Wave Pressure and Energy Cascade Rate of Kink Waves Computed with Elsässer Variables

Abstract

Numerical simulations have revealed a new type of turbulence of unidirectional waves in a plasma that is perpendicularly structured, named uniturbulence . For this new type of turbulence, the transverse structuring modifies the upward propagating wave to have both Elsässer variables, leading to the well-known perpendicular cascade. In this paper, we study an analytical description of the nonlinear evolution of kink waves in a cylindrical flux tube that are prone to uniturbulence. We show that they lead to a nonlinear cascade for both propagating and standing waves. We calculate explicit expressions for the wave pressure and energy cascade rate. The computed damping rate depends on the density contrast of the flux tube and the background plasma and is inversely proportional to the amplitude of the kink wave. The dependence on the density contrast shows that it plays a role especially in the lower solar corona. These expressions may be added in Alfvén wave driven models of the solar atmosphere (such as the Alfvén Wave Solar Model (AWSOM)), modifying it to UAWSOM (Uniturbulence and the Alfvén Wave Solar Model).