Overtopping of solitary waves and solitary bores on a plane beach

T. E. Baldock*, D. Peiris, A. J. Hogg

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

42 Citations (Scopus)


The overtopping of solitary waves and bores present major hazards during the initial phase of tsunami inundation and storm surges. This paper presents new laboratory data on overtopping events by both solitary waves and solitary bores. Existing empirical overtopping scaling laws are found to be deficient for these wave forms. Two distinct scaling regimes are instead identified. For solitary waves, the overtopping rates scale linearly with the deficit in run-up freeboard. The volume flux in the incident solitary wave is also an important parameter, and a weak dependence on the nonlinearity of the waves (H/d) is observed. For solitary bores, the overtopping cannot be scaled uniquely, because the fluid momentum behind the incident bore front is independent of the bore height, but it is in close agreement with recent solutions of the nonlinear shallow water equations. The maximum overtopping rate for the solitary waves is shown to be the lower bound of the overtopping rate for the solitary bores with the same deficit in freeboard. Thus, for a given run-up, the solitary bores induce greater overtopping rates than the solitary waves when the relative freeboard is small.

Original languageEnglish
Pages (from-to)3494-3516
Number of pages23
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2147
Publication statusPublished - 8 Nov 2012


  • Inundation
  • Overtopping
  • Solitary bores
  • Solitary waves
  • Tsunami


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