Results for the transparent vortex problem. The color map (left panel) displays the magnitude of the velocity field for the model with ﹩{v}_{{{\rm{\max }}}}=0.1﹩, with velocity vectors overlaid (in white). The color map in the middle panel displays the rms energy, ε_rms,0 − ε_rms, where ε_rms,0 ≈ 15.6 is the value at the inner boundary (r = 2). In this panel, the dotted white line traces out the circle where ﹩v={v}_{{{\rm{\max }}}}=0.1﹩. The right panel plots the relative difference in the radial component of the energy-integrated number flux (relative to a model with ﹩{v}_{{{\rm{\max }}}}=0﹩) vs. polar angle for models with various values of ﹩{v}_{{{\rm{\max }}}}﹩: 0.1 (solid), 0.032 (dashed), and 0.01 (dotted).