Effect of magnetic field on temporal development of Rayleigh-Taylor instability induced interfacial nonlinear structure (original) (raw)
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Combined Effect of Magnetic Field and Compressibility on Rayleigh Taylor Instability
Open Journal of Fluid Dynamics, 2015
The nonlinear analysis of the combined effect of magnetic field and compressibility on the growth rate of Rayleigh-Taylor (RT) instability has been investigated for inviscid two fluid interface. We have considered an interface-parallel density dependent magnetic field and used Layzer's approach to analyze the problem. We have also investigated the relative effect of magnetic pressure and hydrodynamic pressure on RT instability through the variation of the ratio of hydromagnetic pressure to magnetic pressure (β). Dynamics of bubble and spike has been studied analytically and numerically. Finally, we have obtained the stability conditions of our result through linear stability analysis
The Effect of the Magnetic Field on the Rayleigh-Taylor Instability in a Couple-Stress Fluid
International Journal of Applied Mechanics and Engineering, 2018
In this study we examine the effect of the magnetic field parameter on the growth rate of the Rayleigh-Taylor instability (RTI) in a couple stress fluids. A simple theory based on fully developed flow approximations is used to derive the dispersion relation for the growth rate of the RTI. The general dispersion relation obtained using perturbation equations with appropriate boundary conditions will be reduced for the special cases of propagation and the condition of instability and stability will be obtained. In solving the problem of the R-T instability the appropriate boundary conditions will be applied. The couple-stress parameter is found to be stabilizing and the influence of the various parameters involved in the problem on the interface stability is thoroughly analyzed. The new results will be obtained by plotting the curves between the dimensionless growth rate and the dimensionless wave number for various physical parameters involved in the problem (viz. the magnetic field, couple-stress, porosity, etc.) in the problem. It is found that the magnetic field and couple-stress have a stabilization effect whereas the buoyancy force (surface tension) has a destabilization effect on the RT instability in the presence of porous media.
ZAMM, 2003
Rayleigh-Taylor instability of a heavy fluid supported by a lighter one, in the presence of a homogeneous horizontal magnetic field pervading both the fluids is investigated. These fluids are considered to be incompressible, viscous, and infinitely conducting. In the lower region, z < 0, the density is constant as well as in the upper region, z > 0. The dispersion relation that defines the growth rate σ is derived as a function of the physical parameters of the system under the condition ky/kx = and numerically analyzed. It is shown that the horizontal magnetic field helps to stabilize the instability. The growth rate depends on the relation between wave number components, where the instability increases with increasing and thereby the role of horizontal magnetic field gradually declines.
Nonlinear interfacial stability for magnetic fluids in porous media
Chaos, Solitons & Fractals, 2003
The weakly nonlinear stability is employed to analyze the interfacial phenomenon of two magnetic fluids in porous media. The effect of an oblique magnetic field to the separation face of two fluids is taken into account. The solutions of equations of motion under nonlinear boundary conditions lead to deriving a nonlinear equation in terms of the interfacial displacement. This equation is accomplished by utilizing the cubic nonlinearity. The method of multiple scale expansion is employed in order to obtain a dispersion relation for the first-order problem and nonlinear Ginzburg-Landau equation, for the higher-order problem, describing the behaviour of the system in a nonlinear approach. Regions of stability and instability are identified for the magnetic field intensity versus the wave number. It is found that the oblique magnetic filed has a stabilizing influence under some certain conditions for the directions of the magnetic fields. The resistance coefficient has a destabilizing influence in the linear description. Further, in the nonlinear scope, the increase of the resistance parameters plays both stabilizing and destabilizing role in the stability criteria.
Physics of Fluids
Nonlinear differential equations that control the propagation of a surface wave through the surface disconnection between two fluids are described by the Helmholtz–Duffing oscillator having imaginary damping forces. This oscillator is solved without using any perturbation techniques. This study is relevant in many fields such as nanotechnology. Along with the nonlinear analysis, the periodic solution and the stability criteria are established. Numerical calculations for stability conditions showed vital changes in the stability behavior due to the presence of the rotation ratio.
Experiments in Fluids, 2011
Shaping arbitrary fluid interfaces opens interesting perspectives for fluid-based processes and experiments. We demonstrate an experimental method to create non-planar static interfaces of almost arbitrary shape between two fluids, one of which is made highly magnetically permeable by the addition of a magnetic compound. By relying on spatially modulated magnetic fields, a nonhomogeneous magnetic force is added to Earth's gravitational force, and a non-planar static interface can be stabilized. Precision experimental measurements are possible because we have developed a general method that allows us to predict numerically the shape of the interface, thereby facilitating the optimal experimental design before actually implementing it. As a first example, we apply this method to the Rayleigh-Taylor instability between two immiscible fluids. The results we obtain demonstrate the feasibility of the experimental method and the accuracy of the numerical predictions.
Acta Mechanica Sinica, 2008
The problem of nonlinear instability of interfacial waves between two immiscible conducting cylindrical fluids of a weak Oldroyd 3-constant kind is studied. The system is assumed to be influenced by an axial magnetic field, where the effect of surface tension is taken into account. The analysis, based on the method of multiple scale in both space and time, includes the linear as well as the nonlinear effects. This scheme leads to imposing of two levels of the solvability conditions, which are used to construct like-nonlinear Schrödinger equations (l-NLS) with complex coefficients. These equations generally describe the competition between nonlinearity and dispersion. The stability criteria are theoretically discussed and thereby stability diagrams are obtained for different sets of physical parameters. Proceeding to the nonlinear step of the problem, the results show the appearance of dual role of some physical parameters. Moreover, these effects depend on the wave kind, short or long, except for the ordinary viscosity parameter. The effect of the field on the system stability depends on the existence of viscosity and differs in the linear case of the problem from the nonlinear one. There is an obvious difference between the effect of the three Oldroyd constants on the system stability. New instability regions in the parameter space, which appear due to nonlinear effects, are shown.
Waves and instability at the interface of two flows of miscible magnetic and non-magnetic fluids
Journal of Fluid Mechanics, 2023
This study presents the results of a numerical simulation of two horizontal flows of miscible magnetic and non-magnetic fluids at low Reynolds numbers in a vertical uniform magnetic field. The problem is solved by taking into account the dependence of the viscosity and magnetization of the fluid on the concentration of the magnetic phase, and the dependence of the magnetic field on the concentration. Four flow modes are found: the diffusion mixing mode with a flat diffusion front, the wave mode and two different plug flow modes. In the first of them, the growing wave instability forms the plugs, whereas in the second, the growing magnetostatic instability does. A combination of dimensionless criteria is found that determines the transition from one mode to another. The dependences of the phase velocity of the waves on the diffusion front and the period of the oscillations of the front near the point of the confluence of the two flows on dimensionless criteria are found.