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.