Using the molecular dynamics simulations we investigate properties of velocity autocorrelation function of Lennard-Jones fluid at long and intermediate time scales in wide ranges of temperature and density. We show that the amplitudes of the leading
and subleading VAF time asymptotes, $a_1$ and $a_2$, show essentially non monotonous temperature and density dependence. There are two lines on temperature-density plain corresponding to maxima of $a_1$ ($a_2$) along isochors and isotherms situated in the supercritical fluid (hydrodynamic anomalies). These lines give insight into the stages of the fluid evolution into gas.
The local order units of dense simple liquid are typically three dimensional (close packed) clusters: hcp, fcc and icosahedrons. We show that the fluid demonstrates the superstable tetrahedral local order up to temperatures several orders of magnitud
e higher than the melting temperature and down to critical density. While the solid-like local order (hcp, fcc) disappears in the fluid at much lower temperatures and far above critical density. We conclude that the supercritical fluid shows the temperature (density) driven two stage melting of the three dimensional local order. We also find that the structure relaxation times in the supercritical fluid are much larger than ones estimated for weakly interactive gas even far above the melting line.
