Atmospheric polar jets on Mars and Earth are wintertime structures with important implications for global circulation and climate. The southern-winter polar jet on Mars is Earth-like in many respects, however its northern counterpart is well established to be considerably stronger. We are using the OpenMARS reanalysis, which spans 9 Mars Years (MY 24 to 32, corresponding to 17 Earth years), to characterize differences between the planets in terms of the Mach number, Ma, the ratio of flow speed to the speed of sound waves, and the Froude number, Fr, the analogous ratio of flow speed to the speed of buoyancy waves (gravity waves). To facilitate an isentropic-coordinate analysis, the vertical coordinate in the OpenMARS reanalysis is recast from pressure to potential temperature, using the EPIC atmospheric model. Earth’s fastest jets satisfy Ma < 0.3, which is the engineer’s rule of thumb for ignoring compressibility effects. Consequently, Earth atmospheric models have not been designed to accurately handle strong compressibility effects, particularly for transonic flow (0.8 < Ma < 1.2). This is a concern, because most if not all Mars atmospheric models derive from Earth models, yet we are finding about 85% of the atmosphere of Mars exceeds Ma = 0.3. In addition, the northern-winter polar jet routinely becomes transonic, and often develops supersonic jet streaks, Ma > 1.0. With the Froude number, Fr, we are searching for supercritical-to-subcritical transitions, which would be associated with hydraulic jumps (akin to shock waves for compressible flow). This follows our identification of significantly large drops in Fr across the northern winter polar jet (Dowling et al 2017, QJRMS 143, 37-52). Hydraulic jumps limit or “control” the mass flow rate, and are associated with strong turbulence, hence a planetary-scale manifestation would significantly affect the polar circulation. We have completed an inventory of meridional-plane animations of Ma and Fr (longitude 2.5°) for the span MY 24 to 32, and are investigating the seasonal and local-time dependence of recurring eddies, including low N2 (squared buoyancy wave frequency) descending filaments that are prominent in meridional-plane plots of the ratio Ma/Fr. We present a summary of our recent results for Mars from the Mach- and Froude-number perspectives.