Generation of Solenoidal Modes and Magnetic Fields in Turbulence Driven by Compressive Driving

Abstract

We perform numerical simulations of hydrodynamic (HD) and magnetohydrodynamic (MHD) turbulence driven by compressive driving, to study the generation of solenoidal velocity components and the small-scale magnetic field. We mainly focus on the effects of mean magnetic field ( B 0 ) and the sonic Mach number ( M s ). The dependence of solenoidal ratio (i.e., ratio of solenoidal to kinetic energies) and magnetic energy density on M s in compressively driven turbulence is already established, but that on B 0 is not yet. We also consider two different driving schemes in terms of the correlation timescale of forcing vectors: a finite-correlated driving and a delta-correlated driving. Our findings are as follows. First, when we fix the value of B 0 , the solenoidal ratio after saturation increases as increases. A similar trend is observed for generation of magnetic field when B 0 is small. Second, when we fix the value of , HD and MHD simulations result in similar solenoidal ratios when B 0 is not strong (say, M A  ≳ 5, where M A is Alfvén Mach number). However, the ratio increases when M A  ≲ 5. Roughly speaking, the magnetic energy density after saturation is a linearly increasing function of B 0 irrespective of M s . Third, generation of the solenoidal velocity component is not sensitive to numerical resolution, but that of magnetic energy density is mildly sensitive. Finally, when initial conditions are same, the finite-correlated driving always produces more solenoidal velocity and small-scale magnetic field components than the delta-correlated driving. We additionally analyze the vorticity equation to understand why higher and B 0 yield a larger quantity of the solenoidal velocity component.