RAYLEIGH-TAYLOR INSTABILITY OF TWO SUPERPOSED MAGNETIZED VISCOUS FLUIDS WITH SUSPENDED DUST PARTICLES

Abstract

The linear Rayleigh-Taylor instability of two superposed incompressible magnetized fluids is investigated incorporating the effects of suspended dust particles and viscosity. The basic magnetohydrodynamic set of equations have been constructed and linearized. The dispersion relation for 2-D and 3-D perturbations is obtained by applying the appropriate boundary conditions. The condition of Rayleigh-Taylor instability is investigated for potentially stable and unstable modes, which depends upon magnetic field, viscosity and suspended dust particles. The stability of the system is discussed by applying the Routh-Hurwitz criterion. It is found that the Alfven mode comes into the dispersion relation for perturbations in x, y-directions and in only x-direction, while it does not come into y-directional perturbation. The stable configuration is found to remain stable even in the presence of suspended dust particles. Numerical calculations have been performed to see the effects of various parameters on the growth rate of Rayleigh-Taylor instability. It is found that magnetic field and relaxation frequency of suspended dust particles both have destabilizing influence on the growth rate of Rayleigh-Taylor instability. The effects of kinematic viscosity and mass concentration of dust particles are found to have stabilized the growth rate of linear Rayleigh-Taylor instability.

Keywords

Dates

  • Submission Date2007-09-16
  • Revision Date2009-04-16
  • Acceptance Date2009-04-23

DOI Reference

10.2298/TSCI1001011S

References

  1. Chandrasekhar, S., Hydrodynamic and Hydromagnetic Stability, Clarendon Press, Oxford, UK, 1961
  2. Roberts, P. H, The Effect of a Vertical Magnetic Field on Rayleigh-Taylor Instability, Astrophys. J., 137 (1963), 2, pp. 679-689
  3. Ogbonna, N., Bhatia, P. K., The Rayleigh-Taylor Instability of Superposed Partially-Ionized Plasmas, Astrophys. and Space Sci., 103 (1984), 2, pp. 233-240
  4. Mikaelian, K. O., Effect of Viscosity on Rayleigh-Taylor and Richtmyer-Meshkov Instabilities, Phys. Rev., E 47 (1993), 1, pp. 375-383
  5. Lange, A., et al., Fingering Instability in a Water-Sand Mixture, Eur. Phys. J., B 4 (1998), 4, pp. 475-484
  6. El-Ansary, N. F., et al., Effect of Surface Tension and Rotation on the Rayleigh-Taylor Instability, Phys. Chem. Chem. Phys., 2 (2002), 4, pp. 1464-1470
  7. Sharma, R. C., Kumar, P., Sharma, S., Rayleigh-Taylor Instability of Rivilin-Ericksen Elastico-Viscous Fluid through Porous Medium, Indian J. Phys., 75B (2001), 4, pp. 337-340
  8. Kumar, P., Lal, R., Stability of Two Superposed Viscous-Viscoelastic Fluids, Thermal Science, 9 (2005), 2, pp. 87-95
  9. Evans, A., The Dusty Universe, Ellis Horwood, New York, USA, 1993
  10. Scanlon, J. W., Segel, L. L. A., Some Effects of Suspended Particles on the Onset of Benard Convection, Phys. Fluids, 16 (1973), 10, pp. 1573-1578
  11. Sharma, R. C., Prakash, K., Dubey, S. N., Effect of Suspended Particles on the Onset of Benard Convection in Hydromagnetics, Acta Phys. Hung., 40 (1976), 4, pp. 3-10
  12. Sharma, R. C., Sharma, K. C., Rayleigh-Taylor Instability of Two Superposed Conducting Fluids in the Presence of Suspended Particles, Acta Phys. Acad. Sci. Hung., 43 (1977), 3-4, pp. 251-258
  13. Sanghavi, R. K., Chhajlani, R. K., Hydromagnetic Kelvin-Helmholtz Instability in the Presence of Suspended Particles and Finite Larmor Radius Effect, Z. Naturforch., 49a (1994), pp. 1102-1110
  14. Gupta, A., Bhatia, P. K., Instability of Partially-Ionized Superposed Plasmas, Astrophys. and Space Sci., 181 (1991), pp. 103-110
  15. Sharma, P. K., Chhajlani, R. K., Effect of Rotation on the Rayleigh-Taylor Instability of Two Superposed Magnetized Conducting Plasma, Phys. Plasmas, 5 (1998), 6, pp. 2203-2209
  16. Sharma, P. K., Chhajlani, R. K., Effect of Finite Larmor Radius on the Rayleigh-Taylor Instability of Two Component Magnetized Rotating Plasma, Z. Naturforsch., 53a (1998), 12, pp. 937-944
  17. Kumar, P., Singh, G. J., Stability of Two Superposed Rivlin-Eriksen Viscoelastic Fluids in the Presence of Suspended Particles, Rom. Journ. Phys., 51 (2006), 9-10, pp. 927-935
  18. Sunil, Chand, T., Rayleigh-Taylor Instability of a Plasma in Presence of a Variable Magnetic Field and Suspended Particles in Porous Medium, Indian J. Phys., 71B (1997), 1, pp. 95-105
  19. Khan, A., Sharma, N., Bhatia, P. K., Kelvin-Helmholtz Discontinuity in Two Superposed Viscous Conducting Fluids in a Horizontal Magnetic Field, Thermal Science, 12 (2008), 3, pp. 103-110
  20. El-Sayed, M. F., Hydromagnetic Transverse Instability of Two Highly Viscous Fluid-Particle Flows with Finite Ion Larmor Radius Corrections, Eur. Phys. J., D 23 (2003), 3, pp. 391-403
Volume 14, Issue 1, Pages11 -29