  We study the statistical correlation functions for the three-dimensional
hydrodynamic turbulence onset when the dynamics is dominated by the
pancake-like high-vorticity structures. With extensive numerical simulations,
we systematically examine the two-points structure functions (moments) of
velocity. We observe formation of the power-law scaling for both the
longitudinal and the transversal moments in the same interval of scales as for
the energy spectrum. The scaling exponents for the velocity structure functions
demonstrate the same key properties as for the stationary turbulence case. In
particular, the exponents depend on the order of the moment non-trivially,
indicating the intermittency and the anomalous scaling, and the longitudinal
exponents turn out to be slightly larger than the transversal ones. When the
energy spectrum has power-law scaling close to the Kolmogorov's one, the
longitudinal third-order moment shows close to linear scaling with the
distance, in line with the Kolmogorov's 4/5-law despite the strong anisotropy.
