Geoscience Reference
In-Depth Information
A distributed resistance thermometer, made of copper wire 0.06 mm in diame-
ter, was used as the temperature sensor. During measurements the frame was set
in the horizontal plane. The dimension of the active area of the sensor amounted
to 10
0
.
1 s. The sen-
sor continuously scanned the area above the piston along the vertical, its velocity
was 1.8 mm s
−
1
. Registration of the readings of the resistance thermometer was
performed with the aid of an online personal computer.
To reveal dynamic modes that may exist in the liquid, in the case of bottom
oscillations, 'scanning' was performed over the amplitude and frequency within
the ranges of 0.22-0.97 mm and 0-70 Hz, respectively. Three main dynamic modes
were revealed:
×
10 cm. The time constant of the temperature sensor was
∼
1. Linear wave formation
2. Dissipative structures—systems of standing waves exhibiting characteristic
hexagonal (Fig. 7.14a) or orthogonal (Fig. 7.14b) symmetry (Faraday ripples)
3. Irregular (chaotic) motion with drops torn away and intense 'fountaining' of liq-
uid (Fig. 7.14c)
When speaking of 'linear wave formation' we intend that waves peculiar to the first
mode can be described as the linear response of an ideal liquid to oscillations of
the bottom.
Determination was to be performed of two most clearly traceable bifurcation
boundaries: 'linear wave formation-dissipative structures' (boundary 1-2) and 'sep-
arate drops-intense fountaining' (boundary 2-3). The results of experiments are
presented in a summary form in Fig. 7.15, from which the bifurcation portrait
of the system, drawn in 'amplitude-frequency' coordinates, reveals three regions,
corresponding to regular linear wave formation (1), to the existence of dissipative
structures (2) and to chaotic motion (3). The boundaries of the regions indicated
correspond to bifurcation combinations of oscillation frequencies and amplitudes, at
which, when achieved, a change of dynamic mode is observed. Note that the respec-
tive amplitude-frequency bifurcation combinations were achieved both by smooth
(b)
(a)
(c)
Fig. 7.14 Structures of standing waves of hexagonal (a) and orthogonal (b) symmetry on the sur-
face of the liquid in the case of bottom oscillations. Chaotic motion of the surface (view through
the transparent lateral wall of the basin) (c). The photographs are obtained with the aid of the mod-
ified version of the set-up
