Abstract
General circle theorems which localize the complex eigenfrequencies arising in the linear stability analysis of conservative steady flows are given. Howard's circle theorem for incompressible plane parallel flow is contained as a special case. Two applications are considered: swirling flow of an inviscid incompressible fluid, and rotating flow of an inviscid, incompressible, perfectly conducting magnetofluid with an axial magnetic field. Circle theorems are obtained for the complex eigenfrequencies of any normal mode.
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