Physics – Fluid Dynamics
Scientific paper
Aug 1983
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983gapfd..25...65f&link_type=abstract
Geophysical and Astrophysical Fluid Dynamics (ISSN 0309-1929), vol. 25, no. 1-2, Aug. 1983, p. 65-75. Research supported by the
Physics
Fluid Dynamics
24
Boundary Conditions, Geomagnetism, Magnetohydrodynamic Stability, Mathematical Models, Rotating Plasmas, Boundary Value Problems, Lorentz Force, Polar Coordinates, Rotating Cylinders, Rotating Fluids
Scientific paper
The conducting fluid presently considered is contained in a cylindrical annulus with rigid, perfectly conducting boundaries, and is permeated by a magnetic field. The equations governing this system's linear stability are separable in the cylindrical polar coordinates theta and z, and time t, and form a tenth-order boundary value problem in the remaining coordinate, s. The system of equations reduces to sixth order, and the no-slip conditions cannot be applied, in the limit where the cylinder is rapidly rotating about its axis. A boundary layer analysis shows that the normal magnetic field and a linear combination of the normal velocity and tangential current must vanish at the edge of the mainstream. The boundary condition derived is applicable when the Lorentz force is a leading order effect in the momentum equation.
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