The Kelvin-Helmholtz (KH) instability is a prototypical hydrodynamic mixing process driven by velocity shear.  I will present simulations of the KH instability in compressible hydrodynamics.  Compressibility introduces baroclinic instabilities which can further enhance mixing.  I compare simulations run at specific Reynolds numbers to ``implicit large eddy simulations'' (ILES) in which numerical errors play the role of a sub-grid scale diffusivity parameterization.  Many of the simulations were run using Dedalus, an open-source spectral code which can solve nearly arbitrary PDEs.  I will then discuss extrapolating our simulations to the limit of Re->infinity, extrapolating the ILES to the limit of resolution approaching infinity, and whether or not these two limits are the same.