Role of Interaction Between Magnetic Rossby Waves and Tachocline Differential Rotation in Producing Solar Seasons

Wednesday, January 24, 2018

Mausumi Dikpati presents 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.

Synoptic maps image
Left panel: Time evolution of the six energy reservoirs (kinetic in red, potential in blue, magnetic in purple) for an example MHD simulation with a toroidal band of 10-degree width and 5 kG peak field strength, placed at 45-degree latitude in each hemisphere. The black line near the top is the total energy of the system, which is conserved over the whole length of the simulation.
Right panel: Sequence of synoptic maps of perturbation velocities (black arrows), magnetic fields (white arrows), top boundary deformations (color maps in which red represent bulges; blue depressions), at times 15, 30, 45, 60 units (arranged top to bottom) for the evolution of the system of HD and MHD Rossby waves along with reference states of 21\% differential rotation and 5 kG toroidal magnetic bands oppositely directed in the N and S hemispheres.

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. But in MHD cases, energy exchange becomes much more complex involving energy-flow among six energy reservoirs by means of eight different energy conversion processes. For toroidal magnetic bands of 5 and 35 kG peak amplitudes, both placed at 45-degree latitude and oppositely directed in North and South hemispheres, we show that the energy transfers responsible for TNO, as well as westward phase propagation, are evident in synoptic maps of the flow, magnetic field and tachocline top-surface deformations. Nonlinear mode-mode interaction is particularly dramatic in the strong field case. We also find that the TNO period increases with decrease in rotation rate, implying that the younger Sun had more frequent seasons.

Publication Name: ApJ