Sustained Magnetoshear Instabilities in the Solar Tachocline

Abstract

Linear theory has demonstrated that toroidal magnetic fields in the solar tachocline are destabilized by the presence of latitudinal differential rotation. Previous nonlinear investigations of these global magnetoshear instabilities have only considered freely evolving scenarios, which will eventually dissipate after the instabilities saturate. Here we consider more realistic nonlinear scenarios in which the rotational shear is maintained indefinitely by mechanical forcing. When a broad toroidal field profile is specified as an initial condition, a so-called clamshell instability ensues, which is the dominant mode predicted by linear theory. After the initial nonlinear saturation, the residual mean fields are apparently too weak to sustain the instability indefinitely despite the mechanical forcing. However, when a mean poloidal field is imposed in addition to the rotational shear, a statistically steady state is achieved in which the clamshell instability is operating continually. This state is characterized by a quasi-periodic exchange of energy between the mean toroidal field and the instability mode with a longitudinal wavenumber m = 1. This quasi-periodic behavior has a timescale of several years and may have implications for tachocline dynamics and field emergence patterns throughout the solar activity cycle.