The Rankine vortex is a simple mathematical model of a vortex in a viscous fluid. It is named after its discoverer, William John Macquorn Rankine.
The vortices observed in the nature are usually modelled with a irrotational (potential or free) vortex. However, in potential vortex, the velocity becomes infinite at the vortex center. In reality, very close to the origin, the motion resembles a solid body rotation. The Rankine vortex model assumes a solid-body rotation inside a cylinder of radius and a potential vortex outside the cylinder. The radius is referred to as the vortex-core radius. The velocity components of the Rankine vortex, expressed in terms of the cylindrical-coordinate system is given by[1]
where is the circulation strength of the Rankine vortex. Since solid-body rotation is characterized by an azimuthal velocity , where is the constant angular velocity, one can also use the parameter to characterize the vortex.
The vorticity field associated with the Rankine vortex is
Inside the vortex core, the vorticity is constant and twice the angular velocity, whereas outside the core, the flow is irrotational. In reality, the vortex cores are not always exactly circular; nor is the vorticity is uniform within the vortex core.
See also[edit]
- Kaufmann (Scully) vortex – an alternative mathematical simplification for a vortex, with a smoother transition.
- Lamb–Oseen vortex – the exact solution for a free vortex decaying due to viscosity.
- Burgers vortex
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