Sunspots and physics of magnetic flux tubes overstability and Kelvin-Helmholtz instability in a magnetic field

Abstract

We have studied the dynamical properties of convective overstability and Kelvin-Helmholtz instability in a vertical magnetic field with a downdraft. The Kelvin-Helmholtz instability and overstability produce the upward downward propagating Alfvén waves depending upon the magnitudes of the kinematic viscosity coefficient (eddy viscosity) ν, and thermometric conductivity κ. It is found that the instability may be driven by the density stratification and the effect of the eddy viscosity is to make the system stable. We discuss also the interaction of the overstability inx<0 and the downdraft inx>0, and the overstability at a vertical boundary of the field.