### Abstract

In this paper we study steady capillary-gravity waves in a two-layer fluid bounded above by a free surface and below by a horizontal rigid boundary with a small obstruction. Two critical speeds for the waves are obtained. Near the smaller critical speed, the derivation of the usual forced KdV equation (FKdV) fails when the coefficient of the nonlinear term in the FKdV vanishes. To overcome this difficulty, a new equation, called a forced extended KdV equation (FEKdV) governing interfacial wave forms, is obtained by a refined asymptotic method. Various solutions and numerical results of this equation are presented.

Original language | English |
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Pages (from-to) | 397-404 |

Number of pages | 8 |

Journal | Physics of Fluids |

Volume | 8 |

Issue number | 2 |

Publication status | Published - 1996 Feb 1 |

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### ASJC Scopus subject areas

- Fluid Flow and Transfer Processes
- Computational Mechanics
- Mechanics of Materials
- Physics and Astronomy(all)
- Condensed Matter Physics

### Cite this

*Physics of Fluids*,

*8*(2), 397-404.

**Internal capillary-gravity waves of a two-layer fluid with free surface over an obstruction - Forced extended KdV equation.** / Choi, Jeongwhan; Sun, S. M.; Shen, M. C.

Research output: Contribution to journal › Article

*Physics of Fluids*, vol. 8, no. 2, pp. 397-404.

}

TY - JOUR

T1 - Internal capillary-gravity waves of a two-layer fluid with free surface over an obstruction - Forced extended KdV equation

AU - Choi, Jeongwhan

AU - Sun, S. M.

AU - Shen, M. C.

PY - 1996/2/1

Y1 - 1996/2/1

N2 - In this paper we study steady capillary-gravity waves in a two-layer fluid bounded above by a free surface and below by a horizontal rigid boundary with a small obstruction. Two critical speeds for the waves are obtained. Near the smaller critical speed, the derivation of the usual forced KdV equation (FKdV) fails when the coefficient of the nonlinear term in the FKdV vanishes. To overcome this difficulty, a new equation, called a forced extended KdV equation (FEKdV) governing interfacial wave forms, is obtained by a refined asymptotic method. Various solutions and numerical results of this equation are presented.

AB - In this paper we study steady capillary-gravity waves in a two-layer fluid bounded above by a free surface and below by a horizontal rigid boundary with a small obstruction. Two critical speeds for the waves are obtained. Near the smaller critical speed, the derivation of the usual forced KdV equation (FKdV) fails when the coefficient of the nonlinear term in the FKdV vanishes. To overcome this difficulty, a new equation, called a forced extended KdV equation (FEKdV) governing interfacial wave forms, is obtained by a refined asymptotic method. Various solutions and numerical results of this equation are presented.

UR - http://www.scopus.com/inward/record.url?scp=0029671790&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029671790&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0029671790

VL - 8

SP - 397

EP - 404

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 2

ER -