Optimal transient growth on a vortex ring and its transition via cascade of ringlets

Mao, X.; Hussain, F.

Abstract

Linear and nonlinear transient growths of perturbations on a vortex ring up to Reynolds number (≡ circulation/viscosity) Re=27,000 are studied. For short time intervals, perturbations around the ring axis undergo the strongest linear transient growth and lead to secondary structures in the form of ringlets, owing to the Orr mechanism and an inviscid vorticity amplification mechanism - in contrast to the well reported instabilities and lobe structures along the vortex ring core. These secondary ringlet structures induce a tertiary group of ringlets through similar transient perturbation growth. This cascade of ringlets lead to the breakup of the main ring even before activation of the vortex-core instabilities. Such a cascade scenario is also observed in the development of a vortex ring perturbed by random disturbance in the axis region. These new modes and mechanisms for the generation and breakup of vortex ring structures bring insights into the dynamics and control of vortex ring flows.

Citation

Mao, X., & Hussain, F. (2017). Optimal transient growth on a vortex ring and its transition via cascade of ringlets. Journal of Fluid Mechanics, 832, 269-286. https://doi.org/10.1017/jfm.2017.675

• Journal Article Type: Article
• Acceptance Date: Sep 16, 2017
• Online Publication Date: Oct 26, 2017
• Publication Date: Dec 10, 2017
• Deposit Date: Oct 10, 2017
• Publicly Available Date: Oct 26, 2017
• Journal: Journal of Fluid Mechanics
• Print ISSN: 0022-1120
• Electronic ISSN: 1469-7645
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• Volume: 832
• Pages: 269-286
• DOI: https://doi.org/10.1017/jfm.2017.675
• Public URL: https://nottingham-repository.worktribe.com/output/899377
• Publisher URL: https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/optimal-transient-growth-on-a-vortex-ring-and-its-transition-via-cascade-of-ringlets/CB78544C362D45F5BE90196E16B0CE1C
• Additional Information: License: © 2017 Cambridge University Press This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.