Nonlinear resonance interaction between the oscillation modes of a spherical liquid layer on the surface of a melting hailstone |
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Authors: | A I Grigor’ev D O Kornienko S O Shiryaeva |
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Institution: | 1.Demidov State University,Yaroslavl,Russia |
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Abstract: | Evolutionary equations are derived and solved that describe the time dependence of the oscillation mode amplitudes on the
surface of a charged conducting liquid layer resting on a solid core. It is assumed that the layer experiences a multimode
initial deformation. The equations are solved asymptotically in the second order of smallness in the small dimensionless amplitude
of capillary oscillations on the surface of the layer. Mechanisms behind internal nonlinear resonance interaction between
the modes of the liquid layer oscillations and behind energy transfer between the modes both in degenerate and in secondary
combination resonances are investigated. It is found that in the degenerate resonance interaction between oscillation modes,
the energy may be transferred not only from lower to higher modes but also vice versa if the higher mode is excited at the
zero time. This conclusion is valid not only for a liquid layer on the surface of a solid core but also for a drop. |
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