Supercritical surface gravity waves generated by a positive forcing

J. W. Choi, S. M. Sun, S. I. Whang

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


Forced surface waves on an incompressible, inviscid fluid in a two-dimensional channel with a small bump on a horizontal rigid flat bottom are studied. The wave motion on the free surface is determined by a nondimensional wave speed F, called Froude number, and F = 1 is a critical value of F. If F = 1 + λ ε{lunate} with ε{lunate} > 0 a small parameter, then a time-dependent forced Korteweg-de Vries (FKdV) equation can be derived to model the wave motion on the free surface. Here, the case λ ≥ 0 (or F ≥ 1, called supercritical case) is considered. The steady FKdV equation is first studied both theoretically and numerically. It is shown that there exists a cut-off value λ0 of λ. For λ ≥ λ0 there are steady solutions, while for 0 ≤ λ < λ0 no steady solution of FKdV exists. For the unsteady FKdV equation, it is found that for λ > λ0, the solution of FKdV with zero initial condition tends to a stable steady solution, whilst for 0 < λ < λ0 a succession of solitary waves are periodically generated and continuously propagating upstream as time evolves. Moreover, the solutions of FKdV equation with nonzero initial conditions are studied.

Original languageEnglish
Pages (from-to)750-770
Number of pages21
JournalEuropean Journal of Mechanics, B/Fluids
Issue number6
Publication statusPublished - 2008 Nov


  • Forced gravity waves
  • Supercritical surface waves

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)


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