 5
0 .1 0
0 .1 5
0 1 2 3 4 5
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0tim e(sec)
-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
surf
ace
elev
atio
n(m
)
ch : 10 x= 55m
0 1 2 3 4 5frequ en cy(H z)
0 .0 0
0 .0 5
0 .1 0
0 .1 5
ampl
itu
de,m
0 1 2 3 4 5frequ en cy(H z)
ampl
itu
de,m
C ase: T est5
kx/2=9.6
kx/2=11.5
kx/2=13.4
kx/2=15.2
kx/2=17.7
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Side band amplitude evolution (EXP. III , case 5)Side band amplitude evolution (EXP. III , case 5)
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 11 x= 61m
0 1 2 3 4 50 .0 0
0 .0 5
0 .1 0
0 .1 5
0 1 2 3 4 5
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 12 x= 67m
0 1 2 3 4 50 .0 0
0 .0 5
0 .1 0
0 .1 5
0 1 2 3 4 5
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 13 x= 73m
0 1 2 3 4 50 .0 0
0 .0 5
0 .1 0
0 .1 5
0 1 2 3 4 5
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 14 x= 79m
0 1 2 3 4 50 .0 0
0 .0 5
0 .1 0
0 .1 5
0 1 2 3 4 5
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0tim e(sec)
-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
surf
ace
elev
atio
n(m
)
ch : 15 x= 85m
0 1 2 3 4 5frequ en cy(H z)
0 .0 0
0 .0 5
0 .1 0
0 .1 5
ampl
itu
de,m
0 1 2 3 4 5frequ en cy(H z)
ampl
itu
de,m
C ase: T est5
kx/2=19
kx/2=20.9
kx/2=22.7
kx/2=24.6
kx/2=26.5
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Side band amplitude evolution (EXP. III , case 5)Side band amplitude evolution (EXP. III , case 5)
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 16 x= 91m
0 1 2 3 4 50 .0 0
0 .0 5
0 .1 0
0 .1 5
0 1 2 3 4 5
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 17 x= 97m
0 1 2 3 4 50 .0 0
0 .0 5
0 .1 0
0 .1 5
0 1 2 3 4 5
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 18 x= 100m
0 1 2 3 4 50 .0 0
0 .0 5
0 .1 0
0 .1 5
0 1 2 3 4 5
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 19 x= 103m
0 1 2 3 4 50 .0 0
0 .0 5
0 .1 0
0 .1 5
0 1 2 3 4 5
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0tim e(sec)
-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
surf
ace
elev
atio
n(m
)
ch : 20 x= 106m
0 1 2 3 4 5frequ en cy(H z)
0 .0 0
0 .0 5
0 .1 0
0 .1 5
ampl
itu
de,m
0 1 2 3 4 5frequ en cy(H z)
ampl
itu
de,m
C ase: T est5
kx/2=28.4
kx/2=30.2
kx/2=31.2
kx/2=32.1
kx/2=33.0
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Side band amplitude evolution (EXP. III , case 5)Side band amplitude evolution (EXP. III , case 5)
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 21 x= 109m
0 1 2 3 4 50 .0 0
0 .0 5
0 .1 0
0 .1 5
0 1 2 3 4 5
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 22 x= 112m
0 1 2 3 4 50 .0 0
0 .0 5
0 .1 0
0 .1 5
0 1 2 3 4 5
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 23 x= 115m
0 1 2 3 4 50 .0 0
0 .0 5
0 .1 0
0 .1 5
0 1 2 3 4 5
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 24 x= 118m
0 1 2 3 4 50 .0 0
0 .0 5
0 .1 0
0 .1 5
0 1 2 3 4 5
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0tim e(sec)
-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
surf
ace
elev
atio
n(m
)
ch : 25 x= 121m
0 1 2 3 4 5frequ en cy(H z)
0 .0 0
0 .0 5
0 .1 0
0 .1 5
ampl
itu
de,m
0 1 2 3 4 5frequ en cy(H z)
ampl
itu
de,m
C ase: T est5
kx/2=34
kx/2=34.9
kx/2=35.9
kx/2=36.8
kx/2=37.7
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Side band amplitude evolution (EXP. III , case 5)Side band amplitude evolution (EXP. III , case 5)
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 51 x= 199m
0 1 2 3 4 50 .0 0
0 .0 5
0 .1 0
0 .1 5
0 1 2 3 4 5
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 52 x= 202m
0 1 2 3 4 50 .0 0
0 .0 5
0 .1 0
0 .1 5
0 1 2 3 4 5
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 53 x= 205m
