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On the limitations of the complex wave velocity for the heterogeneous swirling flows

  • Prakash Shanmugam ORCID logo EMAIL logo
Published/Copyright: September 25, 2023
Zeitschrift für Naturforschung A
From the journal Zeitschrift für Naturforschung A Volume 78 Issue 11

Abstract

The hydrodynamic instability of variable density swirling flows under gravity between two infinite coaxial cylinders is investigated for axisymmetric disturbances. It is shown that the complex wave velocity of any arbitrary unstable axisymmetric mode must lie within the semi-elliptical region whose minor axis depends on the density stratification parameter J(r). The stabilizing effect of density stratification is shown by reducing the semi-circular instability region of [G. K. Batchelor and A. E. Gill, “Analysis of the stability of axisymmetric jets,” J. Fluid Mech., vol. 14, p. 529, 1962]. Furthermore, we have obtained two parabolic instability regions which intersect and reduce the semi-elliptical instability region for density-stratified flows. These parabolic instability regions are uniformly valid for both variable density and density homogeneous flows also.

Keywords: hydrodynamic stability; heterogeneous flows; eigenvalue bounds; instability regions; richardson number
MSC 2010: 76E05
Corresponding author: Prakash Shanmugam, Department of Mathematics, SAS, Vellore Institute of Technology - AP, Amaravathi, Andhra Pradesh, 522237 India, E-mail:

Acknowledgments

Author thank Prof. M. Subbiah for discussions which forms the basis of this work.

  1. Research ethics: Not applicable.

  2. Author contributions: Entire work is done by single author Prakash Shanmugam.

  3. Competing interests: Author declares that he has no conflict of interest in this work.

  4. Research funding: The author acknowledges with thanks to the Council of Scientific and Industrial Research (CSIR), India for financial support under the grant 09/559(0134)/2019-EMR-I.

  5. Data availability: No data is used in this research.

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Received: 2023-07-28
Accepted: 2023-09-01
Published Online: 2023-09-25
Published in Print: 2023-11-27

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/zna-2023-0208
Keywords for this article
hydrodynamic stability; heterogeneous flows; eigenvalue bounds; instability regions; richardson number

Articles in the same Issue

  1. Frontmatter
  2. General
  3. Impact of temperature asymmetry and small fraction of static positive ions on the relaxed states of a relativistic hot pair plasma
  4. Dynamical Systems & Nonlinear Phenomena
  5. Similarity solutions for cylindrical shock wave in a self-gravitating and rotating gas under the influence of monochromatic radiation and azimuthal or axial magnetic field by using Lie invariance method
  6. Chaotic dynamics of an extended Duffing-van der Pol system with a non-smooth perturbation and parametric excitation
  7. Hydrodynamics
  8. On the limitations of the complex wave velocity for the heterogeneous swirling flows
  9. Solid State Physics & Materials Science
  10. Photocatalytic decomposition of Congo red dye by black paste@TiO2 as an efficient recyclable photocatalyst
  11. Theoretical investigation on the elastic and mechanical properties of high-entropy alloys with partial replacement of Sc in Hf0.25Ti0.25Zr0.25Sc0.25−xAl x (x ≤ 15 %)
  12. Synthesis, structure, and luminescence properties of double perovskites Ba2.9Sr0.1WO6: Eu3+ red emitting phosphor
  13. Unveiling transport properties in rare-earth-substituted nanostructured bismuth telluride for thermoelectric application
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