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Generation of water waves and bores by impulsive bottom flux

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Practical Asymptotics

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Abstract

The inviscid free-surface flow due to an impulsive bottom flux on constant depth is investigated analytically and numerically. The following classes of two-dimensional flow are considered: an upwelling flow which is uniform over a half-plane, a line source/sink, and a dipole aligned along the bottom. The bottom flux is turned on impulsively and may decay with time. The fully nonlinear problem is solved numerically. A smalltime asymptotic expansion to third order is found for the nonlinear problem. An asymptotic large-time solution is found for the linearized problem. A steady source will generate a pair of symmetric bores, and their breaking is investigated. A steady sink generates a depression wave if it is weak, and dip instability if it is strong. Wave breaking will occur for intermediate sink strengths. A decaying source emits solitary waves.

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Author information

Authors and Affiliations

  1. INSEAN, The Italian Ship Model Basin, Via di Vallerano 139, 00128, Roma, Italy

    M. Landrini

  2. Department of Agricultural Engineering, Agricultural University of Norway, Box 5065, N-1432, Aas, Norway

    P. A. Tyvand

Authors
  1. M. Landrini
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  2. P. A. Tyvand
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Editor information

Editors and Affiliations

  1. Eindhoven University of Technology, Eindhoven, The Netherlands

    H. K. Kuiken

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© 2001 Springer Science+Business Media Dordrecht

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Landrini, M., Tyvand, P.A. (2001). Generation of water waves and bores by impulsive bottom flux. In: Kuiken, H.K. (eds) Practical Asymptotics. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0698-9_8

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  • DOI: https://doi.org/10.1007/978-94-010-0698-9_8

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-3827-0

  • Online ISBN: 978-94-010-0698-9

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