Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-22T05:40:32.125Z Has data issue: false hasContentIssue false
  • English
  • Français

Hydromagnetic stability of parallel flow of an ideal heterogeneous fluid

Published online by Cambridge University Press:  29 March 2006

Stanley David Gedzelman
Stanley David Gedzelman
Affiliation:
Massachusetts Institute of Technology Present address: City College of New York and Lamont-Doherty Geological Observatory of Columbia University.
Get access Rights & Permissions [Opens in a new window]

Abstract

The magnetohydrodynamic and Boussinesq approximations are used on a fully ionized ideal fluid with a longitudinal magnetic field. The flow is in a direction normal to the gravity vector and all variations in velocity, density and magnetic field. The stability characteristics, mainly for normal-mode perturbations, are investigated. Two simple problems with discontinuous profiles are solved analytically. For a double shear layer, an appropriate range of magnetic field values destabilizes the flow. A long wave theory is presented and applied to several problems, some of which are destabilized by an appropriate magnetic field. Finally, the solution for continuous profiles is presented and shown to decay algebraically in time for any stable stratification.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 58 , Issue 4 , 22 May 1973 , pp. 777 - 794
Copyright
© 1973 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

Axford, W. I. 1960 Quart. J. Mech. & Appl. Math. 13, 314.
Boller, B. & Stolov, H. 1970 J. Geophys. Res. 75, 6073.
Case, K. M. 1960 Phys. Fluids, 3, 143.
Drazin, P.G. & Howard, L. N. 1961 Proc. Am. Soc. Engng, E.M. Div. 87, 101–116.
Drazin, P. G. & Howard, L. N. 1962 J. Fluid Mech. 14, 257.
Drazin, P. G. & Howard, L. N. 1966 Hydrodynamic stability of parallel flow of an inviseid fluid Adv. Appl. Mech. 9, 1.Google Scholar
Gedzelman, S. 1970 Ph.D. Thesis, Dept. of Meteorology, Massachusetts Institute of Technology.
Gilman, P. G. 1967 J. Atmos. Sci. 24, 101.
Howard, L. N. 1961 J. Fluid Mech. 10, 509.
Howard, L. N. 1963 J. Fluid Mech. 16, 333.
Kent, A. 1966 Phys. Fluids, 9, 1286.
Kent, A. 1968 J. Plasma Phys. 2, 543.
Michael, D. H. 1955 Proc. Camb. Phil. Soc. 51, 528.
Rosenbluth, M. & Simon, A. 1964 Phys. Fluids, 7, 557.
Stern, M. E. 1963 Phys. Fluids, 6, 636.