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.
Highlights
The manner in which vortices decay in flows of an incompressible viscous fluid is of particular importance in studying the phenomenon of turbulence in a fluid
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
Summary
The manner in which vortices decay in flows of an incompressible viscous fluid is of particular importance in studying the phenomenon of turbulence in a fluid. As a further extension of this work, Prusa and Rajagopal [10] found a new exact solution to the above problem studied by Taylor [1] in the case when the nonlinear inertial term in the momentum equation is not identically zero They showed that in this case the streamlines for an incompressible viscous flow are streamlines for a second grade fluid (viscoelastic fluid). On the other hand in a two-dimensional flow of an incompressible viscous electrically conducting fluid where the vorticity is perpendicular to the plane of the flow, a magnetic field in the plane of the flow leads to suppression (or decay) of vorticity. The effect of a magnetic field on the decay of vortices is studied in this paper
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