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

PROFILES ( )

sensor of conductivity

CALIBRATION

04.11, run1 04.11, run 2

cm5.19

DATA SCHEME 0F EXPERIMENT CALIBRATION

adc4 adc2 adc1 adc0

VISUALIZATION

04.11 (a=8.2 cm)

VISUALIZATION

26.10 (a=6.2 cm)

VISUALIZATION

02.11 (a=5.3 cm)

SHAPE

a=8.2 cm (super-critical regime)

a=5.3 cm (sub-critical regime)

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

PROFILES ( )SCHEME 0F EXPERIMENT

07.12, run1 07.12, run2

cm8

DATArun1, a=8.1 cm

adc3 adc2 adc1 adc0

SHAPEadc3 adc0

VISUALIZATION

07.12 (a=8.1 cm)

VISUALIZATION

09.12 (a=4.4 cm)

VISUALIZATION

13.12 (a=3.9 cm)

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.