BIFURCATION OF SWIRL IN LIQUID CONES

We show that rotation appears owing to bifurcation in primarily pure m eridional steady motion of viscous incompressible fluid. This manifest ation of the laminar axisymmetric 'swirl dynamo' occurs in flows insid e liquid conical menisci with the cone half-angle theta(c) < 90 degree s. The liquid flows towards the cone apex near the surface and moves a way along the axis driven by (i) surface shear stresses (typical for e lectrosprays) or (ii) by body Lorentz forces (e.g. in the process of c athode eruption). When the motion intensity increases and passes a cri tical value, new swirling regimes appear resulting from the supercriti cal pitchfork bifurcation. This agrees with recent observations of swi rl in Taylor cones. We find that when the swirl Reynolds number Gamma( c), reaches a threshold value, flow separation occurs and the meridion al motion becomes two-cellular with inflows near both the surface and the axis, and an outflow near the cone theta = theta(s), 0 < theta(s) < theta(c). In the limit of high Gamma(c), the angular thickness of th e near-surface cell tends to zero. In case (i) the swirl is concentrat ed near the surface while the motion inside the inner cell becomes pur ely meridional with the radial velocity being uniform. We also study t he two-phase flow of a liquid inside and a gas outside the meniscus. F low separation occurs in both media and then swirl is concentrated nea r the interface. In case (ii) we reveal another interesting effect: a cascade of flow separations near the axis. As the driving forces incre ase, meridional motion becomes multi-cellular although very slow in co mparison with swirl. To cover all ranges of parameters we combine nume rical calculations and asymptotic analyses.