The effect of magnetic fields on the nonlinear instability of two superposed magnetic streaming fluids, each of a finite depth

1995 ◽  
Vol 73 (3-4) ◽  
pp. 163-173 ◽  
Author(s):  
Abdel Raouf F. Elhefnawy
Keyword(s):  
Magnetic Field ◽  
Multiple Scale ◽  
Finite Depth ◽  
Nonlinear Instability ◽  
Helmholtz Instability ◽  
Perturbed System ◽  
Stability Diagrams ◽  
The Stability ◽  
Normal Magnetic Field ◽  
Horizontal Interface

The nonlinear Kelvin–Helmholtz instability of a horizontal interface separating two flowing superposed magnetic fluids of finite depths is described in the presence of a normal magnetic field. The fluids are taken to be incompressible and inviscid and the motion is assumed to be irrotational. The method of multiple-scale perturbations is used to obtain two nonlinear Schrödinger equations describing the behaviour of the perturbed system. The stability of the system is discussed both theoretically and numerically and the stability diagrams are obtained. The nonlinear cutoff magnetic field that separates the regions of instability from those of stability is also obtained.

The Rayleigh–Taylor instability in magnetic fluids and nonlinear interfacial waves

1992 ◽  
Vol 70 (8) ◽  
pp. 603-609 ◽  
Author(s):  
Abdel Raouf F. Elhefnawy
Keyword(s):  
Nonlinear Evolution ◽  
Multiple Scale ◽  
Magnetic Fluids ◽  
Wave Number ◽  
Perturbed System ◽  
Stability Diagrams ◽  
Rayleigh Taylor Instability ◽  
The Stability ◽  
Normal Magnetic Field ◽  
Horizontal Interface

The nonlinear evolution of a horizontal interface separating two magnetic fluids of different densities, including surface tension effects, is investigated. The fluids are considered incompressible and inviscid, being stressed by the force of gravity, the normal magnetic field, and a constant acceleration in a direction normal to the interface. The method of multiple-scale perturbations is used to obtain two nonlinear Schrödinger equations describing the behavior of the perturbed system. The stability of the perturbed system is discussed both analytically and numerically, and the stability diagrams are obtained. We also obtain the nonlinear cutoff wave number, which separates the region of stability from that of instability.

Kelvin--Helmholtz instability of a horizontal interface between a finite subsonic gas and a finite magnetic liquid

1998 ◽  
Vol 76 (5) ◽  
pp. 361-374 ◽  
Author(s):  
K Zakaria
Keyword(s):  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Solid Surfaces ◽  
Wave Number ◽  
Magnetic Liquid ◽  
Helmholtz Instability ◽  
Perturbed System ◽  
Progressive Waves ◽  
The Stability ◽  
Horizontal Interface

The nonlinear Kelvin-Helmholtz instability of a horizontal interface between a magnetic inviscid incompressible liquid and an inviscid laminar subsonic gas is investigated. The gas and the liquid are assumed to have finite thicknesses. The applied magnetic field is parallel to the solid surfaces of the considered system. The method of multiple scales is used to obtain two nonlinear Schrodinger equations describing the behaviour of the perturbed system. The stability of the progressive waves is discussed theoretically. The nonlinear cutoff wave number is obtained, where the stability conditions of the standing waves are obtained. A numerical example is applied to discuss the stability diagrams.PACS Nos.: 51.60 and 47.20

scholarly journals Stability analysis of magnetic fluids in the presence of an oblique field and mass and heat transfer

2020 ◽  
Vol 330 ◽  
pp. 01035
Author(s):  
Rabah Djeghiour ◽  
Bachir Meziani
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Magnetic Fluids ◽  
Physical Parameters ◽  
Stability Diagrams ◽  
Stability And Instability ◽  
Mass And Heat Transfer ◽  
Model Equations ◽  
The Stability ◽  
Oblique Magnetic Field

In this paper, we investigate an analysis of the stability of a basic flow of streaming magnetic fluids in the presence of an oblique magnetic field is made. We have use the linear analysis of modified Kelvin-Helmholtz instability by the addition of the influence of mass transfer and heat across the interface. Problems equations model is presented where nonlinear terms are neglected in model equations as well as the boundary conditions. In the case of a oblique magnetic field, the dispersion relation is obtained and discussed both analytically and numerically and the stability diagrams are also obtained. It is found that the effect of the field depends strongly on the choice of some physical parameters of the system. Regions of stability and instability are identified. It is found that the mass and heat transfer parameter has a destabilizing influence regardless of the mechanism of the field.

