Flow structure beneath rotational water waves with stagnation points

The purpose of this work is to explore in detail the structure of the interior flow generated by periodic surface waves on a fluid with constant vorticity. The problem is mapped conformally to a strip and solved numerically using spectral methods. Once the solution is known, the streamlines, pressur...

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Bibliographic Details
Published inJournal of fluid mechanics Vol. 812; pp. 792 - 814
Main Authors Ribeiro, Roberto, Milewski, Paul A., Nachbin, André
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 10.02.2017
Subjects
Fluid mechanics
Mathematical models
Vortices
Water waves
shear layers
surface gravity waves
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Summary:The purpose of this work is to explore in detail the structure of the interior flow generated by periodic surface waves on a fluid with constant vorticity. The problem is mapped conformally to a strip and solved numerically using spectral methods. Once the solution is known, the streamlines, pressure and particle paths can be found and mapped back to the physical domain. We find that the flow beneath the waves contains zero, one, two or three stagnation points in a frame moving with the wave speed, and describe the bifurcations between these flows. When the vorticity is sufficiently strong, the pressure in the flow and on the bottom boundary also has very different features from the usual irrotational wave case.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2016.820