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 ENG  Vol.3 No.12 , December 2011
Decay of Vortices in an Electrically Conducting Fluid in the Presence of a Magnetic Field
Abstract: The decay of vortices in flows of an electrically conducting fluid in the presence of a magnetic field is studied. Two flow configurations are considered: 1) flow in a double array of vortices; 2) flow behind a two-dimensional grid. It is found that in the presence of a uniform transverse magnetic field, the vortices decay much faster than those in a viscous fluid in the absence of magnetic field. It is observed that in the steady flow behind a two-dimensional grid in the presence of a uniform transverse magnetic field, a pair of bound eddies appear behind the single elements of the grid. The scale of these eddies depends on the strength of the magnetic field. It is also found that the distance from the stagnation point over which the vortices decay to zero decreases with increase in the magnetic field. At large distance, however, the streamlines become parallel as in the case of a viscous fluid.
Cite this paper: nullM. Reza, S. Panigrahi and A. Gupta, "Decay of Vortices in an Electrically Conducting Fluid in the Presence of a Magnetic Field," Engineering, Vol. 3 No. 12, 2011, pp. 1207-1212. doi: 10.4236/eng.2011.312150.
References

[1]   G. I. Taylor, “On the Decay of Vortices in a Viscous Fluid,” Philosophical Magazine, Vol. 46, 1923, pp. 671-674.

[2]   L. I. G. Kovasznay, “Laminar Flow behind a Two Dimensional Grid,” Proceedings of Cambridge Philosophical Society, Vol. 44, No. 1, 1948, pp. 58-62. doi:10.1017/S0305004100023999

[3]   H. J. Lugt and E. W. Schwiderski, “Birth and Decay Vor- tices,” The Physics of Fluids, Vol. 9, 1966, pp. 851-859. doi:10.1063/1.1761785

[4]   M. D. Gunzburger, “Motion of Decaying Vortex Ring with Non-Similar Vorticity Distribution,” Journal of Engineering Mathematics, Vol. 6, No. 1, 1972, pp. 53-61. doi:10.1007/BF01535239

[5]   M. R. Smith, R. J. Donnelly, N. Goldenfeld and W. F. Vinen, “Decay of Vorticity in Homogeneous Turbulence,” Physical Review Letters, Vol. 71, No. 16, 1993, pp. 2583- 2586. doi:10.1103/PhysRevLett.71.2583

[6]   A. S. Gupta, “Decay of Vortices in a Visco-Elastic Liquid,” Meccanica, Vol. 7, No. 4, 1972, pp. 232-235. doi:10.1007/BF02133721

[7]   H. M. Markovitz and B. D. Coleman, “Advances in Ap- plied Mechanics,” Academic Press, New York, 1964.

[8]   K. R. Rajagopal, “On the Decay of Vortices in a Second Grade Fluid,” Meccanica, Vol. 15, 1980, pp. 185-186. doi:10.1007/BF02128929

[9]   R. L. Fosdick and K. R. Rajagopal, “Uniqueness and Drag for Fluids of Second Grade in Steady Motion,” International Journal of Non-Linear Mechanics, Vol. 13, No. 5-6, 1978, pp. 131-137.

[10]   V. Prusa and K. R. Rajagopal, “A Note on the Decay of Vortices in a Viscous Fluid,” Meccanica, Vol. 46, No. 6, 2010, pp. 875-880.

[11]   J. A. Shercliff, “A Textbook of Magnetohydrodynamics,” Pergamon Press, Oxford, 1965

[12]   H. K. Moffatt, “On the Suppression of Turbulence by a Uniform Magnetic Field,” Journal of Fluid Mechanics, Vol. 28, No. 3, 1967, pp. 571-592. doi:10.1017/S0022112067002307

[13]   B. Sreenivasan and T. Alboussière, “Experimental Study of a Vortex in a Magnetic Field,” Journal of Fluid Me- chanics, Vol. 464, No. 1, 2002, pp. 287-309.

 
 
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