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Evolution of vortex-surface fields in viscous Taylor–Green and Kida–Pelz flows

Yang, Yue and Pullin, D. I. (2011) Evolution of vortex-surface fields in viscous Taylor–Green and Kida–Pelz flows. Journal of Fluid Mechanics, 685 . pp. 146-164. ISSN 0022-1120.

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In order to investigate continuous vortex dynamics based on a Lagrangian-like formulation, we develop a theoretical framework and a numerical method for computation of the evolution of a vortex-surface field (VSF) in viscous incompressible flows with simple topology and geometry. Equations describing the continuous, timewise evolution of a VSF from an existing VSF at an initial time are first reviewed. Non-uniqueness in this formulation is resolved by the introduction of a pseudo-time and a corresponding pseudo-evolution in which the evolved field is ‘advected’ by frozen vorticity onto a VSF. A weighted essentially non-oscillatory (WENO) method is used to solve the pseudo-evolution equations in pseudo-time, providing a dissipative-like regularization. Vortex surfaces are then extracted as iso-surfaces of the VSFs at different real physical times. The method is applied to two viscous flows with Taylor–Green and Kida–Pelz initial conditions respectively. Results show the collapse of vortex surfaces, vortex reconnection, the formation and roll-up of vortex tubes, vorticity intensification between anti-parallel vortex tubes, and vortex stretching and twisting. A possible scenario for understanding the transition from a smooth laminar flow to turbulent flow in terms of topology of vortex surfaces is discussed.

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Additional Information:© 2011 Cambridge University Press. Received 23 January 2011; revised 22 June 2011; accepted 25 June 2011. Online publication October 06 2011. This work has been supported in part by the National Science Foundation under grant DMS-1016111.
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Subject Keywords:topological fluid dynamics; turbulence theory; vortex dynamics
Record Number:CaltechAUTHORS:20111212-100604994
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:28417
Deposited By: Tony Diaz
Deposited On:13 Dec 2011 16:57
Last Modified:03 Oct 2019 03:32

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