The stability of a compositional plume rotating in the presence of a magnetic field

Abstract

A column of finite thickness containing compositionally buoyant fluid is found to rise in an infinite less buoyant fluid in the presence of uniform rotation and magnetic field. The fluids both within and outside the column have the same finite viscosity, ν, thermal diffusivity, κ and magnetic diffusivity, η. The stability of the column to harmonic disturbances of its interfaces, governed by five dimensionless parameters: the Taylor number, τ2 (which measures the ratio of Coriolis to viscous forces), the Chandrasekhar number, Qc (which measures the ratio of Lorenz to viscous forces), the thickness of the plume, x 0, the Reynolds number, Re (which here measures the strength of the forcing) and Bz and ω H (which measure the inclinations of the ambient magnetic field and rotation vector to the vertical respectively), is studied. The order of the growth rate of the instability in terms of Re is determined by rotation. The column is unstable for all values of the parameters τ, Qc, x 0, Bz , ω H when Re is small. The instability is necessarily three-dimensional. It takes the form of a varicose or sinuous mode propagating at an angle to both field and rotation. The presence of the horizontal component of rotation tends to stabilize the system while that of the vertical field tends to destabilize it. The introduction of a magnetic field inclined to the vertical to an inclined rotation model can reverse the role of the horizontal component of rotation by making it enhance the instability. The dependence of the preference of the varicose and sinuous modes on the parameters of the system is illustrated in regime diagrams. The helicity and α-effect of the unstable motions are discussed briefly.