The trajectory of slender curved liquid jets for small Rossby number

Alsharif, Abdullah M. and Decent, Stephen Paul and Părău, E. I. and Simmons, Mark J. H. and Uddin, Jamal (2019) The trajectory of slender curved liquid jets for small Rossby number. IMA Journal of Applied Mathematics, 84 (1). 96–117. ISSN 0272-4960

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Abstract

Wallwork et al. (2002) and Decent et al. (2002) developed an asymptotic method for describing the trajectory and instability of slender curved liquid jets. Decent et al. (2018) showed that this method is accurate for slender curved jets when the torsion of the centreline of the jet is small or O(1), but the asymptotic method may become invalid when the torsion is asymptotically large. This paper examines the torsion for a slender steady curved jet which emerges from an orifice on the outer surface of a rapidly rotating container. The torsion may become asymptotically large close to the orifice when the Rossby number Rb≪1, which corresponds to especially high rotation rates. This paper examines this asymptotic limit in different scenarios and shows that the torsion may become asymptotically large inside a small inner region close to the orifice where the jet is not slender. Outer region equations which describe the slender jet are determined and the torsion is found not to be asymptotically large in the outer region, and these equations can always be used to describe the jet even when the torsion is asymptotically large close to the orifice. It is in this outer region where travelling waves propagate down the jet and cause it to rupture in the unsteady formulation, and so the method developed by Wallwork et al. (2002) and Decent et al. (2002) can be used to accurately study the jet dynamics even when the torsion is asymptotically large at the orifice.

Item Type:
Journal Article
Journal or Publication Title:
IMA Journal of Applied Mathematics
Additional Information:
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in IMA Journal of Applied Mathematics following peer review. The definitive publisher-authenticated version Abdullah Madhi Alsharif, Stephen P Decent, Emilian I Părău, Mark J H Simmons, Jamal Uddin; The trajectory of slender curved liquid jets for small Rossby number, IMA Journal of Applied Mathematics, , hxy054, https://doi.org/10.1093/imamat/hxy054 is available online at: http://imamat.oxfordjournals.org/
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2604
Subjects:
ID Code:
127513
Deposited By:
Deposited On:
14 Sep 2018 10:24
Refereed?:
Yes
Published?:
Published
Last Modified:
26 Sep 2020 05:29