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On parabolic instability regions for inviscid incompressible annular flows

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Abstract

We consider the azimuthal instability problem of inviscid incompressible swirling flows following the work of Fung (J Fluid Mech 127:83–90, 1983) and we obtain parabolic instability regions for two classes of variable density flows. It is shown that these parabolic regions intersect and reduce the semielliptical instability region of Fung (J Fluid Mech 127:83–90, 1983). Moreover it is shown that the parabolic instability regions are uniformly valid for both variable density and density homogeneous flows and in the homogeneous case they intersect and reduce the semicircular instability region of Lalas (J Fluid Mech 69:65–72, 1975).

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Acknowledgements

The work of Prakash S was supported by CSIR -SRF(NET) with Award number: 09/559(0134)/2019-EMR-I which is acknowledged. We are thankful to the anonymous reviewers, whose comments helped us in improving the manuscript.

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  1. Department of Mathematics, Pondicherry University, Pondicherry, 605014, India

    S. Prakash & M. Subbiah

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  1. S. Prakash
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  2. M. Subbiah
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Correspondence to S. Prakash.

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Prakash, S., Subbiah, M. On parabolic instability regions for inviscid incompressible annular flows. J Anal 31, 2741–2754 (2023). https://doi.org/10.1007/s41478-023-00596-1

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