  The primordial clouds in the mini-halos hatch the first generation stars of
the universe, which play a crucial role in cosmic evolution. In this paper, we
investigate how the turbulence impacts the structure of primordial star-forming
cloud. Previous cosmological simulations of the first star formation predicted
a typical mass of around $\mathrm{ 100 \, M_\odot}$, which conflicts with
recent observations of extremely metal-poor stars suggesting a lower mass scale
of around $\mathrm{25 \, M_\odot}$. The discrepancy may arise from unresolved
turbulence in the star-forming cloud, driven by primordial gas accretion during
mini-halo formation in the previous simulation. To quantitatively examine the
turbulence effect on the primordial cloud formation, we employ the adaptive
mesh refinement code $\mathtt{Enzo}$ to model the gas cloud with primordial
composition, including artificial-driven turbulence on the cloud scale and
relevant gas physics. This artificial-driven turbulence utilizes a stochastic
forcing model to mimic the unresolved turbulence inside mini-halos. Our results
show that turbulence with high Mach number and compressional mode effectively
fragments the cloud into several clumps, each with dense cores of $\mathrm{22.7
- 174.9 \, M_\odot}$ that undergo Jeans instability to form stars.
Fragmentation caused by intense and compressive turbulence prevents the runaway
collapse of the cloud. The self-bound clumps with smaller masses in turbulent
primordial cloud suggest a possible pathway to decrease the theoretical mass
scale of first stars, further reconciling the mass discrepancy between
simulations and observations.
