A contribution to the problem of vortex breakdown

Vortex breakdown is promoted by adverse pressure gradients. According to a summary of the role of an applied pressure gradient by Hall (1972), in the case of an increase in an adverse pressure gradient, less swirl is required to maintain breakdown, or, if the same level of swirl is maintained, the breakdown is moved upstream. The present paper is concerned with an investigation of the considered situation. The analysis was motivated by a numerical study conducted by Shi and Krause (1983). It is assumed that the flow upstream of the point of breakdown is incompressible, steady, and axisymmetric. The assumption of steady flow conditions is confirmed by experiments. Attention is given to the governing equations, the equations in a dimensionless form, and the derivation of an equation which shows that to zeroth order the pressure gradient along the axis is influenced by convectional and viscous terms. This equation confirms Hall's observation.