  Turbulence in the interstellar medium (ISM) is crucial in the process of star
formation. Shocks produced by supernova explosions, jets, radiation from
massive stars, or galactic spiral-arm dynamics are amongst the most common
drivers of turbulence in the ISM. However, it is not fully understood how
shocks drive turbulence, in particular whether shock driving is a more
solenoidal(rotational, divergence-free) or a more compressive (potential,
curl-free) mode of driving turbulence. The mode of turbulence driving has
profound consequences for star formation, with compressive driving producing
three times larger density dispersion, and an order of magnitude higher star
formation rate than solenoidal driving. Here, we use hydrodynamical simulations
of a shock inducing turbulent motions in a structured, multi-phase medium. This
is done in the context of a laser-induced shock, propagating into a foam
material, in preparation for an experiment to be performed at the National
Ignition Facility (NIF). Specifically, we analyse the density and velocity
distributions in the shocked turbulent medium, and measure the turbulence
driving parameter $b=(\sigma^{2 \Gamma}_{\rho /\langle \rho \rangle}-1)^{1/2}
(1-\sigma_{\rho \langle \rho
\rangle}^{-2})^{-1/2}\mathcal{M}^{-1}\Gamma^{-1/2}$ with the density dispersion
$\sigma_{\rho / \langle \rho \rangle}$, the turbulent Mach number
$\mathcal{M}$, and the polytropic exponent $\Gamma$. Purely solenoidal and
purely compressive driving correspond to $b \sim 1/3$ and $b \sim 1$,
respectively. Using simulations in which a shock is driven into a multi-phase
medium with structures of different sizes and $\Gamma < 1$, we find $b \sim 1$
for all cases, showing that shock-driven turbulence is consistent with strongly
compressive driving.
