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 language | English |
|---|---|
| Pages (from-to) | 750-770 |
| Number of pages | 21 |
| Journal | European Journal of Mechanics, B/Fluids |
| Volume | 27 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 2008 Nov 1 |
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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 journal › Article
}
TY - JOUR
T1 - Supercritical surface gravity waves generated by a positive forcing
AU - Choi, Jeongwhan
AU - Sun, S. M.
AU - Whang, S. I.
PY - 2008/11/1
Y1 - 2008/11/1
N2 - 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.
AB - 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.
KW - Forced gravity waves
KW - Supercritical surface waves
UR - http://www.scopus.com/inward/record.url?scp=50849117783&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=50849117783&partnerID=8YFLogxK
U2 - 10.1016/j.euromechflu.2008.01.006
DO - 10.1016/j.euromechflu.2008.01.006
M3 - Article
VL - 27
SP - 750
EP - 770
JO - European Journal of Mechanics, B/Fluids
JF - European Journal of Mechanics, B/Fluids
SN - 0997-7546
IS - 6
ER -