  The role played by velocity fields in the fragmentation of a cold medium and
in the formation of protostars is studied.
  The velocity field is modeled with a compressible turbulent flow. A
supersonic turbulent velocity field can fragment the medium into clumps of mass
smaller than a local Jeans' mass, and therefore stabilize the medium against
the formation of protostars. Based on this idea, the protostar formation
efficiency and the protostar mass distribution are determined as functions of
the following ambient parameters: average density $n_{0}$, average temperature
$T_{0}$, r.m.s. turbulent velocity $\sigma_{v,0}$ (or its Mach number
${\cal{M}}_{t}$), postshock cooling time (e.g. chemistry).
  The main results are: i) the protostar mass distribution and its dependence
on the ambient parameters are quantified; ii) the characteristic protostar mass
is $M_{J,cl}\propto n_{0}^{-1/2}T_{0}^{2} \sigma_{v,0}^{-1}$; iii) the
protostar formation efficiency $e$ is higher for larger mean density, larger
mean temperature, lower velocity dispersion on a given scale and longer
postshock cooling time (e.g. lower metallicity): $e\propto
n_{0}^{{3/2}(\beta-1)}T_{0}^{\beta -1}
\sigma_{v,0}^{-5(\beta-1)}L_{0}^{3(\beta-1)}$, where $\beta>1$ is the exponent
of the clump mass distribution; iv) the efficiency is quite sensitive to the
ambient parameters and therefore to the dynamical evolution of the star forming
system.
