STABILITY OF SOURCE-VORTEX AND DOUBLET FLOWS

A linear stability analysis is performed for steady source-vortex and sink-vortex flows for viscous and inviscid incompressible fluids. The analysis is based on a method recently developed by the authors [Phys. Fluids 7, 2345 (1995)], which utilizes the irrotational nature of the basic flow and takes vorticity as a perturbation. It is shown that so urce-vortex flows are always unstable. Sink-vortex flows are found sta ble except for low flow-rate flows of viscous fluid. The potential vor tex is unstable for three-dimensional perturbations, but stable for tw o-dimensional perturbations if the fluid is inviscid. For inviscid flu id the linear stability of doublet and higher-order singularities for plane perturbations is also studied. The general integral of the linea rized vorticity equations is found and used for stability analysis. On ly doublet flow is found stable. A mathematical criterion for stabilit y of certain types of steady two-dimensional flows of inviscid incompr essible fluid is formulated. (C) 1996 American Institute of Physics.