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The Relaxation of Vorticity Fuctuations in Approximately Elliptical Streamlines


Bassom, AP and Gilbert, AD, The Relaxation of Vorticity Fuctuations in Approximately Elliptical Streamlines, Proceedings of the Royal Society A. Mathematical, Physical and Engineering Sciences, 456, (1994) pp. 295-314. ISSN 1364-5021 (2000) [Refereed Article]

Copyright Statement

copyright 2000 The Royal Society

DOI: doi:10.1098/rspa.2000.0518


This paper generalizes previous asymptotic studies which describe the winding-up of vorticity ®uctuations in axisymmetric streamlines. We consider a steady Euler ®ow in the plane that possesses a region of closed streamlines of general form. At the centre of the streamlines is assumed to be a stagnation point around which the streamlines are approximately elliptical. A long-time asymptotic solution is obtained that describes how superposed weak ­ ne-scale vorticity ®uctuations in the region of closed streamlines can be subject to spiral wind-up and ­ ne scaling. At the elliptic point in the centre this process is less e¬ective and an inner analysis yields scaling exponents that characterize the behaviour here. In particular the vorticity ®uctuations increase as a power law of the distance from the elliptic point with the scaling exponent given in terms of the vorticity and angular velocity of the basic Euler ®ow. We also determine the contribution to the far ­ eld from the perturbation vorticity and show that it exhibits a power-law decay at large times.

Item Details

Item Type:Refereed Article
Keywords:planar vortex, inviscid relaxation, spiral wind-up, elliptical streamlines
Research Division:Mathematical Sciences
Research Group:Applied mathematics
Research Field:Theoretical and applied mechanics
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Bassom, AP (Professor Andrew Bassom)
ID Code:107125
Year Published:2000
Web of Science® Times Cited:7
Deposited By:Mathematics and Physics
Deposited On:2016-03-04
Last Modified:2016-07-08

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