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Understanding evolution of vortex rings in viscous fluids

Tinaikar, Aashay and Advaith, S and Basu, S (2017) Understanding evolution of vortex rings in viscous fluids. In: JOURNAL OF FLUID MECHANICS, 836 . pp. 873-909.

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Official URL: http://dx.doi.org/ 10.1017/jfm.2017.815

Abstract

The evolution of vortex rings in isodensity and isoviscosity fluid has been studied analytically using a novel mathematical model. The model predicts the spatiotemporal variation in peak vorticity, circulation, vortex size and spacing based on instantaneous vortex parameters. This proposed model is quantitatively verified using experimental measurements. Experiments are conducted using high-speed particle image velocimetry (PIV) and laser induced fluorescence (LIF) techniques. Non-buoyant vortex rings are generated from a nozzle using a constant hydrostatic pressure tank. The vortex Reynolds number based on circulation (Gamma / v) is varied in the range 100-1500 to account for a large range of operating conditions. Experimental results show good agreement with theoretical predictions. However, it is observed that neither Saffman's thin-core model nor the thick-core equations could correctly explain vortex evolution for all initial conditions. Therefore, a transitional theory is framed using force balance equations which seamlessly integrate short-and long-time asymptotic theories. It is found that the parameter A = (a / sigma)(2), where a is the vortex half-spacing and sigma denotes the standard deviation of the Gaussian vorticity profile, governs the regime of vortex evolution. For higher values of A, evolution follows short-time behaviour, while for A = O (1), long-time behaviour is prominent. Using this theory, many reported anomalous observations have been explained.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the CAMBRIDGE UNIV PRESS, 32 AVENUE OF THE AMERICAS, NEW YORK, NY 10013-2473 USA
Department/Centre: Division of Mechanical Sciences > Mechanical Engineering
Depositing User: review EPrints Reviewer
Date Deposited: 13 Jan 2018 07:21
Last Modified: 13 Jan 2018 07:21
URI: http://eprints.iisc.ac.in/id/eprint/58575

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