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Self-destabilising loop of a low-speed water jet emanating from an orifice in microgravity

Published online by Cambridge University Press:  16 May 2016

Akira Umemura
Akira Umemura*
Affiliation:
Department of Aerospace Engineering, Nagoya University, Nagoya 464-8603, Japan
*
†Email address for correspondence: akira@nuae.nagoya-u.ac.jp
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Abstract

A one-dimensional global mode analysis is conducted for low-speed water jets emanating from a circular orifice in microgravity, in which the observed spontaneous convective instability causes almost periodic jet disintegrations at a fixed location for each jet-issue speed that exceeds a certain threshold. The inviscid spatial linear stability analysis identifies four wave modes excitable at the frequency: the Plateau–Rayleigh (PR) unstable wave, its complex conjugate and two neutral waves which may transfer energy upstream. Their linear combination satisfying the orifice exit condition may describe the synchronised reproduction of a PR unstable wave from each neutral wave at the orifice exit. On the other hand, a weakly nonlinear analysis shows that the growth of the nonlinear PR unstable wave produces the two neutral waves near the orifice. Thus, the same PR unstable wave can be reproduced on a newly issued liquid surface owing to the neutral waves produced by its own nonlinear growth. This self-destabilising loop, dominantly operating for the most unstable PR wave, determines the initial PR unstable wave amplitude and, consequently, the breakup length as a function of jet-issue speed. The predicted initial amplitude of the PR unstable wave is in reasonably good agreement with the value calculated from the average breakup length measured in our microgravity experiments. It is found that that the loop consists mainly of the downstream- and upstream-moving neutral waves at relatively high and low jet speeds, respectively. The stability of the self-destabilising loop is also discussed.

JFM classification

Waves/Free-surface Flows: Capillary waves Instability: Instability Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 797 , 25 June 2016 , pp. 146 - 180
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Copyright
© 2016 Cambridge University Press 

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Footnotes

‡

Present status: Emeritus Professor.

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