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

Published online by Cambridge University Press:  06 October 2011

Yue Yang  and
D. I. Pullin
Yue Yang*
Affiliation:
Graduate Aerospace Laboratories, 205-45, California Institute of Technology, Pasadena, CA 91125, USA
D. I. Pullin
Affiliation:
Graduate Aerospace Laboratories, 205-45, California Institute of Technology, Pasadena, CA 91125, USA
*
†Email address for correspondence: yy@caltech.edu
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Abstract

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.

JFM classification

Mathematical Foundations: Topological fluid dynamics Turbulent Flows: Turbulence theory Vortex Flows: Vortex dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 685 , 25 October 2011 , pp. 146 - 164
Copyright
Copyright © Cambridge University Press 2011

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