Abstract
We study the stability of an interface between two inviscid magnetic fluids of different densities flowing parallel to each other in an oscillatory manner. The system is pervaded by a uniform oblique magnetic field distribution. The analysis allows for mass and heat transfer across the interface. A general eigenvalue relation is derived and discussed analytically. The classical stability criterion is found to be substantially modified due to the effect of the oblique magnetic field with mass and heat transfer. Some previous studies are reported for appropriate data choices. The longitudinal magnetic field has a strong stabilizing influence on all wavelengths, which can be used to suppress the destabilizing influence of the mass and heat transfer. We conclude with a discussion of the stability of unsteady shear layers on the basis of the results. The parametric excitation of the surface waves is analyzed by means of the multiple-time-scales method. The transition curves are obtained analytically.
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References
Chandrasekhar, S. (1961).Hydrodynamic and Hydromagnetic Stability, Oxford University Press, Oxford.
Drazin, P. G. (1961). Discontinuous velocity profiles for the Orr-Sommerfeld equation,Journal of Fluid Mechanics,10, 571–584.
El-Dib, Y. O. (1993). Nonlinear stability of surface waves in magnetic fluids. Effect of a periodic tangential magnetic field.Journal of Plasma Physics,49(2), 317–330.
Hsieh, D. Y. (1972). Effects of heat and mass transfer on Rayleigh-Taylor instability,Transactions of the ASME,49D, 156–162.
Hsieh, D. Y. (1978). Interfacial stability with mass and heat transfer.Physics of Fluids,21(5), 745–748.
Kelly, R. E. (1965). The stability of an unsteady Kelvin-Helmholtz flow,Journal of Fluid Mechanics,22(4), 547–560.
Moatimid, G. M. (1994). Effects of a periodic electric field, with mass and heat transfer, on the Rayleigh-Taylor instability,Arabian Journal of Science and Engineering,19(4A), 715–724.
Nayfeh, A. H. (1985).Problems in Perturbation, Wiley, New York.
Nayak, A. R., and Chakraborty, B. B. (1984). Kelvin-Helmholtz stability with mass and heat transfer,Physics of Fluids,27(8), 1937–1941.
Roberts, B. (1973). On the hydromagnetic stability of an unsteady Kelvin-Helmholtz flow,Journal of Fluid Mechanics,59(1), 65–76.
Rosensweig, R. E. (1979). Fluid dynamics and science of magnetic liquids,Advances in Electron Physics,48, 103–199.
Rosensweig, R. E. (1985).Ferrohydrodynamics, Cambridge University Press, Cambridge.
Walker, J. S., Talmage, G., Brown, S. H., and Sondergaard, N. A. (1993). Kelvin-Helmholtz instability of Couette flow between vertical walls with a free surface,Physics of Fluids A,5(6), 1466–1471.
Wilcock, W. S. D., and Whitehead, J. A. (1991). The Rayleigh-Taylor instability of an embedded layer of low-viscosity flow,Journal of Geophysical Research,96(B7), 12,193–12,200.
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Moatimid, G.M., El-Dib, Y.O. Kelvin-Helmholtz instability of miscible ferrofluids. Int J Theor Phys 35, 425–443 (1996). https://doi.org/10.1007/BF02083825
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DOI: https://doi.org/10.1007/BF02083825