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We present numerical simulations designed to test some of the hypotheses and predictions of recent models of star formation. We consider a set of three numerical simulations of randomly driven, isothermal, non‐magnetic, self‐gravitating turbulence with different rms Mach numbers  M  s  and physical sizes  L , but with approximately the same value of the virial parameter,  α≈ 1.2 . We obtain the following results: (i) we test the hypothesis that the collapsing centres originate from locally Jeans unstable (‘super‐Jeans’), subsonic fragments; we find no such structures in our simulations, suggesting that collapsing centres can arise also from regions that have supersonic velocity dispersions but are nevertheless gravitationally unstable. (ii) We find that the fraction of small‐scale super‐Jeans structures is larger in the presence of self‐gravity. (iii) There exists a trend towards more negative values of the velocity field's mean divergence in regions with higher densities, implying the presence of organized inflow motions within the structures analysed. (iv) The density probability density function (PDF) deviates from a lognormal in the presence of self‐gravity, developing an approximate power‐law high‐density tail, in agreement with previous results. (v) Turbulence alone in the large‐scale simulation  ( L = 9 pc)  does not produce regions with the same size and mean density as those of the small‐scale simulation  ( L = 1 pc) . Items (ii)–(v) suggest that self‐gravity is not only involved in causing the collapse of Jeans‐unstable density fluctuations produced by the turbulence, but also in their  formation .  We then measure the ‘star formation rate per free‐fall time’, SFR ff , as a function of  M  s  for the three runs, and compare with the predictions of recent semi‐analytical models. We find marginal agreement to within the uncertainties of the measurements. However, within the   L = 9  pc simulation, subregions with similar density and size to those of the   L = 1  pc simulation differ qualitatively from the latter in that they exhibit a global convergence of the velocity field  ∇· v  ∼−0.6 km s −1  pc −1  on average. This suggests that the assumption that turbulence in clouds and clumps is purely random is incomplete. We conclude that (i) part of the observed velocity dispersion in clumps must arise from clump‐scale inwards motions, even in driven‐turbulence situations, and (ii) analytical models of clump and star formation need to take into account this dynamical connection with the external flow and the fact that, in the presence of self‐gravity, the density PDF may deviate from a lognormal.

The nature of the velocity field in molecular clouds – I. The non‐magnetic case