Hydraulic/shock jumps in protoplanetary disks

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 postshock 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.