We investigate modification of Kolmogorov wave turbulence in QCD calculating
gluon spectra as functions of time in the presence of a low energy source which
feeds in energy density in the infrared region at a time-dependent rate. Then
considering the picture of saturation constraints as has been constructed in
the "bottom-up" thermalization approach we revisit that picture for RHIC
center-mass energy, W=130GeV, and also extend it to LHC center-mass
energy, W=5500GeV, thus for two cases having an opportunity to calculate
the equilibration time, taueq∣therm, of the gluon system produced in a
central heavy ion collision at mid-rapidity region. Thereby, at RHIC and LHC
energies we can match the equilibration time, obtained from the late stage
gluon spectrum of the modified Kolmogorov wave turbulence, onto that of the
"bottom-up" thermalization and other evolutional approaches as well. In
addition, from the revised "bottom-up" approach we find the gluon liberation
coefficient to be on the average, c=0.81−1.06 at RHIC and c=0.50−0.56 at LHC. We also present other phenomenological estimates of tautherm
which, at QCD realistic couplings, yield 0.45fm−0.65fm<tautherm<0.97fm−2.72fm at RHIC and 0.31fm−0.40fm<tautherm<0.86fm−2.04fm
at LHC, both reflecting the original and modified Kolmogorov wave turbulent
scenarios. In the latter case, at certain conditions, taking also into account
both very small and realistic couplings we give estimates - 0.65fm<tautherm<1.29fm at RHIC and 0.52fm<tautherm<1.16fm at LHC, as
well as at realistic couplings we find 0.53<tautherm<0.7fm at RHIC and
0.41<tautherm<0.65fm at LHC.Comment: 37 pages, 8 figures and 5 tables: typos were corrected, content
changed in Abstract and Conclusions, 2 tables were added in Conclusion