On the complex eigenvalue problem of inviscid swirling flows
DOI:
https://doi.org/10.14311/AP.2026.66.0310Keywords:
hydrodynamic stability, eigenvalue problem, annular flows, complex phase velocity, non-dissipative flowsAbstract
The stability of inviscid, incompressible flows is investigated in the presence of axisymmetric disturbances with axial and azimuthal velocity components. We obtained parabolic bounds for complex eigenvalues that depend on the Richardson number J and the discriminant Ψ, which plays a significant role in deciding the stability of the basic axial flow. These bounds are unbounded, unlike Howard and Gupta’s semicircular and Singh and Hankey’s semielliptical bounds, which do not depend on discriminant Ψ. We also derived the condition under which these parabolic bounds intersect and reduce Singh and Hankey’s semielliptical bounds. Moreover, it is also shown that this reduction is uniformly valid for flows in the absence of a swirl velocity component.
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