On the stability of circular Rayleigh problem of hydrodynamic stability

  • S. Prakash VIT-AP University, Inavolu, Beside AP Secretariat, Amaravati AP, India
  • Nagarohini Challa VIT-AP University, Inavolu, Beside AP Secretariat, Amaravati AP, India
DOI: https://doi.org/10.5269/bspm.78538

Abstract

This study presents a detailed analytical investigation into the stability of incompressible swirling flows. A necessary condition is derived for the emergence of both neutral and unstable disturbance modes within subcritical region. To determine a sufficient condition for the existence of unstable modes, the variational structure of the inviscid stability problem is examined under the assumption of a monotonic axial velocity profile. A Sturm-Liouville framework is then employed to establish the existence of a regular neutral mode. Moreover, it is demonstrated that the total number of linearly unstable modes does not exceed the number of neutral modes admitted by the system.

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Published
2026-04-27
Issue
Vol 44 No 13 (2026): Applied Mathematics and Computing (ICAMC2025)
Section
Conf. Issue: Applied Mathematics and Computing (ICAMC-25)

Copyright (c) 2026 Boletim da Sociedade Paranaense de Matemática

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