Uniturbulence due to non-linear damping of surface Alfvén waves

We consider a simple 1-D planar equilibrium model with piece-wise constant density. We completed analytical computations in incompressible MHD. First, we derived mathematical formulas for the wave energy density, the rate of energy dissipation, and the energy cascade damping time. Following that, we developed an analytical model to estimate the damping time for the evolution of uniturbulence in surface Alfvén waves. According to the derived equation, the damping time is inversely proportional to the perpendicular wavenumber and the amplitude of the surface Alfvén waves. Next, we determined the numerical energy dissipation rate using the Fourier transform through numerical simulations. Finally, we approximated the damping time using the fundamental mode of a perpendicular wavenumber.
Consequently, we compared our theoretical model to a series of 3D ideal MHD simulations and observed a remarkable resemblance. The numerical findings demonstrate, in particular, that the damping time is inversely related to the density contrast and amplitude of surface Alfvén waves. Besides, we studied third-order structure-function (Yaglom's law) for Uniturbulence. We compared Yaglom's law (predicted energy dissipation) statistics obtained through simulation with our analytical model. In addition, we estimated the inertial range of the turbulent flow.