Download - EXPERIMENTS ON TRANSFORMATION AND BREAKING OF INTERNAL SOLITARY WAVES BY LOCAL CONSTRICTION
STRONGLY NONLINEAR INTERNAL WAVES IN LAKES:
GENERATION, TRANSFORMATION, MEROMIXIS
Grant INTAS 03-51-3728
EXPERIMENTS ON TRANSFORMATION AND BREAKING OF
INTERNAL SOLITARY WAVES BY LOCAL CONSTRICTION
Institute of Hydromechanics of NAS of the UkraineKiev, Ukraine
Ph. (38044) 455-64-34; Fax: 38044 – 455-6432); e-mail: vin @ visti.com
EQUIPMENT
BASIN (length 7 m; width 0.40 m; height 1.5 m) ADC2, ADC3, ADC4 – sensors of capacity
WAVE GENERATOR ADC 5, ADC6 –sensors of conductivity
MODELS OF CONSTRICTIONS
SHAPE OF CONSTRICTIONS
L=120 cm L=97 cmB=19.5 cm B=32 cm
L=177.5 cm, B=19.5 cm (with rectangular inserting)
22sin1
2)(
LxB
xf
PARAMETERS- phase speed of an infinitely long,
infinite- simally small waves
- solitary wave speed (KdV)
- speed of strongly nonlinear solitary wave
Wave length: 1. - half-amplitude point: Total energy2.
In the reference frame moving with ISW Conservation law
2/121
0
Hhhgс
21
120
* )(211
hhhha
сс
21)( axx5.0
Hahahgс )()( 21**
1
0
)()( 2
0
2t
t
tdtgcxdtgE
1
0
)()(1 t
tW tdt
aсxdx
aL
)()( 111 xhxuchc
)()( 221 xhxuchc
cuFr /11
cuFr /22
2
2
2
1
22
122
21
2
aha
aha
cu
cu
FrFrG
0020
2 BaBa
RESULTS(B=19.5 cm)
Scheme of experiment02.11, B=19.5 cm, run1, =30 cm, =2.16 cm, =0.6 cm
Scheme of experiment26.10, B=19.5 cm, run1, =30 cm, =2.8 cm, =1.1 cm
a c c0 c* E*g
adc4_i
5.3 20.8 11.1 5.5 11.7 43.2 827..9
adc3_i
7.9
adc2_i
5.3
adc1_p
3.9 19.3 c*=10 5.5 10 37.4 415.7
adc0_p
3.5 12.8 11.3(c*=9.5)
5.5 9.5 31.0 244
2/1wL
a c c0 c* E*g
adc4_i
6.23 21.7 11.3 6.2 12.3 44.3 1215
adc3_i
7.36
adc2_p
6.48 27.1 54.3 1676
adc1_p
5.12 3 c*=11.2 6.2 11.2
adc0_p
3.38 13.3 (c*=9.5) 6.2 9.5 26.3 202
totalH1h h
totalH
1h h 2/1
CONCLUSIONS
1. It is found that effect of constriction results in the substantial transformation of flow, instability of solitary waves and strong dissipation.
2. Passed and reflected solitary waves are generated due to interaction of solitary waves with constriction. The energy of these waves are considerably less than energy of initial wave. The interaction is an effective mechanism of decreasing of scales.
3. It is shown that sharp steepening is accompanied be the growth of the amplitude and subsequent breaking of wave. At strong interaction the dividing of wave depending of amplitude are observed: the leading part go through narrowing but last part is trapped and forms the reflected wave and “tail” of the leading part.
4. After passing the narrowing the system of vortices arise in convergent part of flow that is the effective mechanism of dissipation.
5. The irregularity of amplitude distribution in cross section in front of constriction is occurred. This is the main reason of transformation of flow near narrowing, dividing of strongly non-linear wave and trapping of rear part.