  The collapse of weakly turbulent prestellar cores is a critical stage in the
process of star formation. Being highly non-linear and stochastic, the outcome
of collapse can only be explored theoretically by performing large ensembles of
numerical simulations. Standard practice is to quantify the initial turbulent
velocity field in a core in terms of the amount of turbulent energy (or some
equivalent) and the exponent in the power spectrum (n \equiv -d log Pk /d log
k). In this paper, we present a numerical study of the influence of the details
of the turbulent velocity field on the collapse of an isolated, weakly
turbulent, low-mass prestellar core. We show that, as long as n > 3 (as is
usually assumed), a more critical parameter than n is the maximum wavelength in
the turbulent velocity field, {\lambda}_MAX. This is because {\lambda}_MAX
carries most of the turbulent energy, and thereby influences both the amount
and the spatial coherence of the angular momentum in the core. We show that the
formation of dense filaments during collapse depends critically on
{\lambda}_MAX, and we explain this finding using a force balance analysis. We
also show that the core only has a high probability of fragmenting if
{\lambda}_MAX > 0.5 R_CORE (where R_CORE is the core radius); that the dominant
mode of fragmentation involves the formation and break-up of filaments; and
that, although small protostellar disks (with radius R_DISK <= 20 AU) form
routinely, more extended disks are rare. In turbulent, low-mass cores of the
type we simulate here, the formation of large, fragmenting protostellar disks
is suppressed by early fragmentation in the filaments.
