Stability of Nonlinear Oscillations of a Spherical Layer of an Ideal Fluid
V. K. Andreev1,2
1Institute of Computational Modeling, Siberian Branch, Russian Academy of Sciences, Krasnoyarsk, 660036, Russia
2Siberian Federal University, Krasnoyarsk, 660036, Russia
Keywords: идеальная жидкость, поверхность раздела, нелинейные колебания, малые возмущения, устойчивость, ideal fluid, interface, nonlinear oscillations, small perturbations, stability
Abstract
The nonstationary motion of a spherical layer of an ideal fluid is investigated taking into account the adiabatic distribution of gas pressure in the internal cavity. The existence of nonlinear oscillations of the layer is established, and their period is determined. It is shown that there is only one equilibrium state of the layer. Amplitude equations taking into account the action of capillary forces on the surfaces of the layer in a linear approximation are obtained and used to study the stability of nonlinear oscillations of the layer. The limiting cases of a spherical bubble and soap film are considered.
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