3D parametric visualization of the vs. and ℰ_x(t, z) fields for different time slices as a function of z (purple curves). The thick red curves show the time averaged (beyond the kinematic regime) vertical profiles for Rm = 500 (left panel), and 1.5 × 10⁴ (right panel). The small Rm simulations have a smoothly evolving circular dependencies while higher Rm cases develop secondary oscillations around the main “torus”. This is consistent with the simulation becoming more “turbulent” as Reynolds number is increased.