vortex ring formation at the edge of a circular tube

This simulation was motivated by a laboratory experiment of Didden which appears in Van Dyke's "An Album of Fluid Motion" (p. 43). At time t=0, a piston begins pushing fluid through the open end of a circular tube. The boundary layer separates and rolls up to form a vortex ring which propagates downstream. The piston stops moving at t=1.6 and thereafter a counter-rotating ring forms at the tube opening. In the simulation results shown below, the shear layer is represented by a free vortex sheet and the circular tube by a bound vortex sheet. Axisymmetry is imposed. Prandtl's slip-flow model is applied to simulate separation at the edge of the tube.


Didden, N. (1979) On the formation of vortex rings: rolling-up and production of circulation, Z. Angew. Math. Phys. 30, 101

Nitsche, M. & Krasny, R. (1994) A numerical study of vortex ring formation at the edge of a circular tube, J. Fluid Mech. 276, 139-161

Van Dyke, M. (1982) An album of fluid motion, The Parabolic Press, 43