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Whither vortex tubes?

Pullin, D. I. and Yang, Yue (2014) Whither vortex tubes? Fluid Dynamics Research, 46 (6). Art. No. 061418. ISSN 0169-5983.

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We review research aimed at the development of an analytical and numerical framework for tracking the evolution, in an incompressible viscous fluid, of scalar fields, called `vortex surface fields' (VSFs), whose instantaneous isosurfaces always contain continuous vortex lines. A set of equations describing the evolution of VSFs starting from a known initial condition is proposed and discussed. Non-uniqueness in the initial-value problem is resolved with the introduction of evolution in a pseudo-time variable where the vorticity, frozen in real time, plays the role of an advecting field. A numerical method for following both the real and pseudo-time evolution is described and its regularization properties are discussed. Examples are given of following VSFs in a viscous Taylor-Green flow (Taylor and Green 1937 Proc. R. Soc. A 158 499-521). The prospects for extending these ideas to fully turbulent flows are discussed.

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Additional Information:© 2014 The Japan Society of Fluid Mechanics and IOP Publishing Ltd. Received 9 July 2014, revised 20 September 2014. Accepted for publication 23 May 2014. Published 6 November 2014. Communicated by Y Hattori. IUTAM Symposium on Vortex Dynamics - Formation, Structure and Function, Kyushu Univ Sch Med, Fukuoka, JAPAN, MAR 10-14, 2013. This work has been supported in part by the National Science Foundation under grant DMS-1016111.
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Issue or Number:6
Record Number:CaltechAUTHORS:20150109-105826366
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Official Citation:Whither vortex tubes? D I Pullin and Yue Yang 2014 Fluid Dyn. Res. 46 061418
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:53466
Deposited By: Ruth Sustaita
Deposited On:09 Jan 2015 19:13
Last Modified:03 Oct 2019 07:49

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