High-resolution R~50 000 long-slit spectroscopy of the inner knots of the highly symmetrical protostellar outflow HH 212 was obtained in the 1-0 S(1) line of H2 at 2.12 micron with a spatial resolution of ~0.45 arcsec. At the resulting velocity resolution of ~6 km s-1, multiple slit oriented observations of the northern first knot NK1 clearly show double-peaked line profiles consistent with either a radiative bow shock or dual (forward and reverse) shocks. In contrast, the velocity distribution of the southern first knot SK1 remains single-peaked, suggesting a significantly lower jet velocity and possibly a different density variation in the jet pulses in the southern flow compared to the northern flow. Comparison with a semi-empirical analytical model of bow shock emission allows us to constrain parameters such as the bow inclination to the line of sight, the bow shock and jet velocities for each flow. Although a few features are not reproduced by this model, it confirms the presence of several dynamical and kinematical asymmetries between opposite sides of the HH 212 bipolar jet. The position-velocity diagrams of both knots exhibit complex dynamics that are broadly consistent with emission from a bow shock and/or jet shock, which does not exclude jet rotation, although a clear signature of jet rotation in HH 212 is missing. Alternative interpretations of the variation of radial velocity across these knots, such as a variation in the jet orientation, as well as for the velocity asymmetries between the flows, are also considered. The presence of a correlation between flow velocity and collimation in each flow is suggested.
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