0 1 2 3 4 50 .0 0
0 .0 5
0 .1 0
0 .1 5
0 1 2 3 4 5
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 54 x= 208m
0 1 2 3 4 50 .0 0
0 .0 5
0 .1 0
0 .1 5
0 1 2 3 4 5
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0tim e(sec)
-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
surf
ace
elev
atio
n(m
)
ch : 55 x= 211m
0 1 2 3 4 5frequ en cy(H z)
0 .0 0
0 .0 5
0 .1 0
0 .1 5
ampl
itu
de,m
0 1 2 3 4 5frequ en cy(H z)
ampl
itu
de,m
C ase: T est5
kx/2=62.1
kx/2=63.0
kx/2=64
kx/2=64.9
kx/2=65.8
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Side band amplitude evolution (EXP. III , case 5)Side band amplitude evolution (EXP. III , case 5)
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 56 x= 214m
0 1 2 3 4 50 .0 0
0 .0 5
0 .1 0
0 .1 5
0 1 2 3 4 5
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 57 x= 217m
0 1 2 3 4 50 .0 0
0 .0 5
0 .1 0
0 .1 5
0 1 2 3 4 5
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 58 x= 220m
0 1 2 3 4 50 .0 0
0 .0 5
0 .1 0
0 .1 5
0 1 2 3 4 5
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 59 x= 223m
0 1 2 3 4 50 .0 0
0 .0 5
0 .1 0
0 .1 5
0 1 2 3 4 5
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0tim e(sec)
-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
surf
ace
elev
atio
n(m
)
ch : 60 x= 226m
0 1 2 3 4 5frequ en cy(H z)
0 .0 0
0 .0 5
0 .1 0
0 .1 5
ampl
itu
de,m
0 1 2 3 4 5frequ en cy(H z)
ampl
itu
de,m
C ase: T est5
kx/2=66.8
kx/2=67.7
kx/2=68.6
kx/2=69.6
kx/2=70.5
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Side band amplitude evolution (EXP. III , case 5)Side band amplitude evolution (EXP. III , case 5)
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 61 x= 229m
0 1 2 3 4 50 .0 0
0 .0 5
0 .1 0
0 .1 5
0 1 2 3 4 5
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 62 x= 232m
0 1 2 3 4 50 .0 0
0 .0 5
0 .1 0
0 .1 5
0 1 2 3 4 5
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 63 x= 235m
0 1 2 3 4 50 .0 0
0 .0 5
0 .1 0
0 .1 5
0 1 2 3 4 5
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
ch : 64 x= 235 .88m
0 1 2 3 4 50 .0 0
0 .0 5
0 .1 0
0 .1 5
0 1 2 3 4 5
1 8 0 1 9 0 2 0 0 2 1 0 2 2 0tim e(sec)
-0 .3 0-0 .2 0-0 .1 00 .0 00 .1 00 .2 00 .3 0
surf
ace
elev
atio
n(m
)
ch : 65 x= 238m
0 1 2 3 4 5frequ en cy(H z)
0 .0 0
0 .0 5
0 .1 0
0 .1 5
ampl
itu
de,m
0 1 2 3 4 5frequ en cy(H z)
ampl
itu
de,m
C ase: T est5
kx/2=71.5
kx/2=72.4
kx/2=73.3
kx/2=73.6
kx/2=74.6
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Non-dimensional amplitude vs. Non-dimensional amplitude vs. kxkx (EXP. III , case 5) (EXP. III , case 5)
a 0 a + a -
0 4 0 8 0 1 20 1 60 2 00 2 40 2 80 3 20 3 60 4 00 4 40
kx
0 .0
0 .2
0 .4
0 .6
0 .8
1 .0
1 .2
1 .4
1 .6
1 .8
2 .0
a /a0
3 8 1 3 1 8 23 2 8 33 38 4 3 48 5 3 5 8 63 6 8 73kx /2
Tainan Hydraulics
Thank you !Thank you !
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Lake et al.(1977)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.
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Waseda and Tulin(1999)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.
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Tulin and Waseda(1999)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.
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
MNDAS-MNDAS-the the MMulti-ulti-NNods ods DData ata AAcquisition cquisition SSystemystem
•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 IPCMInternet Internet
InternetInternet
ADAM4520 ADAM4520NODE 0 NODE 1 NODE M
ADAM5510NODE 1
ADAM5510NODE 2
ADAM5510NODE N
ADAM5510NODE 1
Internet
ADAM
sensors…
卓越計畫卓越計畫 ----斜坡上非線性波浪傳動特性之研究斜坡上非線性波浪傳動特性之研究
Tainan Hydraulics
Wave generator, the Super TankWave generator, the Super Tank