Nonuniversality and Dissipative Anomaly in Compressible Magnetohydrodynamic Turbulence

We systematically study the dissipative anomaly in compressible magnetohydrodynamic (MHD) turbulence using direct numerical simulations, and show that the total dissipation remains finite as viscosity diminishes. The dimensionless dissipation rate C_ε fits well with the model C_ε = C_ε,∞ + D/R_L for all the level of flow compressibility considered here, where R_L is the generalized large-scale Reynolds number. The asymptotic value C_ε,∞ describes the total energy transfer flux, and decreases with increase of the flow compressibility, indicating nonuniversality of the dimensionless dissipation rate in compressible MHD turbulence. After introducing an empirically modified dissipation rate, the data from compressible cases collapse to a form similar to the incompressible MHD case depending only on modified Reynolds number.