Stability of relativistic transverse cold plasma waves. Part 2. Linearly polarized waves

1979 ◽  
Vol 22 (2) ◽  
pp. 201-222 ◽  
Author(s):  
F. J. Romeiras
Keyword(s):  
Nonlinear Wave ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Transverse Modes ◽  
Electron Positron ◽  
Polarized Waves ◽  
Linearly Polarized ◽  
Linear Differential ◽  
Unmagnetized Plasma ◽  
The Stability

This is part 2 of a paper concerned with the stability against small perturbations of a certain class of nonlinear wave solutions of the equations that describe a cold unmagnetized plasma. It refers to transverse linearly polarized waves in an electron-positron plasma. A numerical method, based on Floquet's theory of linear differential equations with periodic coefficients, is used to solve the perturbation equations and obtain the instability growth rates. All the three possible types of perturbations are discussed for a typical value of the (large) amplitude of the nonlinear wave: electrically longitudinal slightly unstable modes (with maximum growth rate γ approximately equal to 0·07ω0, where ω0is the frequency of the nonlinear wave); purely transverse moderately unstable modes (with γ ≃ 0·26ω0); and highly unstable electrically transverse modes (with γ ≃ l·5ω0).

Non-normal stability analysis of a shear current under surface gravity waves

2008 ◽  
Vol 609 ◽  
pp. 49-58
Author(s):  
D. AMBROSI ◽  
M. ONORATO
Keyword(s):  
Growth Rate ◽  
Modal Analysis ◽  
Gravity Waves ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Surface Gravity ◽  
Horizontal Shear ◽  
Surface Gravity Waves ◽  
Shear Current ◽  
The Stability

The stability of a horizontal shear current under surface gravity waves is investigated on the basis of the Rayleigh equation. As the differential operator is non-normal, a standard modal analysis is not effective in capturing the transient growth of a perturbation. The representation of the stream function by a suitable basis of bi-orthogonal eigenfunctions allows one to determine the maximum growth rate of a perturbation. It turns out that, in the considered range of parameters, such a growth rate can be two orders of magnitude larger than the maximum eigenvalue obtained by standard modal analysis.

Instabilities of a Baroclinic, Double Diffusive Frontal Zone

2008 ◽  
Vol 38 (4) ◽  
pp. 840-861 ◽  
Author(s):  
W. D. Smyth
Keyword(s):  
Growth Rate ◽  
Frontal Zone ◽  
Baroclinic Instability ◽  
Flux Ratio ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Variable Diffusivity ◽  
The Stability ◽  
Parameter Values ◽  
Double Diffusive

Abstract The linear theory of double diffusive interleaving is extended to take account of baroclinic effects. This study goes beyond previous studies by including the possibility of modes with nonzero tilt in the alongfront direction, which allows for advection by the baroclinic frontal flow. This requires that the stability equations be solved numerically. The main example is based on observations of interleaving on the lower flank of Meddy Sharon, but a range of parameter values is covered, leading to conclusions that are relevant in a variety of oceanic regimes. The frontal zone is treated as infinitely wide with uniform gradients of temperature, salinity, and alongfront velocity. The stationary, vertically symmetric interleaving mode is shown to have maximum growth rate when its alongfront wavenumber is zero, providing validation for previous studies in which this property was assumed. Besides this, there exist two additional modes of instability: the ageostrophic Eady mode of baroclinic instability and a mode not previously identified. The new mode is oblique (i.e., it tilts in the alongfront direction), vertically asymmetric, and propagating. It is strongly dependent on boundary conditions, and its relevance in the ocean interior is uncertain as a result. Effects of variable diffusivity and buoyancy flux ratio are also considered.

Electrohydrodynamic stability of a slightly viscous jet

1994 ◽  
Vol 274 ◽  
pp. 93-113 ◽  
Author(s):  
A. J. Mestel
Keyword(s):  
Surface Charge ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Small Fields ◽  
Weakly Conducting ◽  
Tangential Field ◽  
Tangential Surface ◽  
The Stability ◽  
Electric Effects ◽  
Phase Differences

