Long wave reflection and transmission over a sloping step

Hsien-Kuo Chang*, Jin Cheng Liou

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


This investigation examines long wave reflection and transmission induced by a sloping step. Bellman and Kalaba's (1959) invariant imbedding is introduced to find wave reflection. An alternative method matching both the surface elevation and its surface slope of each region at the junction is applied to the determination of wave reflection and transmission. The proposed methods are compared with the accurate numerical results of Porter and Porter (2000) and those of Mei (1983) for a vertical step. The wave reflection obtained for a mildly sloping step differs significantly from the result of Mei. The wave reflection is found to fluctuate owing to wave trapping for the mild sloping step. The height and the face slope of the step are important for determining wave reflection and transmission coefficients.

Original languageEnglish
Pages (from-to)371-380
Number of pages10
JournalChina Ocean Engineering
Issue number3
StatePublished - 1 Sep 2004


  • Long wave
  • Reflection coefficient
  • Wave transmission
  • Wave trapping

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