We study the formation of hydrogen HI Lyα forest lines in turbulent media accounting for the effects of a finite correlation length, l, in the velocity field. This is in contrast to the usual procedure, in which line formation is treated in the microturbulent limit (l≡0). Our results show clearly that a finite velocity correlation length (l > 0) affects strongly (i) the profile of the Lyα line, (ii) its equivalent width, and (iii) the intensity ratios of Lyα and higher order Lyman lines. We argue that the column density distribution function f(N) has to be reexamined. A deficit of absorption systems revealed in the Lyα forest in the range 1019 cm−2≤N ≤ 1016 cm−2 may simply be an artifact.