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On the motion of a rigid cylinder in a rotating electrically conducting fluid

Published online by Cambridge University Press:  26 April 2006

David E. Loper
David E. Loper
Affiliation:
Department of Mathematics and Geophysical Fluid Dynamics Institute, Florida State University, Tallahassee, FL 32306-3017, USA
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Abstract

The flow structures generated and drag experienced by a rigid cylinder moving in an arbitrary direction through a rotating electrically conducting fluid in the presence of an applied magnetic field are investigated, with he aim of understanding better the nature of the small-scale flow in the core of the Earth which may be responsible for maintaining the geomagnetic field through dynamo action. Three cases are considered in the limit of small Rossby and magnetic Reynolds numbers. In the case of very weak rotation, the possible flow structures consist of a thin Hartmann layer and a long wake extending in the direction of the magnetic field, in which Lorentz and viscous forces balance, but only the long wake plays a dynamical role. The dominant drag force is experienced for motion that cuts magnetic lines of force. Motion of the cylinder parallel to its axis induces a much weaker drag, while that in the direction of the magnetic field induces none to dominant order. The cylinder also experiences weak lateral forces due to the Coriolis effect. In the case of weak rotation, the balance in the long wake is now magnetostrophic: between Lorentz and Coriolis forces. The drag is qualitatively identical to that in the first case, but the drag induced by motion parallel to the axis of the cylinder is increased, though still smaller than that for motions cutting magnetic lines of force. In the case of strong rotation, the flow structures consist of a thin Ekman layer and a foreshortened Taylor column extending in the direction of the rotation axis. In this column, the force balance is again magnetostrophic. Again only the large-scale structure plays a dynamical role. Motion of the cylinder perpendicular to its axis induces a larger drag than does motion parallel to its axis. The cylinder also experiences large lateral Coriolis forces.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 260 , 10 February 1994 , pp. 299 - 314
Copyright
© 1994 Cambridge University Press

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References

Braginsky, S. I. 1960 Magnetohydrodynamics of weakly conducting liquids. Sov. Phys. JETP 37, 1005–1014.Google Scholar
Braginsky, S. I. 1963 Structure of the F layer and reasons for the convection in the Earth's core. Sov. Phys. Dokl. 149, 8–10.Google Scholar
Chen, C. F. & Chen, F. 1991 Experimental study of directional solidification of aqueous ammonium chloride solution. J. Fluid Mech. 227, 567–586.Google Scholar
Eltayeb, I. A. & Loper, D. E. 1991 On the stability of vertically oriented double-diffusive interfaces. Part 1: A single plane interface. J. Fluid Mech. 228, 149–181.Google Scholar
Gradshteyn, I. S. & Ryzhik, I. M. 1980 Tables of Integrals, Series and Products. Academic.
Hasimoto H. 1960 Steady longitudinal motion of a cylinder in a conducting fluid. J. Fluid Mech. 8, 61–81.Google Scholar
Loper, D. E. & Moffatt, H. K. 1993 Small-scale hydromagnetic flow in the Earth's core: rise of a vertical buoyant plume. Geophys. Astrophys. Fluid Dyn. 68, 177–202.Google Scholar
Lowes, F. J. 1984 The geomagnetic dynamo—elementary energetics and thermodynamics. Geophys. Surv. 7, 91–107.Google Scholar
Moffatt, H. K. & Loper, D. E. 1993 The magnetostrophic rise of a buoyant parcel in the Earth's core. Geophys. J. Intl (to appear).Google Scholar
Moore, D. W. & Saffman, P. G. 1969 The structure of free vertical shear layers in a rotating fluid and the motion produced by a slowly rising body. Phil. Trans. R. Soc. Lond. A 264, 597–634.Google Scholar
Ruan, K. 1993 On the motion of a rigid cylinder parallel to its axis in a rotating electrically conducting fluid. PhD dissertation, Florida State University.
Ruan, K. & Loper, D. E. 1993 On small-scale hydromagnetic flow in the Earth's core: Motion of a rigid cylinder parallel to its axis. J. Geomag. Geoelec. (to appear).Google Scholar
Tait, S. & Jaupart, C. 1989 Compositional convection in viscous melts. Nature 338, 571–574.Google Scholar
Tait, S. & Jaupart, C. 1992 Compositional convection in a reactive crystalline mush and melt differentiation. J. Geophys. Res. 97, 6735–6756.Google Scholar