A simple mathematical model of channel bifurcation

H. Mizushima, N. Izumi, G. Parker

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish (US)
Title of host publicationRiver, Coastal and Estuarine Morphodynamics
Subtitle of host publicationRCEM 2007 - Proceedings of the 5th IAHR Symposium on River, Coastal and Estuarine Morphodynamics
Pages193-199
Number of pages7
StatePublished - Dec 1 2008
Event5th IAHR-Symposium on River, Coastal and Estuarine Morphodynamics, RCEM 2007 - Enschede, Netherlands
Duration: Sep 17 2007Sep 21 2007

Publication series

NameRiver, Coastal and Estuarine Morphodynamics: RCEM 2007 - Proceedings of the 5th IAHR Symposium on River, Coastal and Estuarine Morphodynamics
Volume1

Other

Other5th IAHR-Symposium on River, Coastal and Estuarine Morphodynamics, RCEM 2007
CountryNetherlands
CityEnschede
Period9/17/079/21/07

Fingerprint

Linear stability analysis
Bifurcation (mathematics)
bifurcation
Erosion
Momentum
Mathematical models
Friction
bottom friction
stability analysis
momentum
erosion

ASJC Scopus subject areas

  • Ecology
  • Environmental Engineering

Cite this

Mizushima, H., Izumi, N., & Parker, G. (2008). A simple mathematical model of channel bifurcation. In 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.

River, Coastal and Estuarine Morphodynamics: RCEM 2007 - Proceedings of the 5th IAHR Symposium on River, Coastal and Estuarine Morphodynamics. 2008. p. 193-199 (River, Coastal and Estuarine Morphodynamics: RCEM 2007 - Proceedings of the 5th IAHR Symposium on River, Coastal and Estuarine Morphodynamics; Vol. 1).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Mizushima, H, Izumi, N & Parker, G 2008, A simple mathematical model of channel bifurcation. in 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.
Mizushima H, Izumi N, Parker G. A simple mathematical model of channel bifurcation. In River, Coastal and Estuarine Morphodynamics: RCEM 2007 - Proceedings of the 5th IAHR Symposium on River, Coastal and Estuarine Morphodynamics. 2008. p. 193-199. (River, Coastal and Estuarine Morphodynamics: RCEM 2007 - Proceedings of the 5th IAHR Symposium on River, Coastal and Estuarine Morphodynamics).
Mizushima, H. ; Izumi, N. ; Parker, G. / A simple mathematical model of channel bifurcation. River, Coastal and Estuarine Morphodynamics: RCEM 2007 - Proceedings of the 5th IAHR Symposium on River, Coastal and Estuarine Morphodynamics. 2008. pp. 193-199 (River, Coastal and Estuarine Morphodynamics: RCEM 2007 - Proceedings of the 5th IAHR Symposium on River, Coastal and Estuarine Morphodynamics).
@inproceedings{a87d9563e24148a8a05bacb20bd6cd8d,
title = "A simple mathematical model of channel bifurcation",
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.",
author = "H. Mizushima and N. Izumi and G. Parker",
year = "2008",
month = "12",
day = "1",
language = "English (US)",
isbn = "9780415441674",
series = "River, Coastal and Estuarine Morphodynamics: RCEM 2007 - Proceedings of the 5th IAHR Symposium on River, Coastal and Estuarine Morphodynamics",
pages = "193--199",
booktitle = "River, Coastal and Estuarine Morphodynamics",

}

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 -