Azimuthal instability of divergent flows

We investigate a new mechanism for instability (named divergent instability), characterized by the formation of azimuthal cells, and find it to be a generic feature of three-dimensional steady axisymmetric flows of viscous incompressible fluid with radially diverging streamlines near a planar or conical surface. Four such flows are considered here: i) Squire-Wang flow in a half-space driven by surface stresses; ii) recirculation of fluid inside a concial meniscus; iii) two-cell regime of free convection above a rigid cone; and iv) Marangoni convection in a half-space induced by a point source of heat (or surfactant) placed at the liquid surface. For all these cases, bifurcation of the secondary steady solutions occurs. (from Authors)