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.

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.

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.

scholarly journals Study on Electrohydrodynamic Rayleigh-Taylor Instability with Heat and Mass Transfer

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Mukesh Kumar Awasthi ◽  
Vineet K. Srivastava
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Electric Field ◽  
Heat And Mass Transfer ◽  
Taylor Instability ◽  
Wave Number ◽  
Physical Parameters ◽  
Tangential Electric Field ◽  
Rayleigh Taylor Instability ◽  
The Stability

The linear analysis of Rayleigh-Taylor instability of the interface between two viscous and dielectric fluids in the presence of a tangential electric field has been carried out when there is heat and mass transfer across the interface. In our earlier work, the viscous potential flow analysis of Rayleigh-Taylor instability in presence of tangential electric field was studied. Here, we use another irrotational theory in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance. Stability criterion is given by critical value of applied electric field as well as critical wave number. Various graphs have been drawn to show the effect of various physical parameters such as electric field, heat transfer coefficient, and vapour fraction on the stability of the system. It has been observed that heat transfer and electric field both have stabilizing effect on the stability of the system.

Nonlinear hydrodynamic Rayleigh—Taylor instability of viscous magnetic fluids: effect of a tangential magnetic field

1994 ◽  
Vol 51 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Yusry O. El-Dib
Keyword(s):  
Magnetic Field ◽  
Multiple Scales ◽  
Magnetic Fluids ◽  
Taylor Instability ◽  
Stable Region ◽  
Solvability Conditions ◽  
System A ◽  
Rayleigh Taylor Instability ◽  
The Stability ◽  
Complex Coefficients

The nonlinear Rayleigh—Taylor instability of viscous magnetic fluids is considered under the influence of gravity and surface tension in the presence of a constant tangential magnetic field. The method of multiple-scales expansion is employed. A nonlinear Schrödinger equation with complex coefficients is imposed from the solvability conditions and used to analyse the stability of the system. A quadratic dispersion relation with complex coefficients is obtained. The Hurwitz criterion for a quadratic polynomial with complex coefficients is used to control the stability of the system. It is found that an increase in the viscosity increases the extent of the stable region in the presence of a magnetic field. Finally it is shown that the magnetic permeability of the fluid affects the stability conditions.

Nonlinear Analysis of Rayleigh–Taylor Instability of Cylindrical Flow With Heat and Mass Transfer

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Mukesh Kumar Awasthi
Keyword(s):  
Mass Transfer ◽  
Nonlinear Analysis ◽  
Heat And Mass Transfer ◽  
Landau Equation ◽  
Taylor Instability ◽  
Ginzburg Landau ◽  
Stability Diagrams ◽  
Rayleigh Taylor Instability ◽  
Mass And Heat Transfer ◽  
The Stability

We study the nonlinear Rayleigh–Taylor instability of the interface between two viscous fluids, when the phases are enclosed between two horizontal cylindrical surfaces coaxial with the interface, and when there is mass and heat transfer across the interface. The fluids are considered to be viscous and incompressible with different kinematic viscosities. The method of multiple expansions has been used for the investigation. In the nonlinear theory, it is shown that the evolution of the amplitude is governed by a Ginzburg–Landau equation. The various stability criteria are discussed both analytically and numerically and stability diagrams are obtained. It has been observed that the heat and mass transfer has stabilizing effect on the stability of the system in the nonlinear analysis.

Non-linear Kelvin–Helmholtz instability

1971 ◽  
Vol 46 (2) ◽  
pp. 209-231 ◽  
Author(s):  
Ali Hasan Nayfeh ◽  
William S. Saric
Keyword(s):  
Viscous Liquid ◽  
Body Force ◽  
External Flow ◽  
Wave Number ◽  
Linear Motion ◽  
Non Linear ◽  
Rayleigh Taylor Instability ◽  
The Stability ◽  
Steady State Amplitude ◽  
Special Case

A non-linear analysis is presented for the stability of a liquid film adjacent to a compressible gas and under the influence of a body force directed either outward from or toward the liquid. The effects of the liquid's surface tension are taken into account. The non-linear Rayleigh–Taylor instability is included as a special case. The analysis considers the case of an inviscid liquid adjacent to a subsonic flow and the case of a very viscous liquid adjacent to a subsonic or a supersonic flow. For a subsonic external flow, it is found that the cut-off wave-number is amplitude dependent in the inviscid case whereas it is amplitude independent in the viscous case. It is found that the non-linear motion of the gas may be stabilizing or destabilizing, whereas the non-linear motion of the liquid is found to be stabilizing in the viscous case. For a supersonic external flow and a viscous liquid, the cut-off wave-number is amplitude dependent. Moreover, unstable disturbances with wave-numbers near the cut-off wave-number do not grow indefinitely with time but achieve a steady-state amplitude.

Influence of viscosity temperature dependence on the spectral characteristics of the thermoviscous liquids flow stability equation

2019 ◽  
Vol 14 (1) ◽  
pp. 52-58 ◽  
Author(s):  
A.D. Nizamova ◽  
V.N. Kireev ◽  
S.F. Urmancheev
Keyword(s):  
Reynolds Number ◽  
Spectral Characteristics ◽  
Wave Number ◽  
Critical Parameters ◽  
Fluid Viscosity ◽  
Flat Channel ◽  
Stability Equation ◽  
The Stability ◽  
Thermoviscous Fluid ◽  
Sommerfeld Equation

The flow of a viscous model fluid in a flat channel with a non-uniform temperature field is considered. The problem of the stability of a thermoviscous fluid is solved on the basis of the derived generalized Orr-Sommerfeld equation by the spectral decomposition method in Chebyshev polynomials. The effect of taking into account the linear and exponential dependences of the fluid viscosity on temperature on the spectral characteristics of the hydrodynamic stability equation for an incompressible fluid in a flat channel with given different wall temperatures is investigated. Analytically obtained profiles of the flow rate of a thermovisible fluid. The spectral pictures of the eigenvalues of the generalized Orr-Sommerfeld equation are constructed. It is shown that the structure of the spectra largely depends on the properties of the liquid, which are determined by the viscosity functional dependence index. It has been established that for small values of the thermoviscosity parameter the spectrum compares the spectrum for isothermal fluid flow, however, as it increases, the number of eigenvalues and their density increase, that is, there are more points at which the problem has a nontrivial solution. The stability of the flow of a thermoviscous fluid depends on the presence of an eigenvalue with a positive imaginary part among the entire set of eigenvalues found with fixed Reynolds number and wavenumber parameters. It is shown that with a fixed Reynolds number and a wave number with an increase in the thermoviscosity parameter, the flow becomes unstable. The spectral characteristics determine the structure of the eigenfunctions and the critical parameters of the flow of a thermally viscous fluid. The eigenfunctions constructed in the subsequent works show the behavior of transverse-velocity perturbations, their possible growth or decay over time.

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