UPDATE:

More has been done since the above movie:

1.  We have gone to higher Mach numbers (almost 5).

2.  Elongation helps, suggested by theory.  We have now run a minor crossection with an elongation of 4.

We find that the wobble is almost eliminated at E=4 and M~5.  The only residual wobble survives at the very center of the plasma (< 5% of the minor radius), presumably because the velocity shear goes to zero there.  If one moves away from the center, the plasma is laminar, that is to say the density and flow profiles in the flanks are identical to the density and flow profiles one gets in the 2D equilibrium (ie, no z-variation and turbulence = 0).

Click below to see how the density approaches laminarity with increasing Mach number.   Cuts of density across the midplane are shown.  The first cut is the reference laminar case, no instability/turbulence.   The next 5 cuts correspond to Mach numbers 0.3, 1.4, 2.2, 3.7, 4.8, with the laminar density superposed for comparison.

Plasma Density Approaches Laminarity with Increasing Mach Number
 

Reference:
S. DeSouza-Machado, A. B. Hassam, and Ramin Sina, "Stabilization of Z-Pinch by Flow Shear", submitted to Phys Plasmas.