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Vorticity dynamics in an oscillatory flow over a rippled bed

Published online by Cambridge University Press:  26 April 2006

P. Blondeaux  and
G. Vittori
P. Blondeaux
Affiliation:
Hydraulic Institute, University of Genoa, Via Montallegro, 1, 16145 Genoa, Italy
G. Vittori
Affiliation:
Hydraulic Institute, University of Genoa, Via Montallegro, 1, 16145 Genoa, Italy
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Abstract

In the present paper we determine the oscillatory flow generated by surface gravity waves near a sea bottom covered with large-amplitude ripples. The vorticity equation and Poisson equation for the stream function are solved by means of a numerical approach based on spectral methods and finite-difference approximations. In order to test the numerical algorithm and in particular the numerical scheme used to generate vorticity along the ripple profile, we also perform an asymptotic analysis, which holds as the time t tends to zero. The main features of the time development of vorticity are analysed and particular attention is paid to the dynamics of the large vortices generated by flow separation at the ripple crests and along the ripple profile. Some of the results obtained by Longuet-Higgins (1981) are recovered; in particular, the present results show a vortex pair shed from the ripple crest every half-cycle. The determination of flow separation along the ripple profile induced by the pressure gradient and the inclusion of viscous effects allows us to obtain accurate quantitative results and detect some important phenomena never observed before.

In particular it is shown that: (i) Whenever a vortex structure moves towards the bottom, a secondary vortex is generated near the ripple profile, which interacts with the primary vortex and causes it to move away from the bottom, (ii) Depending on the values of the parameters, the time development of the free shear layer shed from the ripple crest may produce two or even more vortex structures, (iii) Occasionally vortices generated previously may coalesce with the free shear layer shed from the ripple crest, generating a unique vortex structure.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 226 , May 1991 , pp. 257 - 289
Copyright
© 1991 Cambridge University Press

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