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Vortex bursting near a free surface

Published online by Cambridge University Press:  11 February 2020

Promode R. Bandyopadhyay Open the ORCID record for Promode R. Bandyopadhyay [Opens in a new window]
Promode R. Bandyopadhyay*
Affiliation:
Naval Undersea Warfare Center, Newport, RI 02841, USA
*
†Present address: 153 Chases Ln., Middletown, RI 02842, USA. Email address for correspondence: promode.r.bandyopadhyay@gmail.com
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Abstract

When the cross-section is reduced, a vortex displays spiralling and elasticity, bursting when the external velocity drops. How are these properties affected near a free surface? To answer, a visualization experiment in water is considered where an oscillating obstruction is pitched orthogonally to a rolling oscillation expending minimum energy. We show that short aerated vortices in adverse pressure gradient and shear remain stable during stretching, bursting into bubbles when relaxed after maximum stretching. A vertical aerated double helix (DH) root vortex of contra-rotating vortex tubes is produced near a Rossby number of 0.20. The vortex approaches an inclination of $45^{\circ }$ to the vertical, where stretching intensifies the vorticity to the maximum extent. Vortex inclinations up to $45^{\circ }$ are stable and unstable thereafter. Vortex bursting commences only when the inclination crosses $45^{\circ }$ by the slightest amount. When relaxed, oscillations are produced, breaking the vortex into arrays of bubbles, sometimes precisely at $45^{\circ }$ inclination. The bubble diameter, modelled by equating the effects of the centrifugal force (CF) on the vortex core pressure, to surface tension scales with the inverse of the square of the rotational velocity. When a high CF is withdrawn, the bursting DH aerated vortex cone is crushed due to surface tension. A root vortex and a coiled-up trailing edge vortex together form a compact Hill’s vortex when the highest CF is relieved, bursting into bubbles spectacularly scattered in the unstable sector. The DH vortex breakup is the connection point of vortices in proximity. At high CF, the DH has stacks of Taylor air tubes at $45^{\circ }$ to the external flow bursting when relaxed. Kelvin waves abound when bursting.

JFM classification

Vortex Flows: Vortex breakdown Waves/Free-surface Flows: Capillary waves Waves/Free-surface Flows: Elastic waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 888 , 10 April 2020 , A27
Copyright
© United States Navy, 2020. This is a work of the U.S. Government and is not subject to copyright protection within the United States. Published by Cambridge University Press

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