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29 2007 11 Proceedings of the 29th Ocean Engineering Conference in Taiwan National Cheng Kung University, November 2007
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( 0 =10)( 0 =15)
Experimental Study on the Effect of Varying Pycnocline Thickness on Internal Solitary Wave Evolution
Tien-Yu Lu Ming-Hung Cheng Te-Wang Lai Wei-Hung Wang Chen-Yuan Chen John R-C. Hsu*
*Professor, Department of Marine Environment and Engineering, National Sun Yat-sen University
ABSTRACT
Internal solitary waves (ISW) have been detected on the interface of a stratified water column in the ocean. It is believed that ISW could affect oil drilling operations, nutrient pumping, and acoustic signal obstruction. In the ocean, the thickness of a pycnocline is finite which differs with the theoretical assumption as being an ultra-thin layer. This paper reports the propagation of an ISW in various pycnocline thicknesses. Our experimental results show that, as the thickness of the pycnoline increases, the values of all the physical parameters (e.g. wave amplitude, phase speed, and wave energy) decreases. Their reduction rates were more significant in the case of small interface displacement (0=10cm) than that with large value of 0=15cm. On the other hand, the physical variables associated with a depression ISW are more significant than those in an elevation ISW.
Key words: psycnocline thickness; internal solitary wave; laboratory experiment
3m/s(Hsu et al., 2000)
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12m
ComputerA/D
Amplifier
MNDAS
Digital Camera
Probe 2 Probe 1Probe 4
0
0.3m3.2m5.5m
Probe 3
H1
H2
Sluice Gate
card
Converter
33 34 35 36 370
1000
2000
3000
4000
33 34 35 36 37 33 34 35 36 37
500
(0)
(m)
(Osborne et al., 1978)
(Johnson
et al., 2001)
( 1)
(pycnocline)
1 2
1
2
(1992)(1997)(1995)
(
)
MNDAS
MATLAB
3
3
3.1
3.1.1
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MATLAB
10
15
4 5
4 H1/H2=10cm/40cm
0=15cm 15
1=999g/cm32=1020g/cm3
5 H1/H2=40cm/10cm
0=15cm 15
1=999g/cm32=1020g/cm3
3.1.2
( 4
5)
H1/H2=10/4015/3535/15 40/10cm
15 6
( )/()( 121 ) 0~1 Z=0
6
(B/H)(f)
0~0.1
5 6 ~
B/H
( 2cm )
6
3.2 (
)
i
nai a
aT = aiT na
ia ( 1
). (1)
i
ta a
aT = aT ta
( 3 ) ia
(2)
i
nEi E
ET = EiT nE
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iE ..(3)
i
tE E
ET = ET tE
iE .(4)
i
nCi C
CT = EiT nC
iC ..(5)
3.2.1
7 8
1510 15
B
7
6 H1/H2=10cm/40cm
0=15cm
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m)
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7 H1/H2=10cm/40cm
0=15cm 1510 15
0 10 20 30 40 50 60 70-2
-1
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(t)(c
m)
time(s)
1st (B=4cm)5th (B=8cm)10th (B=10cm)15th (B=14cm)
8 H1/H2=40cm/10cm0=15cm 1510 15
3.2.2
9
(0=15cm)
(ai)
10 H1/H2
(0=15cm)
10
2 4 6 8 10 12 140.75
0.8
0.85
0.9
0.95
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1.05
1.1
1.15
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(cm)
T ai
9 0=15cm H1/H2
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2 4 6 8 10 12 140.65
0.7
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
(cm)
T a
10 0=15cm H1/H2
3.2.3
Wessels and Hutter (1996)
C0
''0 HgC = . .(6)
( )2121 /' HHHHH += ( ) 112 /' = gg 11 (0=15cm)
C(cm/sec)
(0)
12
(0=15cm)
0
(H1/H2=10cm/40cm)
(%/cm)(H1/H2=40cm/10cm)
0
0
2 4 6 8 10 12 148
8.5
9
9.5
10
10.5
11
(cm)
C (cm
/s)
11 0=15cm H1/H2
2 4 6 8 10 12 140.92
0.94
0.96
0.98
1
1.02
1.04
(cm)
Ci
12 0=15cm H1/H2
3.2.4
13 H1/H2
(0=15cm)
(Koop and Butler, 1981Michallet and Barthelemy,
1997)(Vlasenko and Hutter, 2002)
14
H1/H2 (0= 10cm)
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2 4 6 8 10 12 140.6
0.7
0.8
0.9
1
1.1
(cm)
T Ei
13 0=15cm H1/H2
2 4 6 8 10 12 140.3
0.4
0.5
0.6
0.7
0.8
0.9
1
(cm)
T E
14 0=10cm H1/H2
12
H=50cm
( H1 H2)
(0=10 15cm)
(H1/H2=10cm/40cm, 15cm/35cm 35cm/15cm
40cm/10cm)
(0=15cm)
(H1/H2=10cm/40cm 35cm/15cm)
1.
2.
NSC 95-2611-M-110 -008
--
1. Hsu, M.K. and Liu, A.K. (2000) Nonlinear
internal waves in the South China Sea, Canadian
Journal of Remote Sensing, 26, pp. 72-81.
2. Johnson, D.R., Weidemann, A. and Pegau, W.S.
(2001) Internal tidal bores and bottom nepheloid
layers, Continental Shelf Research, 21, pp.
1473-1484.
3. Koop, C.G. and Butler, G. (1981) An investigation
of internal solitary waves in a two-fluid system, J.
Fluid Mech., 112, pp. 225-251.
4. Michallet, H. and Barthelemy, E. (1997)
Ultrasonic probes and data processing to study
interfacial solitary waves, Experiments in Fluid,
22, pp. 380-386.
5. Osborne, A.R., Burch, T.L. and Scarlet, T.I. (1978)
The influence of internal waves on deepwater
drilling, J. Petroleum Tech., 30, pp. 1497-1504.
6. Vlasenko, V. and Hutter, K. (2002) Numerical
experiments on the breaking of solitary internal
waves over a slope-shelf topography, J. Physical
Oceanography, 32(6), pp. 1779-1793.
7. Wessels, F. and Hutter, K. (1996) Interaction of
internal waves with a topographic sill in a
two-layered fluid, J. Phys. Oceanogr., 26(1), pp.
5-20.
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