### 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 |

### ASJC Scopus subject areas

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

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## Cite this

Choi, J., Sun, S. M., & Shen, M. C. (1996). Internal capillary-gravity waves of a two-layer fluid with free surface over an obstruction - Forced extended KdV equation.

*Physics of Fluids*,*8*(2), 397-404.