  We study the origin of Na I absorbing gas in ultraluminous infrared galaxies
motivated by the recent observations by Martin of extremely superthermal
linewidths in this cool gas. We model the effects of repeated supernova
explosions driving supershells in the central regions of molecular disks with
M_d=10^10 M_\sun, using cylindrically symmetric gas dynamical simulations run
with ZEUS-3D. The shocked swept-up shells quickly cool and fragment by
Rayleigh-Taylor instability as they accelerate out of the dense, stratified
disks. The numerical resolution of the cooling and compression at the shock
fronts determines the peak shell density, and so the speed of Rayleigh-Taylor
fragmentation. We identify cooled shells and shell fragments as Na I absorbing
gas and study its kinematics. We find that simulations with a numerical
resolution of \le 0.2 pc produce multiple Rayleigh-Taylor fragmented shells in
a given line of sight. We suggest that the observed wide Na I absorption lines,
<v> = 320 \pm 120 km s^-1 are produced by these multiple fragmented shells
traveling at different velocities. We also suggest that some shell fragments
can be accelerated above the observed average terminal velocity of 750 km s^-1
by the same energy-driven wind with an instantaneous starburst of \sim 10^9
M_\sun. The bulk of mass is traveling with the observed average shell velocity
330 \pm 100 km s^-1. Our results show that an energy-driven bubble causing
Rayleigh-Taylor instabilities can explain the kinematics of cool gas seen in
the Na I observations without invoking additional physics relying primarily on
momentum conservation, such as entrainment of gas by Kelvin-Helmholtz
instabilities, ram pressure driving of cold clouds by a hot wind, or radiation
pressure acting on dust. (abridged)
