Gas bubble oscillations in a fluid in the presence of 2:1 resonance between the radial and deformation oscillation frequencies

Петров, А. Г.; Фомичев, А. В.

doi:10.1134/s0015462809020100

Cited by 2 publications

(3 citation statements)

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“…We recall that in order to find the period in seconds, we should subdi vide the current dimensionless period by ω ε (11). These results agree well with [8], where the oscillation transfer is considered for n = 2.…”

Section: Asymptotic Integration Of the Hamiltonian Equationssupporting

confidence: 88%

“…We performed an investigation similar to [8,9] for the energy transfer of the radial mode into the arbitrary three dimensional deformation mode. It is shown that, during the energy transfer, the amplitude of the deformational mode increases anomalously, which can be one mechanism of bubble subdivision.…”

Section: Introductionmentioning

confidence: 99%

“…The authors of [1][2][3] used the method of two scales and other rather cumbersome methods of solution. The problem of free ellipsoidal oscillations of the gas bub ble was investigated analytically by the method of the Hamiltonian norm form [7] in [8]. The asymptotic solution for the energy transfer into an arbitrary axially symmetric mode was found by the method of the Hamiltonian norm form in [9].…”

Section: Introductionmentioning

confidence: 99%

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The resonant mechanism of subdivision of a gas bubble in a fluid

Vanovskii

Петров

2012

Dokl. Phys.

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Small nonlinear oscillations of a bubble in a fluid at the resonance of the frequencies of the radial mode and an arbitrary deformational mode 2 : 1 are considered. The deformational mode is determined by the associated Legendre polynomial with indices n = 2, 3, …, m = 0, 1, …, n. The energy transfer from the radial mode into the Legendre deformational mode is described by the method of invariant normalization. An analogy is established with oscillations of the material point on the string with the frequency ratio of the vertical mode to the horizontal one of 2. During the transfer, the amplitude of the Legendre mode with indices n, m exceeds the amplitude of radial oscillations by a factor of 3n at m = 0. As index m increases, the transfer time increases considerably and the maximal amplitude of the Legendre mode increases insignificantly in this case. From here, it is concluded that the deformational Legendre mode with indices n, m = n has the greatest probability to rise. The considered effect can serve as a mechanism of subdivision of gas bubbles under varying the external pressure in the fluid.

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Section: Asymptotic Integration Of the Hamiltonian Equationssupporting

confidence: 88%

Section: Introductionmentioning

confidence: 99%