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The generation and diffusion of vorticity in three-dimensional flows: Lyman's flux

Published online by Cambridge University Press:  25 March 2021

S.J. Terrington Open the ORCID record for S.J. Terrington [Opens in a new window] ,
K. Hourigan Open the ORCID record for K. Hourigan [Opens in a new window]  and
M.C. Thompson Open the ORCID record for M.C. Thompson [Opens in a new window]
S.J. Terrington*
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, VIC3800, Australia
K. Hourigan
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, VIC3800, Australia
M.C. Thompson
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, VIC3800, Australia
*
†Email address for correspondence: [email protected]
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Abstract

We examine Lyman's (Appl. Mech. Rev., vol. 43, issue 8, 1990, pp. 157–158) proposed definition of the boundary vorticity flux, as an alternative to the traditional definition provided by Lighthill (Introduction: boundary layer theory. In Laminar Boundary Layers (ed. L. Rosenhead), chap. 2, 1963, pp. 46–109. Oxford University Press). While either definition may be used to describe the generation and diffusion of vorticity, Lyman's definition offers several conceptual benefits. First, Lyman's definition can be interpreted as the transfer of circulation across a boundary, due to the acceleration of that boundary, and is therefore closely tied to the dynamics of linear momentum. Second, Lyman's definition allows the vorticity creation process on a solid boundary to be considered essentially inviscid, effectively extending Morton's (Geophys. Astrophys. Fluid Dyn., vol. 28, 1984, pp. 277–308) two-dimensional description to three-dimensional flows. Third, Lyman's definition describes the fluxes of circulation acting in any two-dimensional reference surface, enabling a control-surface analysis of three-dimensional vortical flows. Finally, Lyman's definition more clearly illustrates how the kinematic condition that vortex lines do not end in the fluid is maintained, providing an elegant description of viscous processes such as vortex reconnection. The flow over a sphere, in either translational or rotational motion, is examined using Lyman's definition of the vorticity flux, demonstrating the benefits of the proposed framework in understanding the dynamics of vortical flows.

JFM classification

Vortex Flows: Vortex dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A106
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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