# Stream function The stream function is a scalar whose contour lines *are* the streamlines of a two-dimensional flow. Its great convenience is that mass conservation is satisfied automatically by construction — any stream function you write down describes an incompressible flow, so one of the governing equations is discharged before you start. The difference in its value between two streamlines is the volumetric flow rate between them, which turns a contour plot into a quantitative instrument. ## Half of a very useful pair In [[Potential_flow]] the stream function and the velocity potential are conjugate: their contours cross at right angles, forming a flow net that can be sketched by hand and was, for decades, how seepage under a dam in [[Hydraulic_engineering]] or flow through a [[Porous_medium]] was actually computed. Paired with [[Vorticity]], it gives the vorticity–streamfunction formulation — advance vorticity in time, solve a Poisson equation for the stream function, differentiate for [[Velocity]], repeat — a compact scheme still used for two-dimensional [[Simulation]] because it enforces incompressibility exactly — see the [[Vorticity_equation]]. ## Reading a flow picture Streamlines crowding together means the flow is speeding up; a closed contour means a recirculating [[Eddy_(fluid_dynamics)|eddy]]; a streamline meeting a wall marks a stagnation point. That vocabulary is how every [[List_of_computational_fluid_dynamics_software|CFD]] plot is read, from a wing section to a river bend on the [[WT!Southern_Agricultural_Center_of_Excellence|southern agricultural]] bridge. The limitation is dimensional: a true stream function exists in two dimensions or axisymmetry, and three-dimensional flows need a vector potential or streamline tracing instead. **Microsim brief (next pass):** Contour field the viewer can seed with obstacles; streamlines drawn as level sets, with a readout of flow rate between any two lines the viewer picks. **On the spine:** [[Potential_flow]] · [[Vorticity]] · [[Fluid_dynamics]] · [[Laminar_flow]] · [[Eddy_(fluid_dynamics)]] · [[WT!Thury_Hydrodynamics_Compendium]]. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Stream_function) : [Wikitube](https://en.wikitube.io/wiki/Stream_function) ## Previous hub tags Hubs: `Life_Physics`, `Systems`. Portals: [[PORTAL_WT!Thury_Hydrodynamics_Compendium]], [[PORTAL_Physics]]. --- *Fluid seed wave · 2026-09-10 · seed register · microsim layer pending.*