Evaluating the quasi-static formulation for compressible magnetohydrodynamic turbulence

The effects of the magnetic Reynolds number, Re_σ on decaying compressible magnetohydrodynamic (MED) turbulence are investigated through direct numerical simulations for the purpose of providing a dataset for e flluating the quasi-static simplifications of the MED equations. The initial relative intensities of, and the correlation between, the fluctuating velocity (u) and magnetic induction (b) fields are also firied, as measured with the respective parameters f and angle θ. The investigations cover the parameter ranges 1 ≤ Re_σ ≤ 250, 0° ≤ θ ≤ 90°,ana 1 ≤ f ≤ 3. The results suggest that, at the lowest Re_σ investigated, the magnetic neid has a negligime impact on the evolution of the turbulence kinetic energy Eκ-At higher Re_σ lues, 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 shows the opposite trend, being rapialy driven from its initialfllues to essentially zero very early in the transient at lower Re_CT lues, while higher Re_σ values significantly retard this decay. An enhancement of density fluctuations is noted in the intermediate Re_σ range. An interesting obseirotion pertaining to the normalizea cross helicity is the fast decay to zero of this quantity when Re_CT =1, independent of the values of 9 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 magnetic fieid acts as a passive, albeit convected, scalar. The conditions required to maintain a high correlation during the evolution are discussed. We have also seen that the decay mode is less sensitive to the value of θ than that of E_k-The relative contribution of E_k, E_band the internal energy E_i to the total energy E_t is discussed in relation to the values of θ and Re_σ