The shallow water, or hydraulic, limit for wave breaking in a single fluid layer is well understood: conservation of mass and momentum completely define the shock (or hydraulic jump), and conservation of energy gives, a posteriori, the rate at which ”internal” energy (mostly in the form of small scale turbulence) is generated. For the case of two layers of miscible fluids, this same shallow water limit is much harder, and, in particular, requires an additional postulate for the mixing rate at the shock. One can imagine that the energy dissipated at the shock can now flow both into small scale turbulence and into mixing the fluid. We discuss three possibilities for deriving the additional constraint on the problem, motivated by: 1. Kinematics, 2. Energy, 3. Entropy maximization. These yield surprisingly similar shock conditions and result in physically reasonable mixing rates.