  We study the three-dimensional distribution of non virialised matter at z~2
using high resolution spectra of QSO pairs and simulated spectra drawn from
cosmological hydrodynamical simulations. We have collected the largest sample
of QSO pairs ever observed with UVES at the ESO-VLT, with angular separations
between ~1 and 14 arcmin. The observed correlation functions of the transmitted
flux in the HI Lyman alpha forest along and transverse to the lines of sight
are in good agreement implying that the distortions in redshift space due to
peculiar velocities are small. The clustering signal is significant up to
velocity separations of ~200 km/s, or about 3 h^{-1} comoving Mpc. The regions
at lower overdensity (rho/<rho> < 6.5) are still clustered but on smaller
scales (Delta v < 100 km/s). The observed and simulated correlation functions
are compatible at the 3 sigma level. A better concordance is obtained when only
the low overdensity regions are selected for the analysis or when the effective
optical depth of the simulated spectra is increased artificially, suggesting a
deficiency of strong lines in the simulated spectra. We found that also a lower
value of the power-law index of the temperature-density relation for the Lyman
alpha forest gas improves the agreement between observed and simulated results.
If confirmed, this would be consistent with other observations favouring a late
HeII reionization epoch (at z~3). We remark the detection of a significant
clustering signal in the cross correlation coefficient at a transverse velocity
separation Delta v_{\perp} ~500 km/s whose origin needs further investigation.
