What is the Rankine vortex model?

The Rankine vortex is a mathematical model used in fluid dynamics to represent a vortex within a viscous fluid. Named after William John Macquorn Rankine, it resolves the unrealistic infinite velocity found at the center of a standard potential vortex by combining a solid-body rotation inside a central cylinder with a potential vortex outside of it.

What we know

• The Rankine vortex model assumes a solid-body rotation inside a cylinder of radius a and a potential vortex outside that cylinder. [1, 2]
• The model is named after its discoverer, William John Macquorn Rankine, and serves as a mathematical formula for a viscous fluid. [1, 2]
• It overcomes the physical limitation of a standard potential vortex, where the velocity becomes infinitely large right at the center. [2]

Where to go next

• whoWho was William John Macquorn Rankine?
• compared withHow does a potential vortex work?
• a case in pointWhat is the Lamb-Oseen vortex?
• the bigger pictureWhat role does viscosity play in fluid dynamics?
• how it workedHow is vorticity calculated in fluid flow?
• an unexpected connectionHow does vorticity relate to aerodynamic lift?Although the Rankine vortex is an idealized mathematical construct for internal fluid rotation, the broader concept of vorticity is essential for understanding how lift is generated on aircraft wings.

Sources

• [1]Rankine vortex (Wikidata Q7293284) · CC0 1.0
• [2]Rankine vortex · CC BY-SA 4.0
• [3]Vortex · CC BY-SA 4.0
• [4]Vorticity · CC BY-SA 4.0
• [5]Lamb–Oseen vortex · CC BY-SA 4.0