We investigate prestellar core formation and accretion based on three-dimensional hydrodynamic simulations .
Our simulations represent local \sim 1 pc regions within giant molecular clouds where a supersonic turbulent flow converges , triggering star formation in the post-shock layer .
We include turbulence and self-gravity , applying sink particle techniques , and explore a range of inflow Mach number { \cal M } = 2 - 16 .
Two sets of cores are identified and compared : t _ { 1 } -cores are identified of a time snapshot in each simulation , representing dense structures in a single cloud map ; t _ { \mathrm { coll } } -cores are identified at their individual time of collapse , representing the initial mass reservoir for accretion .
We find that cores and filaments form and evolve at the same time .
At the stage of core collapse , there is a well-defined , converged characteristic mass for isothermal fragmentation that is comparable to the critical Bonner-Ebert mass at the post-shock pressure .
The core mass functions ( CMFs ) of t _ { \mathrm { coll } } -cores show a deficit of high-mass cores ( \gtrsim 7 M _ { \sun } ) compared to the observed stellar initial mass function ( IMF ) .
However , the CMFs of t _ { 1 } -cores are similar to the observed CMFs and include many low-mass cores that are gravitationally stable .
The difference between t _ { 1 } -cores and t _ { \mathrm { coll } } -cores suggests that the full sample from observed CMFs may not evolve into protostars .
Individual sink particles accrete at a roughly constant rate throughout the simulations , gaining one t _ { \mathrm { coll } } -core mass per free-fall time even after the initial mass reservoir is accreted .
High-mass sinks gain proportionally more mass at late times than low-mass sinks .
There are outbursts in accretion rates , resulting from clumpy density structures falling into the sinks .