Abstract
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 source-vortex flows are always unstable. Sink-vortex flows are found stable except for low flow-rate flows of viscous fluid. The potential vortex is unstable for three-dimensional perturbations, but stable for two-dimensional perturbations if the fluid is inviscid. For inviscid fluid the linear stability of doublet and higher-order singularities for plane perturbations is also studied. The general integral of the linearized vorticity equations is found and used for stability analysis. Only doublet flow is found stable. A mathematical criterion for stability of certain types of steady two-dimensional flows of inviscid incompressible fluid is formulated.
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