Generation of Solenoidal Modes and Magnetic Fields in Turbulence Driven
  by Compressive Driving
  We perform numerical simulations of hydrodynamic (HD) and magnetohydrodynamic
(MHD) turbulence driven by compressive driving to study generation of
solenoidal velocity component and small-scale magnetic field. We mainly focus
on the effects of mean magnetic field ($B_0$) and the sonic Mach number
($M_s$). We also consider two different driving schemes in terms of correlation
timescale of forcing vectors: a finite-correlated driving and a
delta-correlated driving. The former has a longer correlation timescale of
forcing vectors, which is comparable to large-eddy turnover time, than the
latter. Our findings are as follows. First, when we fix the value of $B_0$, the
level of solenoidal velocity component after saturation increases as $M_s$
increases. A similar trend is observed for generation of magnetic field when
$B_0$ is small. Second, when we fix the value of $M_s$, HD and MHD simulations
result in similar level of the solenoidal component when $B_0$ $\lesssim$ 0.2
(or Alfven Mach number of $\sim$ 5). However, the level increases when $B_0$
$\gtrsim$ 0.2. Roughly speaking, the magnetic energy density after saturation
is a linearly increasing function of $B_0$ irrespective of $M_s$. Third,
generation of solenoidal velocity component is not sensitive to numerical
resolution, but that of magnetic energy density is mildly sensitive. Lastly,
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 $M_s$ and $B_0$ yield larger quantity of the solenoidal
velocity component.
