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.

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.

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).

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.

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.

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.

On the inviscid stability of bi-layer axisymmetric coatings

2008 ◽  
Vol 605 ◽  
pp. 389-400
Author(s):  
P. A. BLYTHE ◽  
P. G. SIMPKINS
Keyword(s):  
Growth Rate ◽  
Double Layer ◽  
Composite Coatings ◽  
Density Ratio ◽  
Maximum Growth ◽  
Reynolds Numbers ◽  
Maximum Growth Rate ◽  
Length Scale ◽  
Layer Composite ◽  
The Stability

This paper is concerned with the stability of fibre coatings at large Reynolds numbers. Both single- and double-layer coatings are considered; no restriction is placed on the coating thicknesses. Calculations for the maximum growth rate, together with the corresponding length scale of the instability, are presented. Rescaling with respect to the maximum growth rate generates universal dispersion relations over the unstable wavenumber range. For double-layer composite coatings, modifications are required when the density ratio becomes large.

Water-bag stability theory for planar bounded plasmas with counter-streaming injection. Part 1. The neutralized diode

1975 ◽  
Vol 14 (1) ◽  
pp. 143-152 ◽  
Author(s):  
K. M. Hu ◽  
E. H. Klevans
Keyword(s):  
Growth Rate ◽  
Lower Order ◽  
Stability Theory ◽  
Electron Distribution ◽  
Electron Beams ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Higher Order Modes ◽  
The Stability ◽  
System Approaches

The stability of a bounded, homogeneous, neutralized plasma with counter- streaming electron beams is analysed. A water-bag model is used to describe the electron distribution in velocity space, so that finite beam temperature and a background plasma are included in the theory. For boundary conditions, the absorber– source wall (the diode boundary) and the reflecting wall are considered. For the former, growth-rate calculations indicate that the instability is a combination of charge bunching (counter-streaming) and diode circuit effect. As the diode length increases, the growth rate of all modes in the system approaches the maximum growth rate. For the reflecting wall, as the length increases, the maximum growth rate transfers to higher and higher order modes with shorter wavelength, while the growth rate of the lower-order modes goes to zero.

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