Numerical simulations have revealed a new type of turbulence of unidirectional
waves in a plasma that is perpendicularly structured (Magyar et al. 2017), named
uniturbulence. For this new type of turbulence, the transverse structuring modifies the upward propagating wave to have both Elsasser variables, leading to the well-known perpendicular cascade.
In this presentation, we show an analytical description of the non-linear evolution of kink waves in a cylindrical flux tube, which are prone to uniturbulence. We calculate explicit expressions for the wave pressure and energy cascade rate. The computed damping rate $\tau/P$ 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.
We compute the damping for both standing and propagating kink waves. The heating by propagating kink waves may be important in global coronal models, such as AWSOM. The damping of the standing kink waves is important for seismology. We compare the analytical results with numerical simulations and
observations. In both cases we find a reasonably good match. The comparison
with the simulations show that the non-linear damping dominates in the high
amplitude regime, while the low amplitude regime shows damping by resonant
absorption. In the comparison with the observations, we find a power law
inversely proportional to the amplitude $\eta^{-1}$ as an outer envelope for
our Monte Carlo data points.