Evolution of amplitude and longitude phase of tachocline Rossby waves diffusing to the photosphere

Physics of magnetohydrodynamic (MHD) Rossby waves in the tachocline-layer were studied by Dikpati et al., using a fluid-particle-trajectory approach along with solving vorticity and induction equations. By extending that model to include a hydrodynamic turbulent convection zone (CZ), we examine how MHD Rossby waves generated in the tachocline might diffuse upward through the CZ to solar surface. We find that pure hydrodynamic Rossby wave amplitudes decline with height due to viscous diffusion at a rate that is independent of viscosity and increases with longitude wavenumber. Fast MHD Rossby waves amplitude declines faster with height for increasing toroidal field, due to their longitude-phase shifting with height, which increases dissipation of kinetic energy in the wave velocities. Slow MHD Rossby waves decline even faster with height because their longitude-phase shifts more rapidly with height, due to their slow phase speed. We conclude that low wavenumber HD and fast MHD Rossby waves, originating in the tachocline, might be detected at the photosphere, but slow MHD Rossby waves should be virtually impossible to detect. We infer from fluid particle trajectories that wave amplitudes declining with height and longitude phase shifting with height associated with decline, implies a powerful mechanism for tangling of magnetic fields, distinct from convective turbulence effects. This could cause a sustained or dissipative local dynamo action triggered by Rossby waves.