Role of interaction between magnetic Rossby waves and tachocline differential rotation in producing solar seasons

We present a nonlinear magnetohydrodynamic shallow-water model for the solar tachocline (MHD-SWT) that generates quasi-periodic tachocline nonlinear oscillations (TNOs) that can be identified with the recently discovered solar "seasons." We discuss the properties of the hydrodynamic and magnetohydrodynamic Rossby waves that interact with the differential rotation and toroidal fields to sustain these oscillations, which occur due to back-and-forth energy exchanges among potential, kinetic, and magnetic energies.

We perform model simulations for a few years, for selected example cases, in both hydrodynamic and magnetohydrodynamic regimes and show that the TNOs are robust features of the MHD-SWT model, occurring with periods of 2-20 months. We find that in certain cases multiple unstable shallow-water modes govern the dynamics, and TNO periods vary with time. In hydrodynamically governed TNOs, the energy exchange mechanism is simple, occurring between the Rossby waves and differential rotation.