Some examples of vortex visualizations are of a possible Euler singularity using Explorer and using Bricks of Bytes and for a series of consecutive times merging of vortex sheets and formation of vortex tubes .
The Explorer and BoB visualizations of a possible Euler singularity are of the same time t=15 from the data set described by Kerr (1993a). The initial condition was two anti-parallel vortices massaged to give the maximum initial growth in singular-like behavior. Only the vorticity in the computational domain, which is one half of one of two interacting vortices due to symmetries, is shown through one of the symmetry planes. This allows one to look inside the vortex in Explorer. Note how the vortex lines curl around the back side. Explorer visualizations of the back side are not yet included because it is very difficult to get a perspective, presumably due to the convoluted nature of the vortex field. The BoB visualization is designed to show that in addition to a central region collapsing with size r going as (t_c-t) and vorticity going as 1/(t_c-t) shown in green, there is an outer region shown in yellow collapsing to a sheet which also has singular behavior, possibly with a different exponent for the growth of vorticity.
The visualizations in numerical turbulence taken from the highest Reynolds number data set described by Herring and Kerr (1993) are near the time and location identified by Kerr (1993b) as having weakly singular behavior. These visualizations are designed to show vortex reconnection. At the first time shown the vorticity field is dominated by sheets, which as discussed by Herring and Kerr is a common feature when starting from very smooth initial conditions. As the sheets become increasingly interleaved something resembling reconnection occurs, with the last figure, that is the last time at the higher threshold, apparently showing one vortex tube in the center and outer sheets moving outwards. This reconnection appears to be topologically very different from the more typical reconnection of vortex tubes, but the analysis in Kerr (1993b) suggests that singular scaling of vorticity, strain, and vorticity production is consistent with the picture from the anti-parallel vortex interaction simulations of Kerr (1993a). Since sheets, with a kink, seem to be the end product of the anti-parallel initial conditions it suggests that the generic interaction that yields a singularity is not between vortex tubes but between vortex sheets. It also suggests that the proposal that sheets must roll-up in the manner proposed by Neu before reconnection can occur as suggested by Passot et al. (1994) is not required, that the observed proliferation of tubes after reconnection seen in 512 cubed movies by Shiyi Chen and Porter and Woodward comes directly from the reconnection process and not from an earlier vortex sheet roll-up.
The vortex lines in Explorer are rendered with a modification of the streakline facility by Aake Nordlund.
