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Generation of spiral waves at parametric excitation in a cuvette with inhomogeneous boundary


S.V. Kiyashko − Dr.Sc. (Phys.-Math.), Senior Research Scientist, Institute of Applied Physics of Russian Academy of Science, Nizhny Novgorod, Russia. E-mail: V.O. Afenchenko − Ph.D. (Phys.-Math.), Institute of Applied Physics of Russian Academy of Science, Nizhny Novgorod, Russia. E-mail: A.V. Nazarovsky − Ph.D. (Phys.-Math.), Institute of Applied Physics of Russian Academy of Science, Nizhny Novgorod, Russia. E-mail:

In the present paper we report results of experimental study of the process of arising of standing spiral waves on the surface of vis-cous liquid layer in an oscillating field of gravity. Parametric pumping creates instability and growth of wave amplitude is limited by the nonlinear dependence of viscous losses on amplitude. Only roll structures of standing waves may exist in a highly viscous liquid because of strong competition. However, spiral waves do not occur in ordinary conditions; instead, parallel rolls in a rectangular cell and circular standing waves in a round cell are formed. This is explained by the fact that, when pump is switched on, strongly damping shear waves appear at the vertical boundary of the cell, that serve as initial perturbations for excitation of standing roll waves. In a round cell, these perturbations repeat the shape of the cell, thus resulting in the onset of stationary regime in the form of circular rolls. However, if there is nouniformity such as a ledge in the wall, then the excitation front will contain a defect that will move to the cen-ter of the cell, which may give rise to a spiral wave. In the current work the process of spiral wave generation in the presence of nonuniformities at the boundary and in the case of perturbations on the liquid surface is studied in experiment. We took highly viscous silicon oil (viscosity 100 times more than water viscosity) as an operating liquid. Vertical vibrations of the cell were produced by means of a vibration table. In the course of the experiment we varied the amplitude and oscillation frequency f~ 41-81 Hz of the cell, as well as liquid depth (4-8 mm). Images of the patterns formed by capillary waves were recorded by a digital video camera and were fed to the computer for further processing. Experiments on studying spiral wave generation in the presence of nonuniformity at the boundary were conducted as follows. A tri-angular ledge was placed at the boundary of a circular cell. After that, sinusoidal voltage was supplied to the amplifier input at fixed liquid depth and with fixed frequency of external signal. Near the walls, there appeared regions of capillary ripples containing defects, with the boundaries parallel to the walls of the cell. Further, the fronts of these regions propagated to the center of the cell, the am-plitude of the standing field balanced, and a spiral structure were established. We investigated generation of spiral waves as a function of parameters of nonuniformity at the boundary. It was revealed that the most effective is nonuniformity with ledge height close to the wavelength of excited spiral waves. It was shown that in the presence of several ledges at the boundary, multi-arm spiral waves with preset number of arms and arm direction may be generated. Regions of the parameters at which a stable spiral structure is formed were found.


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