The long time energy decay of vortices for several different initial flow scenarios is investigated both theoretically and numerically. The theoretical analysis is based on the energy method. Numerical calculations are done by solving the compressible Navier-Stokes equations using a high order stable finite difference method. The simulations verify the theoretical conclusion that vortices decay at a slow rate compared to other types of flows. Several Reynolds numbers and grid sizes in both two and three dimensions are considered.