Uniturbulence and Alfvén wave solar model

Context. Alfvén wave solar models (AWSOMs) have been very successful in describing the solar atmosphere by incorporating the Alfvén wave driving as extra contributions in the global MHD equations. However, they lack the contributions from other wave modes. Aims. We aim to write governing equations for the energy evolution equation of kink waves. In a similar manner to AWSOM, we combine the kink-wave-evolution equation with MHD. Our goal is to incorporate the extra heating provided by the uniturbulent damping of the kink waves. We attempt to construct the UAWSOM equations (uniturbulence and Alfvén wave driven solar models). Methods. We recently described the MHD equations in terms of the Q variables. These make it possible to follow the evolution of waves in a co-propagating reference frame. We transformed the Q-variable MHD equations into an energy evolution equation. First we did this generally, and then we focused on the description of kink waves. We model the resulting UAWSOM system of differential equations in a 1D solar atmosphere configuration using a Python code. We also couple this evolution equation to the slowly varying MHD formulation and solve the system in 1D. Results. We find that the kink-wave-energy evolution equation contains non-linear terms, even in the absence of counter-propagating waves. Thus, we confirm earlier analytical and numerical results. The non-linear damping is expressed solely through equilibrium parameters, rather than an ad hoc perpendicular correlation term (popularly quantified with a length scale L⊥), as in the case of the AWSOM models. We combined the kink evolution equation with the MHD equations to obtain the UAWSOM equations. A proof-of-concept numerical implementation in python shows that the kink-wave driving indeed leads to radial outflow and heating. Thus, UAWSOM may have the necessary ingredients to drive the solar wind and heat the solar corona against losses. Conclusions. Not only does our current work constitute a pathway to fix shortcomings in heating and wind driving in the popular AWSOM model, it also provides the mathematical formalism to incorporate more wave modes (e.g. the parametric decay instability) for additional driving of the solar wind.