In *Double-Diffusive Convection*
(eds. A. Brandt and H.J.S. Fernando)
American Geophysical Union: Washington (1995) 171-184.
## The shearing instability in magnetoconvection

A.M.Rucklidge and
P.C. Matthews

Department of Applied Mathematics and Theoretical Physics,

University of Cambridge, Cambridge, CB3 9EW, UK

**Abstract.**
Magnetoconvection is an example of double-diffusive convection where the
stabilizing secondary conponent is an imposed magnetic field. Numerical
experiments on two- and three-dimensional convection in the presence of a
vertical magnetic field reveal a bewildering variety of periodic and aperiodic
oscillations. Steady two-dimensional rolls can develop a shearing instability,
in which rolls turning over in one direction grow at the expense of rolls
turning over in the other, resulting in a net shear across the layer. As the
temperature difference across the fluid is increased, two-dimensional pulsating
waves occur, in which the direction of shear alternates. In three dimensions,
more complicated alternating pulsating waves are observed: the fluid develops
rolls with their axes aligned along the *x*-axis, which are unstable to
shear and a strong streaming motion in the *y*-direction is generated,
suppressing the *x*-rolls and stretching out the magnetic field in the
*y*-direction. Rolls with their axes aligned along the *y*-axis are
not suppressed by this field; these rolls grow, and in turn are suppressed by
streaming in the *x*-direction. This pattern repeats periodically, with
the streaming rotating by 90 degrees during each quarter cycle. The numerical
experiments are interpreted in terms of low-order models, which confirm that
pulsating waves appear in a global bifurcation.

gzipped PostScript version of this paper (0.4MB)