88
V. Liapidevskii and N. Gavrilov
soliton-like waves (“solibores”) containing trapped dense core is the common feature
of the run-up process of internal waves. It can be observed in any shelf zone with high
internal wave activity as well as in laboratory experiments. Breaking of internal solitary waves is closely connected with shear-induced instability at interfaces, which is
an object of recent intense investigations in laboratory and field observations [1, 6,
16, 20, 23].
In the paper the multi-layer shallow water model describing the nonstationary
interaction and decaying of large internal solitary waves is presented. The equations
are the direct extension of the Green–Naghdi equations developed for open channel
flows of multi-layer stratified fluids. It is shown that the two- and three-layer shallow water equations taking into account the dispersion effects, can describe large
amplitude internal wave evolution for different types of flows (intrusions, bottom
and subsurface internal waves in field and laboratory conditions).
Laboratory Experiments
Here we describe briefly the laboratory experiments performed in the Lavrentyev
Institute of Hydrodynamics, which will be used in next sections to validate the
mathematical models. More detailed description of the experiments can be found in
[7–11].
Experiments were carried out in a test tank of length 3.2 m, width 0.2 m and
depth 0.35 m, the walls of the test tank were made of Perspex. The test tank was
divided by a vertical removable wall in two parts as it is shown in Fig. 1. The geometrical set-up of the experiments is clear from the sketches shown in the figure.
Figure 1a illustrates the experiments on the symmetric solitary wave evolution along
the interface. It shows the special installation (inclined bottom and lid in the flume)
to provide the shoaling of symmetric solitary waves of the second mode over a shelf
(í µí»¼ = í µí»½) or the shoaling of the subsurface waves of depression (í µí»¼ > 0, í µí»½ = 0). Various applications of solitary wave dynamics revealed in laboratory experiments to
the shoaling of large internal waves in a shelf zone have been discussed in [11, 12].
Here we focus our attention mostly on the special features of internal solitary wave
propagation over the flat bottom (í µí»¼ = í µí»½ = 0). Figure 1b sketches the nonsymmetric
solitary wave generation in the lock-exchange problem.
The experimental setup is shown in Fig. 2. For visualization of the flow pattern
LIF-technique (Laser Induced Fluorescence) is used. The method is based on the
fact that at low concentrations of fluorescein its luminosity during laser irradiation
is directly proportional to the concentration. This allows not only to get qualitative
information (for example, about mixing processes), but also quantitative information
about the density of the liquid in any part of the investigated area. To create the light
sheet, the diode-pumped solid-state laser “Mozart” is used, it provides a powerful
continuous radiation at a wavelength of 532 nm. By changing thermostat temperature
the radiation power could be varied from a few mW up to 5 W. The control system
allows to change the width of the sheet and the direction of the light, also the mirror
V. Liapidevskii and N. Gavrilov
soliton-like waves (“solibores”) containing trapped dense core is the common feature
of the run-up process of internal waves. It can be observed in any shelf zone with high
internal wave activity as well as in laboratory experiments. Breaking of internal solitary waves is closely connected with shear-induced instability at interfaces, which is
an object of recent intense investigations in laboratory and field observations [1, 6,
16, 20, 23].
In the paper the multi-layer shallow water model describing the nonstationary
interaction and decaying of large internal solitary waves is presented. The equations
are the direct extension of the Green–Naghdi equations developed for open channel
flows of multi-layer stratified fluids. It is shown that the two- and three-layer shallow water equations taking into account the dispersion effects, can describe large
amplitude internal wave evolution for different types of flows (intrusions, bottom
and subsurface internal waves in field and laboratory conditions).
Laboratory Experiments
Here we describe briefly the laboratory experiments performed in the Lavrentyev
Institute of Hydrodynamics, which will be used in next sections to validate the
mathematical models. More detailed description of the experiments can be found in
[7–11].
Experiments were carried out in a test tank of length 3.2 m, width 0.2 m and
depth 0.35 m, the walls of the test tank were made of Perspex. The test tank was
divided by a vertical removable wall in two parts as it is shown in Fig. 1. The geometrical set-up of the experiments is clear from the sketches shown in the figure.
Figure 1a illustrates the experiments on the symmetric solitary wave evolution along
the interface. It shows the special installation (inclined bottom and lid in the flume)
to provide the shoaling of symmetric solitary waves of the second mode over a shelf
(í µí»¼ = í µí»½) or the shoaling of the subsurface waves of depression (í µí»¼ > 0, í µí»½ = 0). Various applications of solitary wave dynamics revealed in laboratory experiments to
the shoaling of large internal waves in a shelf zone have been discussed in [11, 12].
Here we focus our attention mostly on the special features of internal solitary wave
propagation over the flat bottom (í µí»¼ = í µí»½ = 0). Figure 1b sketches the nonsymmetric
solitary wave generation in the lock-exchange problem.
The experimental setup is shown in Fig. 2. For visualization of the flow pattern
LIF-technique (Laser Induced Fluorescence) is used. The method is based on the
fact that at low concentrations of fluorescein its luminosity during laser irradiation
is directly proportional to the concentration. This allows not only to get qualitative
information (for example, about mixing processes), but also quantitative information
about the density of the liquid in any part of the investigated area. To create the light
sheet, the diode-pumped solid-state laser “Mozart” is used, it provides a powerful
continuous radiation at a wavelength of 532 nm. By changing thermostat temperature
the radiation power could be varied from a few mW up to 5 W. The control system
allows to change the width of the sheet and the direction of the light, also the mirror