Long-time properties of magnetohydrodynamic turbulence and the role of symmetries -

Stawarz, Julia E. and Pouquet, Annick and Brachet, Marc-EtiennePHYSICAL REVIEW E 86,

(2012) LPS

Abstract : Using direct numerical simulations with grids of up to 5123 points, we
investigate long-time properties of three-dimensional
magnetohydrodynamic turbulence in the absence of forcing and examine in
particular the roles played by the quadratic invariants of the system
and the symmetries of the initial configurations. We observe that when
sufficient accuracy is used, initial conditions with a high degree of
symmetries, as in the absence of helicity, do not travel through
parameter space over time, whereas by perturbing these solutions either
explicitly or implicitly using, for example, single precision for long
times, the flows depart from their original behavior and can either
become strongly helical or have a strong alignment between the velocity
and the magnetic field. When the symmetries are broken, the flows evolve
towards different end states, as already predicted by statistical
arguments for nondissipative systems with the addition of an energy
minimization principle. Increasing the Reynolds number by an order of
magnitude when using grids of 643-5123 points does not alter these
conclusions. Furthermore, the alignment properties of these flows,
between velocity, vorticity, magnetic potential, induction, and current,
correspond to the dominance of two main regimes, one helically dominated
and one in quasiequipartition of kinetic and magnetic energies. We also
contrast the scaling of the ratio of magnetic energy to kinetic energy
as a function of wave number to the ratio of eddy turnover time to
Alfven time as a function of wave number. We find that the former ratio
is constant with an approximate equipartition for scales smaller than
the largest scale of the flow, whereas the ratio of time scales
increases with increasing wave number.