Supercritical surface gravity waves generated by a positive forcing

Jeongwhan Choi, S. M. Sun, S. I. Whang

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

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
Volume27
Issue number6
DOIs
Publication statusPublished - 2008 Nov 1

Fingerprint

Korteweg-de Vries equation
Gravity Waves
Gravity waves
Surface Waves
gravity waves
Korteweg-de Vries Equation
Surface waves
Forcing
Free Surface
Initial conditions
Froude number
Motion
Wave Speed
Solitary Waves
Solitons
Small Parameter
upstream
surface waves
Critical value
Horizontal

Keywords

  • Forced gravity waves
  • Supercritical surface waves

ASJC Scopus subject areas

  • Mechanical Engineering

Cite this

Supercritical surface gravity waves generated by a positive forcing. / Choi, Jeongwhan; Sun, S. M.; Whang, S. I.

In: European Journal of Mechanics, B/Fluids, Vol. 27, No. 6, 01.11.2008, p. 750-770.

Research output: Contribution to journalArticle

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