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On the stability and dynamics of flows past bubble-shaped rigid bluff bodies

Published online by Cambridge University Press:  12 December 2025

Ragavendiran Muniyammal Open the ORCID record for Ragavendiran Muniyammal [Opens in a new window] ,
Shyam Sunder Gopalakrishnan Open the ORCID record for Shyam Sunder Gopalakrishnan [Opens in a new window] ,
Sanjay Kumar Open the ORCID record for Sanjay Kumar [Opens in a new window]  and
Alakesh Chandra Mandal Open the ORCID record for Alakesh Chandra Mandal [Opens in a new window]
Ragavendiran Muniyammal*
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Kanpur , Kanpur 208016, India
Shyam Sunder Gopalakrishnan*
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India
Sanjay Kumar*
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Kanpur , Kanpur 208016, India
Alakesh Chandra Mandal*
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Kanpur , Kanpur 208016, India
*
Corresponding authors: Ragavendiran Muniyammal, ragavcandela@gmail.com; Shyam Sunder Gopalakrishnan, shyamsg@iitk.ac.in; Sanjay Kumar, skmr@iitk.ac.in; Alakesh Chandra Mandal, alakeshm@iitk.ac.in
Corresponding authors: Ragavendiran Muniyammal, ragavcandela@gmail.com; Shyam Sunder Gopalakrishnan, shyamsg@iitk.ac.in; Sanjay Kumar, skmr@iitk.ac.in; Alakesh Chandra Mandal, alakeshm@iitk.ac.in
Corresponding authors: Ragavendiran Muniyammal, ragavcandela@gmail.com; Shyam Sunder Gopalakrishnan, shyamsg@iitk.ac.in; Sanjay Kumar, skmr@iitk.ac.in; Alakesh Chandra Mandal, alakeshm@iitk.ac.in
Corresponding authors: Ragavendiran Muniyammal, ragavcandela@gmail.com; Shyam Sunder Gopalakrishnan, shyamsg@iitk.ac.in; Sanjay Kumar, skmr@iitk.ac.in; Alakesh Chandra Mandal, alakeshm@iitk.ac.in
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Abstract

The stability and dynamics of flows past axisymmetric bubble-shaped rigid bluff bodies have been numerically and experimentally investigated. Motivated by the shapes of bubbles rising in quiescent liquids the bluff bodies were modelled as spherical and elliptical caps. The geometries are characterised by their aspect ratio, $\chi$, defined as the ratio of the height of the bubble to the base radius, which is varied from $0.2$ to $2.0$. Linear stability analyses were carried out on axisymmetric base flow fields subject to three-dimensional perturbations. As observed in earlier studies on bluff-body wakes, the primary bifurcation is stationary, followed by an oscillatory secondary bifurcation, with the leading global mode corresponding to azimuthal wavenumber $m = 1$. The domain of stability is found to increase with aspect ratio for both of the geometries considered in the present study. The critical Reynolds number corresponding to the primary bifurcation is found to be independent of the aspect ratio when re-scaled using the extent of the recirculation region and the maximum of the reverse-flow velocity as the length and velocity scales, respectively. The wake flow features were characterised experimentally using laser-induced fluorescence and particle-image-velocimetry techniques. It is observed that the flow has a planar symmetry following the primary bifurcation, which is retained beyond the secondary bifurcation. The experimentally measured wavelengths and frequencies are in excellent agreement with the results obtained from global stability analyses. These observations were further corroborated using direct numerical simulations of the three-dimensional flow field. The critical Reynolds numbers corresponding to both primary and secondary bifurcations, and the dominant modes obtained using proper orthogonal decomposition of the experimentally measured velocity fields, are found to agree well with the global mode shapes and numerically computed flow fields.

JFM classification

Wakes/Jets: Wakes Vortex Flows: Vortex shedding Instability: Absolute/convective instability

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JFM Papers
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Journal of Fluid Mechanics , Volume 1025 , 25 December 2025 , A5
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© The Author(s), 2025. Published by Cambridge University Press

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