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.

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