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Evolution of the flow field associated with a streamwise diffusing vortex. (English) Zbl 0561.76039
The vortex is assumed to be of infinite extent in the stream direction, and to be a potential vortex (vortex filament) turned on at time zero, and subsequently allowed to diffuse under the action of viscosity. The ambient flow is taken to be, initially, a linear shear profile; the flow then evolves under the joint action of viscosity and convection induced by the vortex. Boundaries are assumed to be infinitely removed from the vortex core. A similarity variable is found which reduces the equation for the induced streamwise velocity perturbation to an ordinary differential equation, which is easily solved numerically.

MSC:
76D05 Navier-Stokes equations for incompressible viscous fluids
76F10 Shear flows and turbulence
76R99 Diffusion and convection
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[1] Willmarth, Adv. Appl. Mech. 15 pp 159– (1975)
[2] DOI: 10.1017/S0022112067001740 · doi:10.1017/S0022112067001740
[3] DOI: 10.1017/S0022112062000014 · Zbl 0131.41901 · doi:10.1017/S0022112062000014
[4] DOI: 10.1017/S0022112071002490 · doi:10.1017/S0022112071002490
[5] DOI: 10.1017/S0022112079001191 · doi:10.1017/S0022112079001191
[6] DOI: 10.1017/S0022112061000196 · Zbl 0096.21201 · doi:10.1017/S0022112061000196
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