ar X iv : a st ro - p h / 05 10 30 5 v 4 1 0 M ar 2 00 6 Accepted for publication in ApJ Hydraulic / Shock Jumps in Protoplanetary Disks

In this paper, we describe the nonlinear outcome of spiral shocks in protoplan-etary 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 hydro-dynamics 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.