Steady gravity waves due to a submerged source

Christopher J. Lustri*, S. Jonathan Chapman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


In the low-Froude-number limit, free-surface gravity waves caused by flow past a submerged obstacle have amplitude that is exponentially small. Consequently, these cannot be represented using an asymptotic series expansion. Steady linearized flow past a submerged source is considered, and exponential asymptotic methods are applied to determine the behaviour of the free-surface gravity waves. The free surface is found to contain longitudinal and transverse waves that switch on rapidly across curves known as Stokes lines on the free surface. The longitudinal waves are present everywhere downstream of the singularity, while the transverse waves are restricted to two downstream wedges. As the depth of the source approaches the surface, the familiar Kelvin-wedge wave behaviour is recovered.

Original languageEnglish
Pages (from-to)660-686
Number of pages27
JournalJournal of Fluid Mechanics
Publication statusPublished - 2013
Externally publishedYes


  • Surface gravity waves
  • Waves/free-surface flows


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