He’s Multiple-Scale Solution for the Three-dimensional Nonlinear KH Instability of Rotating Magnetic Fluids

2019 ◽  
Vol 9 (1) ◽  
pp. 52-69 ◽  
Author(s):  
Yusry Osman El-Dib ◽  
Amal A Mady
Keyword(s):  
Multiple Scales ◽  
Velocity Ratio ◽  
Three Dimensional ◽  
Multiple Scale ◽  
Stability Criteria ◽  
Helmholtz Instability ◽  
Vertical Field ◽  
Horizontal Flux ◽  
The Stability ◽  
Transition Curves

This paper elucidates a trend in solving nonlinear oscillators of the rotating Kelvin-Helmholtz instability. The system is constituted by the vertical flux or the horizontal flux. He’s multiple-scales perturbation methodology has been applied and therefore the system is represented by a generalized homotopy equation. This approach ends up in a periodic answer to a nonlinear oscillator with high nonlinearity. The cubic-quintic nonlinear Duffing equation is obligatory as a condition to uniformly answer. This equation is employed to derive the stability criteria. The transition curves are plotted to investigate the stability image. It's shown that the angular velocity suppresses the instability. The tangential flux plays a helpful role, whereas the vertical field encompasses a destabilizing influence. Within the existence of the rotation, the velocity ratio reduces stability configuration.

scholarly journals Inertial instability of intense stratified anticyclones. Part 1. Generalized stability criterion

2013 ◽  
Vol 732 ◽  
pp. 457-484 ◽  
Author(s):  
Ayah Lazar ◽  
A. Stegner ◽  
E. Heifetz
Keyword(s):  
Stability Criterion ◽  
Finite Depth ◽  
Marginal Stability ◽  
Rayleigh Criterion ◽  
Rankine Vortex ◽  
Stability Diagrams ◽  
Suitable Parameter ◽  
Inertial Instability ◽  
The Stability ◽  
Vertical Eddy

AbstractThe stability of axisymmetric vortices to inertial perturbations is investigated by means of linear stability analysis, taking into account stratification, vertical eddy viscosity, as well as finite depth of the flow. We consider different types of circular barotropic vortices in a linearly stratified shallow layer confined with rigid lids. For the simplest case of the Rankine vortex we develop an asymptotic analytic dispersion relation and a marginal stability criterion, which compares well with numerical results. This is a further generalization to the well-known generalized Rayleigh criterion, which is only valid for non-dissipative and non-stratified eddies. Unlike the Rayleigh criterion, it predicts that intense anticyclones may be stable even with a core region of negative absolute vorticity, and that the dissipation and stratification work together to stabilize the flow. Numerical analysis reveals that the stability diagrams for various types of vortices are almost identical in the Rossby, Burger and Ekman parameter space. This allows extension of our analytical solutions for the Rankine vortex to a wide variety of vortices. Furthermore, we show that a more suitable parameter for the intensity of the vortex is the vortex Rossby number, while for the inviscid case it is the local normalized vorticity. These predictions are in agreement with laboratory experiments presented in part 2 (J. Fluid Mech., vol. 732, 2013, pp. 485–509).

On the Hydromagnetic Kelvin-Helmholtz Instability between Compressible Fluids

1974 ◽  
Vol 29 (6) ◽  
pp. 888-892 ◽  
Author(s):  
K. M. Srivastava
Keyword(s):  
Magnetic Field ◽  
Uniform Magnetic Field ◽  
Compressible Fluids ◽  
Plane Interface ◽  
Helmholtz Instability ◽  
Solar Plasma ◽  
The Stability ◽  
Conducting Fluids ◽  
Equal Density

We have discussed the effect of gravity on the hydromagnetic Kelvin-Helmholtz instability of a plane interface between compressible, inviscid, infinitely conducting fluids. The stability of the interface is investigated including gravity. The solar plasma and the magnetospheric medium are supposed to be of equal density and to carry a uniform magnetic field (H ) in the direction of streaming. The cases (i) H1 ≠ H2 and x1 (x = cp/cv) not necessarily equal to x2 , (ii) H1= H2 x1 ≠ x2 and (iii) H1 = H2, x1=x2 are discussed for perturbations, transverse as well as parallel to the direction of streaming. It is concluded that the interface is unstable in all the cases except for transverse perturbations, the two media carrying the same magnetic field and being characterized by the same x, when it is found to be verlocity.