Many electro-spraying devices raise to a high electric potential a pendant drop of weakly conducting fluid, which may adopt a conical shape from whose apex a thin, charged jet is emitted. Such a jet eventually breaks up into fine droplets, but often displays surprising longevity. This paper examines the stability of an incompressible cylindrical jet carrying surface charge in a tangential electric field, allowing for the finite rate of charge relaxation. The viscosity is assumed to be small so that the shear resulting from the tangential surface stress can be large, even for relatively small fields. This shear can suppress surface tension instabilities, but if too large, it excites electrical ones. For imperfect conductors, surface charge is redistributed by the rapid fluid reaction to variations in tangential stress as well as by conduction. Phase differences between the effects due to the tangential field and the surface charge lead to charge ‘over-relaxation’ instabilities, but the maximum growth rate can still be lower than in the absence of electric effects.

scholarly journals Stability of an electrified liquid jet approaching to critical point

2020 ◽  
Vol 12 (7) ◽  
pp. 168781402093637
Author(s):  
Zixuan Fang ◽  
Ping Wang
Keyword(s):  
Surface Tension ◽  
Critical Point ◽  
Weber Number ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Wave Number ◽  
Electrical Field ◽  
Electric Stress ◽  
Electrical Field Intensity ◽  
The Stability

This article reports the linear stability analysis of a thermodynamic-transcritical jet sprayed to a radial electrical field. An asymptotic approach was used to obtain the stability solution of a supercritical jet subjected to electrical field. In order to obtain the solutions for the electrified supercritical jet, the surface tension was decreased and consequently led the increase in Weber number in the linear governing equation of subcritical charged jet. To investigate the role of surface tension and electric stress playing in the destabilizing process when approaching the critical point, the energy budget is performed by tracing the energy sources. It was found that, when the Weber number is increased to a sufficiently large value, the solution will become an asymptotic value, which can be considered as a solution under the supercritical conditions. The electric stress can increase both the maximum growth rate and the dominant wave number of electrified supercritical jet, that is, higher electrical field intensity would enhance the instability of the electrified supercritical jet and decrease the wavelength of the disturbances.

Stability of the solar wind against the whistler mode

1978 ◽  
Vol 20 (2) ◽  
pp. 225-230 ◽  
Author(s):  
P. Revathy
Keyword(s):  
Growth Rate ◽  
Solar Wind ◽  
Relative Velocity ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
The Sun ◽  
Thermal Velocity ◽  
Whistler Mode ◽  
Minimum Value ◽  
The Stability

The stability of the solar wind against the whistler mode is analyzed. It is shown that the solar wind can become unstable owing to this mode after a distance of 100 R from the sun. The minimum value of the relative velocity (Ur) between ∝-particles and protons for the excitation of this instability is the proton thermal velocity αi. The maximum growth rate at 200 R occurs for the values of the parameters kρi = 0·3,(T┤/T∥)i = 0·3 and Ur/αi = 0·5.

On self-consistent waves and their stability in warm plasmas. Part 2. Instability of circularly polarized waves both in the presence and the absence of an ambient magnetic field

1980 ◽  
Vol 24 (1) ◽  
pp. 89-102 ◽  
Author(s):  
M. A. Lee ◽  
I. Lerche
Keyword(s):  
Magnetic Field ◽  
Nonlinear Wave ◽  
Large Scale ◽  
Wave Amplitude ◽  
Circularly Polarized ◽  
Polarized Waves ◽  
Large Scale Magnetic Field ◽  
Self Consistent ◽  
Warm Plasma ◽  
The Stability

The stability of a self-consistent, large-amplitude, circularly polarized wave in a warm plasma is investigated. For perturbations to the system propagating normal to the plane of circular polarization, a dispersion relation is derived employing an expansion in the nonlinear wave amplitude and the momentum of the plasma particles in the plane of polarization. Instability results both in the absence and presence of a large-scale magnetic field with a growth rate of the order of the nonlinear wave amplitude.

