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Parametric Third‐Subharmonic Resonance in Nonlinear Electrohydrodynamic Rayleigh‐Taylor Instability with Mass and Heat Transfer
Author(s) -
Mahmoud Y.D.
Publication year - 1999
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/(sici)1521-4001(199912)79:12<855::aid-zamm855>3.0.co;2-x
Subject(s) - electrohydrodynamics , rayleigh–taylor instability , nonlinear system , instability , physics , mechanics , parametric oscillator , electric field , resonance (particle physics) , classical mechanics , parametric statistics , heat transfer , quantum electrodynamics , mathematical analysis , mathematics , atomic physics , quantum mechanics , statistics
The nonlinear electrohydrodynamic Rayleigh‐Taylor instability with mass and heat transfer is investigated. The fluids are stressed by a periodic acceleration and a normal electric field. Based on the method of multiple scales, a parametric nonlinear Schrödinger equation with complex coefficients is derived in the third‐subharmonic resonance case. A standard nonlinear Schrödinger equation with complex coefficients is obtained in the non‐resonance case. A temporal solution is carried out for the parametric nonlinear Schrödinger equation. Necessary and sufficient conditions for stability are obtained. Numerical calculations show that the thickness of the fluid, the normal electric field, and the coefficient of mass and heat transfer have destabilizing effect. It is found that the external frequency plays a dual role in the stability criteria.