Approximate streamsurfaces for flow visualization

Instantaneous features of three-dimensional velocity fields are most directly visualized via streamsurfaces. It is generally unclear, however, which streamsurfaces one should pick for this purpose, given that infinitely many such surfaces pass through each point of the flow domain. Exceptions to this rule are vector fields with a non-degenerate first integral whose level surfaces globally define a continuous, one-parameter family of streamsurfaces. While generic vector fields have no first integrals, their vortical regions may admit local first integrals over a discrete set of streamtubes, as Hamiltonian systems are known to do over Cantor sets of invariant tori. Here we introduce a method to construct such first integrals approximately from velocity data, and show that their level sets indeed frame vortical features of the velocity field in examples in which those features are known from Lagrangian analysis. Moreover, we test our method in numerical datasets, including a flow inside a V-junction and a turbulent channel flow. For the latter, we propound an algorithm to pin down the most salient barriers to momentum transport up to a given scale providing a way out of the occlusion conundrum that typically accompanies other vortex visualization methods.

Automated summary

Instantaneous features of three-dimensional velocity fields can be visualized most directly through streamsurfaces, but it is often unclear which streamsurfaces to choose given the infinite possibilities passing through each point. However, vector fields with a non-degenerate first integral can define a continuous family of streamsurfaces, while vortical regions in generic vector fields may have local first integrals over a discrete set of streamtubes. In this study, a method is introduced to construct such first integrals from velocity data and it is shown that their level sets accurately frame vortical features in known examples.