### Abstract

Any weak, steady vortical flow is a solution, to leading order, of the inviscid fluid equations with a free surface, so long as this flow has horizontal streamlines coinciding with the undisturbed free surface. This work considers the propagation of long irrotational surface gravity waves when such a vortical flow is present. In particular, when the vortical flow and the irrotational surface waves are both periodic and have comparable length scales, resonant interactions can occur between the various components of the flow. The interaction is described by two coupled Korteweg-de Vries equations and a two-dimensional streamfunction equation.

Original language | English |
---|---|

Pages (from-to) | 225-256 |

Number of pages | 32 |

Journal | Studies in Applied Mathematics |

Volume | 94 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Apr 1995 |

### Fingerprint

### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

**Resonant Interactions between Vortical Flows and Water Waves. Part II : Shallow Water.** / Milewski, P. A.

Research output: Contribution to journal › Article

*Studies in Applied Mathematics*, vol. 94, no. 3, pp. 225-256. https://doi.org/10.1002/sapm1995943225

}

TY - JOUR

T1 - Resonant Interactions between Vortical Flows and Water Waves. Part II

T2 - Shallow Water

AU - Milewski, P. A.

PY - 1995/4/1

Y1 - 1995/4/1

N2 - Any weak, steady vortical flow is a solution, to leading order, of the inviscid fluid equations with a free surface, so long as this flow has horizontal streamlines coinciding with the undisturbed free surface. This work considers the propagation of long irrotational surface gravity waves when such a vortical flow is present. In particular, when the vortical flow and the irrotational surface waves are both periodic and have comparable length scales, resonant interactions can occur between the various components of the flow. The interaction is described by two coupled Korteweg-de Vries equations and a two-dimensional streamfunction equation.

AB - Any weak, steady vortical flow is a solution, to leading order, of the inviscid fluid equations with a free surface, so long as this flow has horizontal streamlines coinciding with the undisturbed free surface. This work considers the propagation of long irrotational surface gravity waves when such a vortical flow is present. In particular, when the vortical flow and the irrotational surface waves are both periodic and have comparable length scales, resonant interactions can occur between the various components of the flow. The interaction is described by two coupled Korteweg-de Vries equations and a two-dimensional streamfunction equation.

UR - http://www.scopus.com/inward/record.url?scp=21844526259&partnerID=8YFLogxK

U2 - 10.1002/sapm1995943225

DO - 10.1002/sapm1995943225

M3 - Article

VL - 94

SP - 225

EP - 256

JO - Studies in Applied Mathematics

JF - Studies in Applied Mathematics

SN - 0022-2526

IS - 3

ER -