### Abstract

It is commonly observed that, in the development processes of channels, a channel head splits into two or more than two branches. By repeating such channel bifurcation, simple patterns of channels, which tend to appear in the initial stages of development, evolve into complex patterns of channel networks. In this study, we propose a simple mathematical model of channel bifurcation, in which a channel head is modeled by an opening on a flat plane composed of erodible bed material. A linear stability analysis is performed with the use of the depth-averaged momentum equations of flow and the Exner equation for beds subject to erosion. The analysis shows that the opening becomes unstable when the Froude critical depth divided by the bottom friction coefficient becomes sufficiently small compared with the radius of the opening. The implication is that channel bifurcation tends to take place as the discharge attracted by the channel head decreases.

Original language | English (US) |
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Title of host publication | River, Coastal and Estuarine Morphodynamics |

Subtitle of host publication | RCEM 2007 - Proceedings of the 5th IAHR Symposium on River, Coastal and Estuarine Morphodynamics |

Pages | 193-199 |

Number of pages | 7 |

State | Published - Dec 1 2008 |

Event | 5th IAHR-Symposium on River, Coastal and Estuarine Morphodynamics, RCEM 2007 - Enschede, Netherlands Duration: Sep 17 2007 → Sep 21 2007 |

### Publication series

Name | River, Coastal and Estuarine Morphodynamics: RCEM 2007 - Proceedings of the 5th IAHR Symposium on River, Coastal and Estuarine Morphodynamics |
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Volume | 1 |

### Other

Other | 5th IAHR-Symposium on River, Coastal and Estuarine Morphodynamics, RCEM 2007 |
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Country | Netherlands |

City | Enschede |

Period | 9/17/07 → 9/21/07 |

### Fingerprint

### ASJC Scopus subject areas

- Ecology
- Environmental Engineering

### Cite this

*River, Coastal and Estuarine Morphodynamics: RCEM 2007 - Proceedings of the 5th IAHR Symposium on River, Coastal and Estuarine Morphodynamics*(pp. 193-199). (River, Coastal and Estuarine Morphodynamics: RCEM 2007 - Proceedings of the 5th IAHR Symposium on River, Coastal and Estuarine Morphodynamics; Vol. 1).

**A simple mathematical model of channel bifurcation.** / Mizushima, H.; Izumi, N.; Parker, G.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*River, Coastal and Estuarine Morphodynamics: RCEM 2007 - Proceedings of the 5th IAHR Symposium on River, Coastal and Estuarine Morphodynamics.*River, Coastal and Estuarine Morphodynamics: RCEM 2007 - Proceedings of the 5th IAHR Symposium on River, Coastal and Estuarine Morphodynamics, vol. 1, pp. 193-199, 5th IAHR-Symposium on River, Coastal and Estuarine Morphodynamics, RCEM 2007, Enschede, Netherlands, 9/17/07.

}

TY - GEN

T1 - A simple mathematical model of channel bifurcation

AU - Mizushima, H.

AU - Izumi, N.

AU - Parker, G.

PY - 2008/12/1

Y1 - 2008/12/1

N2 - It is commonly observed that, in the development processes of channels, a channel head splits into two or more than two branches. By repeating such channel bifurcation, simple patterns of channels, which tend to appear in the initial stages of development, evolve into complex patterns of channel networks. In this study, we propose a simple mathematical model of channel bifurcation, in which a channel head is modeled by an opening on a flat plane composed of erodible bed material. A linear stability analysis is performed with the use of the depth-averaged momentum equations of flow and the Exner equation for beds subject to erosion. The analysis shows that the opening becomes unstable when the Froude critical depth divided by the bottom friction coefficient becomes sufficiently small compared with the radius of the opening. The implication is that channel bifurcation tends to take place as the discharge attracted by the channel head decreases.

AB - It is commonly observed that, in the development processes of channels, a channel head splits into two or more than two branches. By repeating such channel bifurcation, simple patterns of channels, which tend to appear in the initial stages of development, evolve into complex patterns of channel networks. In this study, we propose a simple mathematical model of channel bifurcation, in which a channel head is modeled by an opening on a flat plane composed of erodible bed material. A linear stability analysis is performed with the use of the depth-averaged momentum equations of flow and the Exner equation for beds subject to erosion. The analysis shows that the opening becomes unstable when the Froude critical depth divided by the bottom friction coefficient becomes sufficiently small compared with the radius of the opening. The implication is that channel bifurcation tends to take place as the discharge attracted by the channel head decreases.

UR - http://www.scopus.com/inward/record.url?scp=84858142145&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84858142145&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84858142145

SN - 9780415441674

T3 - River, Coastal and Estuarine Morphodynamics: RCEM 2007 - Proceedings of the 5th IAHR Symposium on River, Coastal and Estuarine Morphodynamics

SP - 193

EP - 199

BT - River, Coastal and Estuarine Morphodynamics

ER -