Magnetohydrodynamic parametric instabilities driven by a standing Alfvén wave in a low-β plasma

1996 ◽  
Vol 56 (2) ◽  
pp. 251-264 ◽  
Author(s):  
L. P. L. Oliveira ◽  
A. C.-L. Chian
Keyword(s):  
Mode Coupling ◽  
Wave Equations ◽  
Maximum Growth ◽  
Finite Amplitude ◽  
Maximum Growth Rate ◽  
Density Fluctuations ◽  
Alfven Wave ◽  
Magnetic Fluctuations ◽  
Parametric Instabilities ◽  
The Stability

The stability of a finite-amplitude standing Alfvén wave of circular polarization in a low-β plasma is studied using a set of nonlinearly coupled MHD wave equations. In the presence of a standing Alfvén pump, two distinct gratings associated with the density fluctuations are excited: those due to the ponderomotive beating of the pump magnetic field, and those due the induced magnetic fluctuations. The roles played by the two gratings in the mode coupling are analysed. Both convective and purely growing regimes of the MHD parametric instabilities can be produced by a standing Alfvén wave. In both regimes, the maximum growth rate increases as the pump amplitude increases, and decreases as increases. Tn the presence of the second grating, a new unstable convective regime appears that widens the overall instability bandwidth.

Propagation of high-frequency electromagnetic waves through a magnetized plasma in curved space-time. II. Application of the asymptotic approximation

1981 ◽  
Vol 374 (1756) ◽  
pp. 65-86 ◽  
Keyword(s):  
High Frequency ◽  
Electromagnetic Waves ◽  
Polarization State ◽  
Space Time ◽  
Magnetized Plasma ◽  
Curved Space ◽  
Polarized Waves ◽  
Background Magnetic Field ◽  
Linearly Polarized ◽  
Unmagnetized Plasma

This is the second of two papers on the propagation of high-frequency electromagnetic waves through an inhomogeneous, non-stationary plasma in curved space-time. By applying the general two-scale W.K.B. method developed in part I to the basic wave equation, derived also in that paper, we here obtain the dispersion relation, the rays, the polarization states and the transport laws for the amplitudes of these waves. In an unmagnetized plasma the transport preserves the helicity and the eccentricity of the polarization state along each ray; the axes of the polarization ellipse rotate along a ray, relative to quasiparallely displaced directions, at a rate determined by the vorticity of the electron fluid; and the norm of the amplitude changes according to a conservation law which can be interpreted as the constancy of the number of quasiphotons. In a magnetized plasma the polarization state changes differently for ordinary and extraordinary waves, according to the angle between the wavenormal and the background magnetic field, and under specified approximation conditions the direction of polarization of linearly polarized waves undergoes a generalized Faraday rotation.

Kinetic theory of the stability of collisional plasma in curved magnetic field

1969 ◽  
Vol 3 (2) ◽  
pp. 155-160 ◽  
Author(s):  
K. Jungwirth
Keyword(s):  
Magnetic Field ◽  
Collisionless Plasma ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Ion Temperature ◽  
Gravitation Field ◽  
Ion Collisions ◽  
Large Gradient ◽  
Field Lines ◽  
The Stability

The effect of curvature of magnetic field lines on plasma instabilities due to a large gradient of the ion temperature has been studied. It is shown that none of the discussed effects can be obtained so long as the curvature of magnetic field lines is simulated by a fictional gravitation field. In configurations with large enough minimum-B, the usual temperature-gradient instability is stabilized in collisionless plasma. However, a new dissipative instability arises due to ion–ion collisions with the maximum growth rate γmax ˜ Vii/40.

Stability of thin, radially moving liquid sheets

1978 ◽  
Vol 87 (2) ◽  
pp. 289-298 ◽  
Author(s):  
Daniel Weihs
Keyword(s):  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Classical Type ◽  
Fluid Viscosity ◽  
Single Wave ◽  
Nozzle Orifice ◽  
Liquid Sheets ◽  
Special Cases ◽  
The Stability ◽  
The Waves

An analysis of the stability of thin viscous liquid sheets, such as those emitted from industrial spraying nozzles, is presented. These sheets are in the form of a circular sector whose thickness reduces as the distance from the nozzle increases.The Kelvin-Helmholtz type of instability usually observed causes the breakup and atomization of the sheet, as required in most industrial spraying processes. Waviness, like that of a flapping flag, is produced and increasing amplitudes finally cause breakup.An analytical solution in the form of hypergeometric functions for the shape of the sheet and the waves is obtained. This solution includes, as special cases, analyses existing in the literature, in addition to establishing the possibility of a new type of instability dependent on the distance from the nozzle. Also, the classical type of instability, in which the waves increase with time, is examined and relations for unstable waves as a function of parameters such as the fluid viscosity, surface tension and sheet velocity are obtained. It is shown that there is no single wave that has a maximum growth rate, but that the wavenumber for maximum instability increases with the distance from the nozzle orifice.

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