The electrohydrodynamic stability of a horizontal interface separating two dielectric streaming fluids stressed by an oblique electric field is studied. The method of multiple scale perturbations is used in order to obtain uniformly valid expansions near the cutoff wavenumber separating stable and unstable deformations. Two nonlinear Schrodinger equations are obtained, one of which leads to the determination of the cutoff wavenumber. The other Schrodinger equation is used to analyze the stability of the system. These equations are derived when the difference between the velocities of the two fluids is less than or equal to the critical velocity. It is shown that, for subcritical values of the velocity difference, the wave train of constant amplitude is unstable against modulations whereas for the supercritical values the instability is governed by a nonlinear Klein-Gordon equation. From the latter equation, the various stability criteria are obtained.

Nonlinear electrohydrodynamic Kelvin-Helmholtz instability under the influence of an oblique electric field

The nonlinear stability of surface waves propagating between two superposed streaming magnetic fluids is investigated. The fluids are stressed by a constant tangential magnetic field and a vertical periodic acceleration. The solution employs the method of multiple scales. Owing to the periodicity, resonant cases appear. Two parametrically nonlinear Schrodinger equations are derived for the resonant cases to describe the elevation of weakly nonlinear capillary waves. The standard nonlinear Schrodinger equation is satisfied for the non-resonant case. Necessary and sufficient conditions for stability are obtained. A formula for the surface elevation is obtained in each case. It is found that the magnetic field, the velocities and the frequency of the applied periodic force play dual roles in the resonant region. Investigation of the stability criterion by nonlinear perturbation shows that an increase in the acceleration frequency has a stabilizing effect. The stabilizing role of the frequency is due to the destabilizing effect of the amplitude of the periodic acceleration.

Nonlinear stability of Kelvin-Helmholtz waves in magnetic fluids stressed by a time-dependent acceleration and a tangential magnetic field

Three-Dimensional Viscous Potential Electrohydrodynamic Kelvin–Helmholtz Instability Through Vertical Cylindrical Porous Inclusions With Permeable Boundaries

A weakly nonlinear interfacial wave propagating between two dielectric fluids and influenced by an oblique electric field is studied. The analysis considers the surface tension and viscoelastic eff...

Nonlinear instability of two dielectric viscoelastic fluids

The nonlinear dispersion relation for an electromagnetic wave propagating through a cold, homogeneous magnetized rotating plasma is derived to investigate certain nonlinear effect for the case where only the Coriolis force part of the consequences of rotation is taken into account. Characteristics of variation of refractive indices with variation of the wave amplitude and rotational frequency are discussed. It is shown that the nonlinear effects considerably influence the propagation of waves in rotating plasmas. >

Nonlinear effects on the propagation of waves in a magnetized rotating plasma

The instability of small but finite amplitude waves propagating at the interface of two layers of highly conducting incompressible fluids in relative motion in presence of external uniform magnetic field is studied. Using the method of multiple scales nonlinear evolution equations are derived for both linearly stable and marginally stable cases. It is found that in the linearly stable case both the modes are modulationally unstable. The nonlinear cut-off wavenumbers are determined.

Nonlinear wavepackets in Kelvin-Helmholtz instability in Hydromagnetics.

The coupled mode equations and coupling coefficients for the resonant nonlinear interaction of three extra-ordinary waves in a hot magnetized plasma are derived by Whitham's method of averaged Lagrangian. The wave vectors of the three waves are taken as noncollinear and perpendicular to the external uniform magnetic field. Of the three waves one is of high frequency mode and the other two are of low frequency mode.

Nonlinear resonant interaction of three extra-ordinary waves in a hot electron plasma

Modulational Instability of Two Longitudinal Waves in a Hot Electron Plasma

Starting from nonlinear evolution equations of a three-dimensional extra-ordinary wavepacket in a magnetized plasma and introducing a correlation function, equations are derived that describe interaction of a coherent low-frequency magneto-acoustic wave with a turbulent spectrum of high frequency extra-ordinary waves. These equations are used to derive the dispersion relation for a low frequency magnetoacoustic wave in the presence of a spectrum of turbulent high frequency extra-ordinary waves. In the narrow spectrum case, it is found that a small but finite spread in the spectrum of turbulence has a stabilizing influence on the instability which exists for vanishing spectral width. In the wide spectrum case, the effect of a weak turbulent spectrum of extra-ordinary waves is to produce a slight shift in frequency of the coherent low frequency magneto-acoustic wave and to damp or excite the wave.

K. P. Das

Papers

Nonlinear wavepackets in Kelvin-Helmholtz instability in Hydromagnetics.

Nonlinear resonant interaction of three extra-ordinary waves in a hot electron plasma

Modulational Instability of Two Longitudinal Waves in a Hot Electron Plasma

Interaction of a low frequency coherent magneto-acoustic wave with a turbulent spectrum of extra-ordinary waves