Kaufmann vortex explained

The Kaufmann vortex, also known as the Scully model, is a mathematical model for a vortex taking account of viscosity.^[1] It uses an algebraic velocity profile.^[2] This vortex is not a solution of the Navier–Stokes equations.

Kaufmann and Scully's model for the velocity in the Θ direction is:

V _{\Theta (r)} = (\Gamma)/(2 \pi) (r)/(r ^{2} _{c} + r ^{2})

The model was suggested by W. Kaufmann in 1962,^[3] and later by Scully and Sullivan in 1972 at the Massachusetts Institute of Technology.^[4]

See also

• Rankine vortex – a simpler, but more crude, approximation for a vortex.
• Lamb–Oseen vortex – the exact solution for a free vortex decaying due to viscosity.

Notes and References

1. Mahendra J. Bhagwat and J. Gordon Leishman, Generalized Viscous Vortex Model for Application to Free-Vortex Wake and Aeroacoustic Calculations, University of Maryland
2. Tamás Gausz, Budapest University of Technology and Economics. Blade vortex interaction problem at helicopter rotors, 12th International Conference on Fluid Flow Technologies, 2003
3. Kaufmann. W.. 1962. Über die Ausbreitung kreiszylindrischer Wirbel in zähen (viskosen) Flüssigkeiten. Ingenieur-Archiv. de. 31. 1. 1–9. 10.1007/BF00538235. 121128702 . 0020-1154.
4. Scully, M. P., and Sullivan, J. P., “Helicopter Rotor Wake Geometry and Airloads and Development of Laser Doppler Velocimeter for Use in Helicopter Rotor Wakes,” Massachusetts Institute of Technology Aerophysics Laboratory Technical Report 183, MIT DSR No. 73032, August 1972