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Vorticity generation and conservation for two-dimensional interfaces and boundaries

Published online by Cambridge University Press:  07 October 2014

M. Brøns ,
M. C. Thompson ,
T. Leweke  and
K. Hourigan
M. Brøns
Affiliation:
Department of Applied Mathematics and Computer Science, Technical University of Denmark, DK-2800 Lyngby, Denmark
M. C. Thompson
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, VIC 3800, Australia
T. Leweke
Affiliation:
IRPHE, UMR 7342, CNRS, Aix-Marseille Université, Centrale Marseille, 13384 Marseille, France
K. Hourigan*
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, VIC 3800, Australia Division of Biological Engineering, Monash University, Melbourne, VIC 3800, Australia
*
†Email address for correspondence: [email protected]
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Abstract

The generation, redistribution and, importantly, conservation of vorticity and circulation is studied for incompressible Newtonian fluids in planar and axisymmetric geometries. A generalised formulation of the vorticity at the interface between two fluids for both no-slip and stress-free conditions is presented. Illustrative examples are provided for planar Couette flow, Poiseuille flow, the spin-up of a circular cylinder, and a cylinder below a free surface. For the last example, it is shown that, although large imbalances between positive and negative vorticity appear in the wake, the balance is found in the vortex sheet representing the stress-free surface.

JFM classification

Mathematical Foundations: General fluid mechanics Vortex Flows: Vortex Flows Vortex Flows: Vortex interactions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 758 , 10 November 2014 , pp. 63 - 93
Copyright
© 2014 Cambridge University Press 

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