  Abridged: We have undertaken a series of hydrodynamical simulations of
multiple star formation in small turbulent molecular clouds. Our goal is to
determine the sensitivity of the properties of the resulting stars and brown
dwarfs to variations in the initial conditions imposed. In this paper we report
on the results obtained by applying two different initial turbulent velocity
fields. The slope of the turbulent power-law spectrum alpha is set to -3 in
half of the calculations and to -5 in the other half. We find that, whereas the
stellar mass function seems to only be weakly dependent on the value of alpha,
the sub-stellar mass function turns out to be more sensitive to the initial
slope of the velocity field. We argue that, since the role of turbulence is to
create substructure from which gravitational instabilities may grow, variations
in other initial conditions that also determine the fragmentation process are
likely to affect the shape of the sub-stellar mass function as well. The
absence of many planetary mass `free-floaters' in our simulations, especially
in the mass range 1-10 MJ, suggests that, if these objects are abundant, they
are likely to form by similar mechanisms to those thought to operate in
quiescent accretion discs, instead of via instabilities in gravitationally
unstable discs. Finally, we find that multiple and single stars share
comparable kinematical properties, both populations being able to attain
velocities in the range 1-10 km/s. From these values we draw the conclusion
that only low-mass star-forming regions such as Taurus-Auriga or Ophiuchus,
where the escape speed is low, might have suffered some depletion of its single
and binary stellar population.
