Magnetic Reynolds number effects in compressible magnetohydrodynamic turbulence

The effects of the magnetic Reynolds number, Reσ, on decaying two-dimensional compressible magnetohydrodynamic (MHD) turbulence are investigated through direct numerical simulations. The initial relative intensities of, and the correlation between, the fluctuating velocity (u) and magnetic induction (b) fields are also varied, as measured with the respective parameters f and angle θ. The investigations cover the parameter ranges 1 ≤ Reσ ≤ 250, 0° ≤ θ ≤ 90°, and 1 ≤ f ≤ 3. The results suggest that, at the lowest Reσ investigated, the magnetic field has a negligible impact on the evolution of the turbulence kinetic energy E_k. At higher Reσ values, when magnetic effects are important, the magnetic field tends to accelerate the decay of the turbulence energy relative to non-MHD flows. On the other hand, the magnetic energy E_b shows the opposite trend, being rapidly driven from its initial values to essentially zero very early in the transient at lower Reσ values, while higher Reσ values significantly retard this decay. An enhancement of density fluctuations is noted in the intermediate Reσ range. An interesting observation pertaining to the normalized cross helicity is the fast decay to zero of this quantity when Reσ = 1, independent of the values of θ and f. That is, the fluctuating u and b fields tend to be uncorrelated when the magnetic Reynolds number is low. In this case, the role of the magnetic field is passive, and it is merely convected by the velocity field. The conditions required to maintain a high correlation during the evolution are discussed. We have also seen that the E_b decay mode is less sensitive to the value of θ than that of E_k. The relative contribution of E_k, E_b, and the internal energy E_i to the total energy E, is discussed in relation to the values of f, θ, and Reσ.