With the introduction of bivelocity in 2004, new models for the prediction of Maxwellian, compressible micro-channel flows have recently been developed. This thesis utilizes a non-kinetic method to explore an analytic prediction of two-dimensional velocity profiles of steady and transient, unbounded, compressible vortex flows. This bivelocity hydrodynamic model is compared to the traditional analytical solutions of the Navier-Stokes Fourier (NSF), Boltzmann, and Burnett equations, as well as to Mandella's 1987 experiments in compressible vorticies, highlighting the stark contrasts between these models. While definitive convergence has yet to be obtained, the bivelocity approach has shown promise in resolving these issues. The importance of these bivelocity addition provides a clean explanation for the poor analytic correlations to experimental data previously attempted. While further investigation is required, bivelocity definitively improves upon the current models..