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Periodic waves over constant vorticity: Some asymptotic results generated by parameter expansions

Lookup NU author(s): Professor Robin Johnson

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Abstract

The problem of steady, periodic waves over constant vorticity (positive and negative) is examined by using parameter expansions. The first analyses, for each of the two signs of vorticity, are constructed by perturbing an existing uniform flow; for positive vorticity it is shown, within the asymptotic structure obtained, that a pattern of streamlines admits a stagnation point on the bottom, below the crest of the wave. On the other hand, the corresponding solution for negative vorticity does not produce a stagnation point at the surface (as would have been expected). An explanation of these two outcomes follows from the natures of the corresponding dispersion relations that underpin the existence of the linear-wave perturbation. The case of large negative vorticity is then considered, and this does permit a solution that is close to stagnation, a conclusion consistent with the linear dispersion relation. No corresponding solution exists for large positive vorticity. Some typical streamlines and velocity profiles below the crest, based on the asymptotic results, are presented. © 2009 Elsevier B.V. All rights reserved.


Publication metadata

Author(s): Johnson R

Publication type: Article

Publication status: Published

Journal: Wave Motion

Year: 2009

Volume: 46

Issue: 6

Pages: 339-349

ISSN (print): 0165-2125

ISSN (electronic):

Publisher: Elsevier BV

URL: http://dx.doi.org/10.1016/j.wavemoti.2009.06.006

DOI: 10.1016/j.wavemoti.2009.06.006


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