NONLINEAR INSTABILITIES IN SHOCK-BOUNDED SLABS

We present an analysis of the hydrodynamic stability of a cold slab bo unded by two accretion shocks. Previous numerical work (Hunter et al. 1986; Stevens, Blondin, & Pollack 1992) has shown that when the Mach n umber of the shock is large, the slab is unstable. Here we show that t o linear order both the bending and breathing modes of such a slab are stable, with a real frequency of c(s)k, where k is the transverse wav enumber. However, nonlinear effects will tend to soften the restoring forces for bending modes, and when the slab displacemcnt is comparable to its thickness this gives rise to a nonlinear instability. The grow th rate of the instability, above this threshold but for small bending angles, is approximately c(s)k(keta)1/2, where eta is the slab displa cement. When the bending angle is large (i.e., keta of order unity) th e slab will contain a local vorticity comparable to c(s)/L, where L is the slab thickness. We discuss the relationship between this work and previous studies of shock instabilities, including the implications o f this work for gravitational instabilities of slabs. Finally, we exam ine the cases of a decelerating slab bounded by a single shock and a s tationary slab bounded on one side by thermal pressure. The latter cas e is stable, but appears to be a special case. The former case is subj ect to a nonlinear overstability driven by deceleration effects. We co nclude that shock-bounded slabs with a high-density compression ratio generically produce substructure with a strong local shear, a bulk vel ocity dispersion like the sound speed in the cold layer, and a charact eristic scale comparable to the slab thickness. We discuss the implica tions of this work for cosmology and the interstellar medium.