The construction of streamlines is one of the most common methods for visualising fluid motion. Streamlines can be computed from the intersection of two nonparallel stream surfaces, which are iso-surfaces of dual stream functions. Stream surfaces are also useful to isolate part of the flow domain for detailed study. This paper introduces a technique for calculating dual stream functions for momentum fields that are defined analytically and depend on only two variables. For axi-symmetric flows, one of the dual stream functions is the well-known Stokes stream function. The analysis reduces the problem from the solution of partial differential equations to the solution of two ordinary differential equations. Example applications include the Moffat  vortex bubble, for which new solutions are presented.
Li, Z., & Mallinson, G. (2006). Dual Stream Function Visualization of flow Fields Dependent on Two Variables. Computing and Visualization in Science, 9(1), 33-41. https://doi.org/10.1007/s00791-006-0015-z