Properties of Nonlinear Torsional Waves Effective on Solar Swirling Plasma Motions

Abstract

Abstract We model the evolution of solar helical structures: swirling motions, tornadoes, and spirals in the context of nonlinear magnetohydrodynamic waves. By considering vorticity and magnetic twist, the nonlinear forces that confine and shape helical or swirling plasma motions are incorporated in nonlinear partial differential equations. The solution to the governing equations provides insight on the significance of the equilibrium conditions. The key in providing explicit expressions for the compressive perturbations in the presence of equilibrium twist and vorticity is the second-order thin flux tube approximation. Nonlinear differential equations for the perturbations of the density, tube cross sectional area, and longitudinal speed are obtained in terms of the characteristics of the torsional wave, which itself is determined by the magnetic twist and vorticity. The analytic nonlinear solutions enable measurement of the efficiency of the equilibrium magnetic twist and vorticity, which confine and shape swirling motions differently as they evolve up the solar atmosphere. For chromospheric and coronal conditions, the nonlinear induced density perturbations increase with vorticity and decrease with magnetic twist. Regarding confinement, the nonlinear forces prove that the vorticity is predominant compared to the twist. The vorticity acts similarly to the shear flow in confining plasma swirling motions. It features in the compressive perturbations due to the ponderomotive force. We conclude that weak vorticities and twists are easily dominated by the plasma-β. For observing swirling plasma motions and tornadoes, focus must be on regions with high vorticity.