Stability properties of cold mantle systems for current-driven modes

1980 ◽  
Vol 23 (3) ◽  
pp. 383-400
Author(s):  
D. Ohlsson
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Stability Diagrams ◽  
Neutral Gas ◽  
Transverse Current ◽  
Laboratory Plasmas ◽  
State Models ◽  
The Stability ◽  
Moderate Magnetic Field ◽  
Parameter Ranges

The stability problem of the boundary regions of cold blanket systems with induced currents parallel to the lines of force is formulated. Particular interest is focused on two types of mode: first electrostatic modes driven by the combined effects of a transverse resistivity gradient due to a spatially non-uniform electron temperature and a longitudinal current, second electromagnetic kink-like modes driven by the torque arising from a transverse current density gradient and magnetic field perturbations. It is found that the combination of various dissipative and neutral gas effects introduces strong stabilizing effects within specific parameter ranges. For particular steady-state models investigated it is shown that these effects become of importance in laboratory plasmas at relatively high densities, low temperatures and moderate magnetic field strengths. Stability diagrams based on specific steady-state cold plasma blanket models will be presented.

scholarly journals Stability Characterization of Three Porous Layers Model in the Presence of Transverse Magnetic Field

2016 ◽  
Vol 8 (2) ◽  
pp. 69 ◽  
Author(s):  
Ahmad R. AlHamdan ◽  
Sameh A. Alkharashi
Keyword(s):  
Magnetic Field ◽  
Porous Media ◽  
Evolution Equations ◽  
Multiple Scales ◽  
Immiscible Fluids ◽  
Horizontal Magnetic Field ◽  
Uniform Velocity ◽  
Stability Diagrams ◽  
The Stability ◽  
Complex Coefficients

The current study concerns, the effect of a horizontal magnetic field on the stability of three horizontal finite layers of immiscible fluids in porous media. The problem examines few representatives of porous media, in which the porous media are assumed to be uniform, homogeneous and isotropic. The dispersion relations are derived using suitable boundary and surface conditions in the form of two simultaneous Mathieu equations of damping terms having complex coefficients. The stability conditions of the perturbed system of linear evolution equations  are investigated  both analytically and numerically and stability diagrams are obtained. The stability diagrams are discussed in detail in terms of various parameters governing the flow on the stability behavior of the system such as the streaming velocity, permeability of the porous medium and the magnetic properties. In the special case of uniform velocity, the fluid motion has been displayed in terms of streamlines concept, in which the streamlines contours are plotted. In the  uniform velocity motion, a fourth order polynomial equation with complex coefficients is obtained. According to the complexity of the mathematical treatments, when the periodicity of the velocity is taken into account, the method of multiple scales is applied to obtain stability solution for the considered system.<br />It is found that a stability effect is found for increasing, the magnetic permeability ratio, the magnetic field, and  the permeability parameter  while the opposite influence is observed for increasing the upper layer velocity.

On the hydromagnetic stability of an unsteady Kelvin-Helmholtz flow

1973 ◽  
Vol 59 (1) ◽  
pp. 65-76 ◽  
Author(s):  
B. Roberts
Keyword(s):  
Magnetic Field ◽  
Basic Flow ◽  
Conducting Fluid ◽  
Helmholtz Instability ◽  
Parallel Magnetic Field ◽  
Oscillatory Component ◽  
The Stability ◽  
The Hill ◽  
The Magnetic Field

An analysis is made of the stability of an unsteady basic flow of a conducting fluid in the presence of a parallel magnetic field. The particular profile investigated is the classical Kelvin–Helmholtz profile modified by the addition of an oscillatory component. Two cases are considered in detail: that of a perfectly conducting fluid and that of a poorly conducting fluid. The investigation leads, in both cases, to an equation of the Hill type. It is concluded that the magnetic field has a stabilizing influence but is nevertheless unable to suppress the Kelvin–Helmholtz instability in an unsteady (basic) flow.

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