Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-19T07:09:39.741Z Has data issue: false hasContentIssue false
  • English
  • Français

Magnetic eddies in an incompressible viscous fluid of high electrical conductivity

Published online by Cambridge University Press:  28 March 2006

H. K. Moffatt
H. K. Moffatt
Affiliation:
Trinity College, Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

It is shown that in an incompressible fluid in which the magnetic diffusivity λ is much less than the kinematic viscosity ν, certain magnetic field distributions of limited spatial extent (conveniently described as magnetic eddies) can exist on a length scale such that the associated Reynolds number and magnetic Reynolds number are respectively small and large compared with unity. The Lorentz forces are in equilibrium with the dynamic forces associated with the fluid motion. The boundary condition imposed on this motion is that at a large distance from a magnetic eddy the velocity field should be a uniform axisymmetric irrotational straining motion. The eddies are steady in the limit λ → 0, but decay slowly in a fluid of finite conductivity. Two particular eddies are considered in detail: a disk-shaped eddy in a compressive straining motion, and a spherical eddy in an extensive straining motion. Possible applications to turbulence in interstellar gas clouds are qualitatively considered.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 17 , Issue 2 , October 1963 , pp. 225 - 239
Copyright
© 1963 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Batchelor, G. K. 1950 Proc. Roy. Soc. A, 201, 405.
Batchelor, G. K. 1956 J. Fluid Mech. 1, 177.
Biermann, L. & Schlüter, A. 1950 Z. Naturforsch. 5a, 237.
Biermann, L. & Schlüter, A. 1951 Phys. Rev. 82, 863.
Bullard, E. C. 1949 Proc. Roy. Soc. A, 197, 433.
Burbidge, G. 1959 Symposium on Plasma Dynamics (ed. F. H. Clauser), p. 267. Pergamon.
Cowling, T. G. 1934 Mon. Not. R. Astr. Soc. 94, 39.
Grad, H. & Rubin, H. 1959 Proc. 2nd Geneva Conf. 31, 190.
Herzenberg, A. 1958 Phil. Trans. A, 250, 543.
Homann, F. 1936 Z. angew. Math. Mech. 16, 153.
Kautrowitz, A. R. & Petschek, H. E. 1957 Magnetohydrodynamics (ed. by R. K. M. Landshoff), pp. 7 and 8. Stanford University Press.
Kruskal, M. D. & Kulsrud, R. M. 1956 Phys. Fluids, 1, 265.
Saffman, P. G. 1963 J. Fluid Mech. 16, 545.
Schlichting, H. 1960 Boundary Layer Theory, 4th ed., p. 81. McGraw-Hill.
Spitzer, L. 1956 Physics of Fully Ionized Gases, p. 83. Interscience.