100
V. Liapidevskii and N. Gavrilov
Internal Solitary Waves in Laboratory and Field Experiments
Internal Waves of Depression
The constructed solutions for ULM and BLM can be compared with numerous laboratory and field experimental data. We consider first the laboratory experiments on
internal solitary waves of depression performed in [6]. These results are the most
appropriate to the three-layer flow scheme of BLM, since the thickness of the intermediate layer was controlled in experiments. Solitary wave profiles calculated by
(19) are shown in Fig. 7 together with the experimental data from [6] (Fig. 3c, d).
Analogously to the laboratory experiments described above in section “Laboratory
Experiments”, the solitary waves of depression were generated by removing the
vertical gate between two stratified fluids at rest (the lock-exchange problem). The
dimensional parameters determining the waves are h 0 = 30 cm, í µí¼ 0 = 5.5 cm, í µí¼ 0 =
5 cm, b = 20cm∕s
2 , ̄
b =
1
2
b, Fr = 0.485 (Fig. 7a) and h 0 = 29.5 cm, í µí¼ 0 = 5.5 cm,
í µí¼ 0 = 1.5 cm, b = 20 cm∕s
2 , ̄
b =
1
2
b, Fr = 0.462 (Fig. 7b) (the runs No. 1 and No.
24 in [6]). Solid black lines on Fig. 7 are the results of calculations, solid white lines
are the experimentally found positions of pycnocline between the layers, the backgrounds are photos of the experiment.
In oceans and seas the density stratification is rather complicated. Nevertheless,
we may apply the three-layer shallow water models for large internal waves in shelf
zones. In Fig. 8a the time-dependence of isopycnal deformation during the subsurface solitary wave passage in the shelf zone of the South China sea is shown [20]
(Fig. 3e). Thick black lines are the result of calculation by BLM with the following
dimensional data: h 0 = 395 m, í µí¼ 0 = 100 m, í µí¼ 0 = 30 m, b = 4 × 10 −2 m∕s
2 , ̄
b = 0.3b,
Fr = 0.447. The total depth is 525 m.
Internal Waves of Elevation
As was mentioned above, UBL is developed for large internal waves of elevation. In
laboratory experiments it can be used for calculations as the spatial patterns so the
temporal patterns of bottom internal waves (Fig. 3a and b). The solid black lines are
the results of calculations by ULM with the parameters: h 0 = 0.3 cm, í µí¼ 0 = 0.8 cm,
í µí¼ 0 = 6.9 cm, b = 5 cm∕s
2 , ̄
b = 0.5b, Fr = 0.476. UBL also can be applied for field
data taken from [18] (Fig. 8b). The measurements of the vertical temperature distribution were performed 09.09.2011 in nearshore waters of the Sea of Japan at the
depth 18 m. In Fig. 8b the contour plot of temperature (thin lines) is shown together
with the calculations by ULM (thick lines). The upper layer was practically homogeneous with the temperature 18 ◦ C. The “bolus” of cold water with the temperature
10–12
◦
C in the wave core passed through the bottom measurement station in 5 min.
The wave amplitude reached half of the total depth. The ULM parameters of the wave
are: h 0 = 0.9 m, í µí¼ 0 = 2 m, í µí¼ 0 = 15.1 m, b = 1.2 × 10
−2
m∕s
2 , ̄
b = 0.3b, Fr = 0.47.
V. Liapidevskii and N. Gavrilov
Internal Solitary Waves in Laboratory and Field Experiments
Internal Waves of Depression
The constructed solutions for ULM and BLM can be compared with numerous laboratory and field experimental data. We consider first the laboratory experiments on
internal solitary waves of depression performed in [6]. These results are the most
appropriate to the three-layer flow scheme of BLM, since the thickness of the intermediate layer was controlled in experiments. Solitary wave profiles calculated by
(19) are shown in Fig. 7 together with the experimental data from [6] (Fig. 3c, d).
Analogously to the laboratory experiments described above in section “Laboratory
Experiments”, the solitary waves of depression were generated by removing the
vertical gate between two stratified fluids at rest (the lock-exchange problem). The
dimensional parameters determining the waves are h 0 = 30 cm, í µí¼ 0 = 5.5 cm, í µí¼ 0 =
5 cm, b = 20cm∕s
2 , ̄
b =
1
2
b, Fr = 0.485 (Fig. 7a) and h 0 = 29.5 cm, í µí¼ 0 = 5.5 cm,
í µí¼ 0 = 1.5 cm, b = 20 cm∕s
2 , ̄
b =
1
2
b, Fr = 0.462 (Fig. 7b) (the runs No. 1 and No.
24 in [6]). Solid black lines on Fig. 7 are the results of calculations, solid white lines
are the experimentally found positions of pycnocline between the layers, the backgrounds are photos of the experiment.
In oceans and seas the density stratification is rather complicated. Nevertheless,
we may apply the three-layer shallow water models for large internal waves in shelf
zones. In Fig. 8a the time-dependence of isopycnal deformation during the subsurface solitary wave passage in the shelf zone of the South China sea is shown [20]
(Fig. 3e). Thick black lines are the result of calculation by BLM with the following
dimensional data: h 0 = 395 m, í µí¼ 0 = 100 m, í µí¼ 0 = 30 m, b = 4 × 10 −2 m∕s
2 , ̄
b = 0.3b,
Fr = 0.447. The total depth is 525 m.
Internal Waves of Elevation
As was mentioned above, UBL is developed for large internal waves of elevation. In
laboratory experiments it can be used for calculations as the spatial patterns so the
temporal patterns of bottom internal waves (Fig. 3a and b). The solid black lines are
the results of calculations by ULM with the parameters: h 0 = 0.3 cm, í µí¼ 0 = 0.8 cm,
í µí¼ 0 = 6.9 cm, b = 5 cm∕s
2 , ̄
b = 0.5b, Fr = 0.476. UBL also can be applied for field
data taken from [18] (Fig. 8b). The measurements of the vertical temperature distribution were performed 09.09.2011 in nearshore waters of the Sea of Japan at the
depth 18 m. In Fig. 8b the contour plot of temperature (thin lines) is shown together
with the calculations by ULM (thick lines). The upper layer was practically homogeneous with the temperature 18 ◦ C. The “bolus” of cold water with the temperature
10–12
◦
C in the wave core passed through the bottom measurement station in 5 min.
The wave amplitude reached half of the total depth. The ULM parameters of the wave
are: h 0 = 0.9 m, í µí¼ 0 = 2 m, í µí¼ 0 = 15.1 m, b = 1.2 × 10
−2
m∕s
2 , ̄
b = 0.3b, Fr = 0.47.