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Quadratic resonance in the three-dimensional oscillations of inviscid drops with surface tensionThe moderate-amplitude, three-dimensional oscillations of an inviscid drop are described in terms of spherical harmonics. Specific oscillation modes are resonantly coupled by quadratic nonlinearities caused by inertia, capillarity, and drop deformation. The equations describing the interactions of these modes are derived from the variational principle for the appropriate Lagrangian by expressing the modal amplitudes to be functions of a slow time scale and by preaveraging the Lagrangian over the time scale of the primary oscillations. Stochastic motions are predicted for nonaxisymmetric deformations starting from most initial conditions, even those arbitrarily close to the axisymmetric shapes. The stochasticity is characterized by a redistribution of the energy contained in the initial deformation over all the degrees of freedom of the interacting modes.
Document ID
19870029392
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Natarajan, R.
(Massachusetts Inst. of Tech. Cambridge, MA, United States)
Brown, R. A.
(MIT Cambridge, MA, United States)
Date Acquired
August 13, 2013
Publication Date
September 1, 1986
Publication Information
Publication: Physics of Fluids
Volume: 29
ISSN: 0031-9171
Subject Category
Fluid Mechanics And Heat Transfer
Accession Number
87A16666
Distribution Limits
Public
Copyright
Other

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