  In this paper, we describe the nonlinear outcome of spiral shocks in
protoplanetary disks. Spiral shocks, for most protoplanetary disk conditions,
create a loss of vertical force balance in the post-shock region and result in
rapid expansion of the gas perpendicular to the disk midplane. This expansion
has characteristics similar to hydraulic jumps, which occur in incompressible
fluids. We present a theory to describe the behavior of these hybrids between
shocks and hydraulic jumps (shock bores) and then compare the theory to
three-dimensional hydrodynamics simulations. We discuss the fully
three-dimensional shock structures that shock bores produce and discuss
possible consequences for disk mixing, turbulence, and evolution of solids.
