## Abstract

Enclosed bodies of water such as lakes or harbours often experience large-scale oscillatory motions (seiching). As a simple model of such flow, we investigate exact solutions to the shallow-water equations which represent oscillatory flow in an elliptical basin with parabolic cross section. Specifically, we consider two fundamental modes of oscillation, in one of which the flow is parallel to the axis of the ellipse, while in the other it is radial. We obtain periodic analytical solutions for sediment transport, including erosion, deposition and advection, under either mode of oscillation, and present a method for obtaining such solutions for a more general class of flow fields and sediment transport models. Our solutions provide estimates of the morphodynamical importance of seiching motions and also reveal a characteristic pattern of net erosion and deposition associated with each mode. In particular, we find that a net flux of suspended sediment can be transported from the deeper to the shallower regions of the basin. These transport patterns, which are driven essentially by settling lag, are highly robust to the formulation of the sediment transport relation and appear not to be substantially affected by

the omission of frictional terms in the hydrodynamics: they should thus provide considerable insight into sediment transport in less-idealised systems

the omission of frictional terms in the hydrodynamics: they should thus provide considerable insight into sediment transport in less-idealised systems

Original language | English |
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Pages (from-to) | 43-70 |

Number of pages | 28 |

Journal | Coastal Engineering |

Volume | 49 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 2003 |

## Keywords

- coastal engineering
- elliptical basins
- sediment transport
- mathematical analysis