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Transcritical flow over obstacles and holes: forced Korteweg–de Vries framework

Published online by Cambridge University Press:  25 October 2019

Roger H. J. Grimshaw Open the ORCID record for Roger H. J. Grimshaw [Opens in a new window]  and
Montri Maleewong Open the ORCID record for Montri Maleewong [Opens in a new window]
Roger H. J. Grimshaw
Affiliation:
Department of Mathematics, University College London, London WC1E 6BT, UK
Montri Maleewong*
Affiliation:
Department of Mathematics, Faculty of Science, Kasetsart University, Bangkok, 10900, Thailand
*
†Email address for correspondence: [email protected]
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Abstract

This paper extends a previous study of free-surface flow over two localised obstacles using the framework of the forced Korteweg–de Vries equation, to an analogous study of flow over two localised holes, or a combination of an obstacle and a hole. Importantly the terminology obstacle or hole can be reversed for a stratified fluid and refers more precisely to the relative polarity of the forcing and the solitary wave solution of the unforced Korteweg–de Vries equation. As in the previous study, our main concern is with the transcritical regime when the oncoming flow has a Froude number close to unity. In the transcritical regime at early times, undular bores are produced upstream and downstream of each forcing site. We then describe the interaction of these undular bores between the forcing sites, and the outcome at very large times.

JFM classification

Geophysical and Geological Flows: Stratified flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 881 , 25 December 2019 , pp. 660 - 678
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Copyright
© 2019 Cambridge University Press 

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