  [Abridged abstract:] Recent numerical simulations show that many $\lyal$
absorption lines of column densities $\nha \la 10^{15}$ cm$^{-2}$ are produced
in transient, mini pancakes. Such pancakes are modeled here, approximating the
initial perturbation leading to the formation of the pancake as a single
sinusoidal wave. The density and temperature profiles of the gas in the pancake
are determined for $z_c \sim 3$, where $z_c$ is the collapse redshift. The
$\lyal$ absorption line profiles for a line of sight through the pancake are
then calculated. The absorption lines in general have wings signifying bulk
motions in the gas. It is shown that the deviation from a single Voigt profile
is large for small H I column density lines, in which the effect of bulk
motions is large. For lines with $\nha > 10^{13}$ cm$^{-2}$, high temperature
tend to wash out the signatures of bulk motion. The analytical modeling of mini
pancakes associated with $\lyal$ forest lines --- with $10^{13} \la \nha \la
10^{15}$ cm$^{-2}$---gives the corresponding mass scales. It is shown here
that, for typical values of cosmological parameters, absorption lines with
$\nha \sim 10^{14}$ cm$^{-2}$ correspond to structures with baryonic mass of
$M_b \sim 10^{10}$ M$_{\odot}$ with an overdensity of $\sim 10$ at $z \sim 3$.
The value of $\nha$ can change by a factor $\sim 3$ in the course of evolution
of the pancake in time. It is also shown that there is an upper limit to $\nha$
from a pancake due to the slow recombination rate and the importance of
collisional ionization at high temperatures. Mini pancakes do not give rise to
$\lyal$ lines with $\nha \ga 10^{14.5}$ cm$^{-2}$, for $\j21=1$ and
$\Omega_{IGM} \sim 0.03$.
