  We present a systematic numerical study of the effect of turbulent velocity
fluctuations on the thermal pressure distribution in thermally bistable flows.
The simulations employ a random turbulent driving generated in Fourier space
rather than star-like heating. The turbulent fluctuations are characterized by
their rms Mach number M and the energy injection wavenumber, k_for. Our results
are consistent with the picture that as either of these parameters is
increased, the local ratio of turbulent crossing time to cooling time
decreases, causing transient structures in which the effective behavior is
intermediate between the thermal-equilibrium and adiabatic regimes. As a
result, the effective polytropic exponent gamma_ef ranges between ~0.2 to ~1.1.
The fraction of high-density zones with P>10^4 Kcm^-3 increases from roughly
0.1% at k_for=2 and M=0.5 to roughly 70% for k_for=16 and M=1.25. A preliminary
comparison with the pressure measurements of Jenkins (2004) favors our case
with M=0.5 and k_for=2. In all cases, the dynamic range of the pressure summed
over the entire density range, typically spans 3-4 orders of magnitude. The
total pressure histogram widens as the Mach number is increased, and develops
near-power-law tails at high (resp.low) pressures when gamma_ef<~ 0.5 (resp.
gamma_ef>~ 1), which occurs at k_for=2 (resp.k_for=16) in our simulations. The
opposite side of the pressure histogram decays rapidly, in an approx. lognormal
form. Our results show that turbulent advection alone can generate large
pressure scatters, with power-law high-P tails for large-scale driving, and
provide validation for approaches attempting to derive the shape of the
pressure histogram through a change of variable from the known form of the
density histogram, such as that performed by MacLow et al.(2004).

Astrophysics