  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 nondegenerate 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 data sets, 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.
