The Shearing Instability in Magnetoconvection

Magnetoconvection is an example of double-diffusive convection where the stabilizing secondary component 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° 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.