Open AccessNonlinear conditions for instability of the free surface of a conducting liquid in an external electric field in a confined axisymmetric geometry
Author(s) -
O. V. Zubareva,
Н. М. Зубарев,
Konstantin E. Bobrov
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1556/1/012015
Subject(s) - rotational symmetry , instability , classical mechanics , physics , electric field , boundary value problem , nonlinear system , amplitude , bounded function , free surface , mechanics , geometry , mathematics , mathematical analysis , optics , quantum mechanics
The behavior of the free surface of a perfectly conducting liquid in an external uniform electric field is considered in the framework of the Hamiltonian formalism for the case of bounded axisymmetric geometry of the system (the fluid is bounded by a cylindrical rigid wall). Taking into account the influence of quadratic nonlinearities, we derive an amplitude equation which describes the evolution of the boundary. Using this equation, we find the condition for the hard excitation of boundary instability that leads to an explosive growth of surface perturbations. The differences in the description of the dynamics of axisymmetric perturbations of the boundary from the cases of plane, square, and hexagonal symmetries of the problem are discussed.