Results are presented for one-dimensional numerical hydrodynamics computations of the structure and evolution of Lya forest clouds gravitationally confined by dark matter minihalos. The clouds are developed from linear perturbations at high redshift and exposed to either a QSO- or galaxy-dominated metagalactic radiation field at moderate redshifts. While the emphasis is on spherical systems, slab symmetry is also considered. Three zones may be identified in a collapsed cloud: (1) a quasi-hydrostatic core in thermal equilibrium, (2) a nonhydrostatic intermediate zone out of thermal equilibrium, and (3) a cosmological accretion layer joining onto the Hubble expansion. Most of the measured Lya forest column densities arise in the intermediate zone. The development of the core would result in a flattening in the column density distribution near an HI column density of 1015-1016 cm**-2. The cloud diameters corresponding to an HI column density of 1014 cm-2 lie in the range 10-60 kpc, while systems with column densities exceeding 1015 cm-2 have diameters smaller than 10 kpc. Systems with circular velocities exceeding 50 km/s result in clouds which contract until they become Jeans unstable and collapse. The critical column density for collapse is 1017-1018 cm**-2. A mild correlation of Doppler parameter with neutral hydrogen column density is found in several models for systems with column densities less than 1013.5 cm-2, with Doppler parameters occurring as low as b > 20 km/s for 1013 cm-2 column density systems. No lines with b < 15 km/s are found.

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