  (substantial changes to section 3.2, otherwise minor) We present an analysis
of the hydrodynamic stability of a cold slab bounded by two accretion shocks.
Previous numerical work has shown that when the Mach number of the shock is
large the slab is unstable. Here we show that to linear order both the bending
and breathing modes of such a slab are stable. However, nonlinear effects will
tend to soften the restoring forces for bending modes, and when the slab
displacement is comparable to its thickness this gives rise to a nonlinear
instability. The growth rate of the instability, above this threshold but for
small bending angles, is $\sim c_sk (k\eta)^{1/2}$, where $\eta$ is the slab
displacement. When the bending angle is large the slab will contain a local
vorticity comparable to $c_s/L$, where $L$ is the slab thickness. We discuss
the implications of this work for gravitational instabilities of slabs.
Finally, we examine the cases of a decelerating slab bounded by a single shock
and a stationary slab bounded on one side by thermal pressure. The latter case
is stable, but appears to be a special case. The former case is subject to a
nonlinear overstability driven by deceleration effects. We conclude that shock
bounded slabs with a high density compression ratio generically produce
substructure with a strong local shear, a bulk velocity dispersion like the
sound speed in the cold layer and a characteristic scale comparable to the slab
thickness.

Astrophysics