TY - JOUR
T1 - Chaotic behavior of Eulerian magnetohydrodynamic turbulence
AU - Ho, Richard
AU - Berera, Arjun
AU - Clark, Daniel
N1 - 11 pages, 7 figures. In Press Physics of Plasmas, 2019
PY - 2019/4/19
Y1 - 2019/4/19
N2 - We study the chaotic properties of a turbulent conducting fluid using direct numerical simulation in the Eulerian frame. The maximal Lyapunov exponent is measured for simulations with varying Reynolds number and magnetic Prandtl number. We extend the Ruelle theory of hydrodynamic turbulence to magnetohydrodynamic turbulence as a working hypothesis and find broad agreement with results. In other simulations we introduce magnetic helicity and these simulations show a diminution of chaos, which is expected to be eliminated at maximum helicity. We also find that the difference between two initially close fields grows linearly at late times, which was also recently found in hydrodynamics. This linear growth rate is found to be dependent on the dissipation rate of the relevant field. We discuss the important consequences this linear growth has on predictability. We infer that the chaos in the system is totally dominated by the velocity field and connect this work to real magnetic systems such as solar weather and confined plasmas.
AB - We study the chaotic properties of a turbulent conducting fluid using direct numerical simulation in the Eulerian frame. The maximal Lyapunov exponent is measured for simulations with varying Reynolds number and magnetic Prandtl number. We extend the Ruelle theory of hydrodynamic turbulence to magnetohydrodynamic turbulence as a working hypothesis and find broad agreement with results. In other simulations we introduce magnetic helicity and these simulations show a diminution of chaos, which is expected to be eliminated at maximum helicity. We also find that the difference between two initially close fields grows linearly at late times, which was also recently found in hydrodynamics. This linear growth rate is found to be dependent on the dissipation rate of the relevant field. We discuss the important consequences this linear growth has on predictability. We infer that the chaos in the system is totally dominated by the velocity field and connect this work to real magnetic systems such as solar weather and confined plasmas.
KW - physics.flu-dyn
KW - astro-ph.CO
KW - nlin.CD
KW - physics.plasm-ph
U2 - 10.1063/1.5092367
DO - 10.1063/1.5092367
M3 - Article
JO - Physics of Plasmas
JF - Physics of Plasmas
SN - 1070-664X
IS - 26
M1 - 042303
ER -