# Rankine vortex The Rankine vortex is the simplest honest model of a real [[Vortex]]: a rotating core of finite radius surrounded by an irrotational outer flow. Inside the core the fluid turns as a solid body, so tangential speed rises linearly with radius and [[Vorticity]] is uniform; outside it, speed falls off as the inverse of radius and vorticity is zero. William Rankine proposed it in the nineteenth century and it survives because it does the one thing the two pure idealisations cannot — it gives a finite speed at the centre while preserving the correct far-field [[Circulation_(physics)|circulation]]. Every practical [[Vortex|vortex]] model since is a smoothing of this two-piece construction, and every [[Simulation|simulation]] that reports a core radius is quoting it. ## Why neither half works alone A pure free vortex, with speed inversely proportional to radius, has infinite [[Velocity]] and infinitely negative pressure at the axis — physically impossible, though perfectly well behaved everywhere else, and useful precisely because its [[Vorticity]] is zero so potential-flow methods apply. A pure rigid-body rotation is finite everywhere but has vorticity filling all space, so it cannot describe an isolated structure. Rankine's move was to accept the discontinuity in vorticity at the core boundary in exchange for physical behaviour on both sides. The Lamb–Oseen vortex removes that kink by letting [[Viscosity]] smooth the profile, the exact solution of the [[Vorticity_equation]] for this geometry — it is the exact viscous solution for a decaying line vortex, with a core that thickens as the square root of time by [[Diffusion]]. ## The pressure signature The model's real payoff is its pressure field, which is what instruments actually see. Pressure falls continuously toward the axis to supply the centripetal [[Force]], reaching its minimum at the centre; the deficit scales with the square of the peak tangential speed. That is why a tornado's core registers a sharp barometric drop, why a strong [[Wingtip_vortices|wingtip vortex]] condenses a visible core in humid air, and why cavitation appears first at the axis of a propeller tip vortex — the local pressure has fallen below the vapour pressure of [[Water]]. Detecting vortices in a [[Simulation]] or in experimental data is very often just detecting this pressure minimum, and it is a more robust marker than [[Velocity]] itself. ## Fitting it to data Two numbers specify a Rankine vortex — core radius and circulation — which makes it the natural fit for field measurements. Lidar scans of aircraft wake vortices on approach are routinely reduced to exactly these two parameters, and the resulting circulation is what wake-separation minima are computed from, a live [[Aviation]] and [[Avionics]] concern at every busy airport. Doppler radar reduces tornado signatures the same way. In [[WT!HealthForce_Center_of_Excellence|clinical]] flow imaging the ventricular vortex is characterised by core size and circulation for comparison between patients. The model's crudeness is a feature: with only two parameters it cannot overfit noisy data. ## Limits Real vortices are neither axisymmetric nor steady. They meander, they are [[Vortex_stretching|stretched]] and tilted by the surrounding strain, they interact with images in the ground plane, and at high [[Reynolds_number]] their cores go [[Turbulence|turbulent]] and grow far faster than [[Diffusion|viscous diffusion]] alone would predict. The Rankine profile is a snapshot of an azimuthal average, not a description of an object. Used with that caveat it is one of the most productive simplifications in [[Fluid_dynamics]] — the vortex equivalent of treating a wing as a [[Horseshoe_vortex]]. See [[WT!Thury_Hydrodynamics_Compendium]] for how it threads the Centers. **On the spine:** [[Vortex]] · [[Vorticity]] · [[Circulation_(physics)]] · [[Wingtip_vortices]] · [[Vortex_ring]] · [[WT!Thury_Hydrodynamics_Compendium]]. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Rankine_vortex) : [Wikitube](https://en.wikitube.io/wiki/Rankine_vortex) ## Previous hub tags Hubs: `Life_Physics`, `Systems`. Portals: [[PORTAL_WT!Thury_Hydrodynamics_Compendium]], [[PORTAL_Physics]], [[PORTAL_Aviation]]. --- *Vorticity wave · 2026-09-10 · original prose · microsim layer deferred to the next pass.*