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17 - Principle of Least Action

Published online by Cambridge University Press:  24 November 2022

Vijay P. Singh
Affiliation:
Texas A & M University
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Summary

Rivers tend to follow the path of least action for transporting the sediment and water loads imposed on them. Because regime hydraulic geometry relations entail more unknowns than the equations of continuity, resistance, and sediment transport, optimization is utilized to determine the preferred cross-section from among many possible cross-sections and this cross-section satisfies the path of least action. This chapter discusses this principle and derives the hydraulic geometry based on this principle.

Type
Chapter
Information
Handbook of Hydraulic Geometry
Theories and Advances
, pp. 436 - 449
Publisher: Cambridge University Press
Print publication year: 2022

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References

Bagnold, R. A. (1966). An approach to the sediment transport problem from general physics. U.S. Geological Survey Professional Paper 422-I, Washington, DC.Google Scholar
Blench, T. (1951). Hydraulics of Sediment Bearing Canals and Rivers, Vol. 1. Evans Industries, Original from the University of Wisconsin, Madison; Digitized, August 10, 2007; Length, 260 pages.Google Scholar
Chang, H. H. (1980). Geometry of gravel streams. Journal of the Hydraulics Division, Vol. 106, No. 9, pp. 14431456.CrossRefGoogle Scholar
DuBoys, P. (1879). Le Rhone et les Rivieres a Lit Affouilable. Annales des Ponts et Chousses, Vol. 18, Series 5, pp. 141195.Google Scholar
Fukuoka, S. (2010). Determination method of river width and cross-section for harmonization between flood control and river environment (Japanese). Advances in River Engineering, pp. 5–10.Google Scholar
Huang, H. Q. (1996). Discussion of alluvial channel geometry theory and applications by Julien and Wargadalam. Journal of Hydraulic Engineering, Vol. 122, pp. 750751.CrossRefGoogle Scholar
Huang, H. Q. and Nanson, G. C. (1995). On a multivariate model of channel geometry. Proceedings of the XXVI Congress of the International Association for Hydraulic Research, Vol. 1, pp. 510515, Thames Telford.Google Scholar
Huang, H. Q. and Nanson, G. C. (1998). The influence of bank strength on channel geometry: an integrated analysis of some observations. Earth Surface Processes and Landforms, Vol. 24, pp. 865876.Google Scholar
Huang, H. Q. and Nanson, G. C. (2000). Hydraulic geometry and maximum flow efficiency as products of the principle of least action. Earth Surface Processes and Landforms, Vol. 25, pp. 116.3.0.CO;2-2>CrossRefGoogle Scholar
Huang, H. Q. and Warner, R. F. (1995). The multivariate controls of hydraulic geometry: A causal investigation in term of boundary shear distribution. Earth Surface Processes and Landforms, Vol. 15, pp. 115130.Google Scholar
Huang, H. Q., Nanson, G. C., and Fagar, S. D. (2002). Hydraulic geometry of straight alluvial channels and principle of least action. Journal of Hydraulic Research, Vol. 40, No. 2, pp. 153160.CrossRefGoogle Scholar
Julien, P. Y. and Wargadalam, J. (1995). Alluvial channel geometry theory and applications. Journal of Hydraulic Engineering, Vol. 121, pp. 312325.Google Scholar
Lacey, G. (1929). Stable channels in alluvium. Proceedings of the Institution of Civil Engineers, Vol. 229, pp. 1647.Google Scholar
Lacey, G. (1933). Uniform flow in alluvial rivers and canals. Proceedings of the Institution of Civil Engineers, Vol. 237, pp. 421423.Google Scholar
Lacey, G. (1946). A general theory of flow in alluvium. Proceedings of the Institution of Civil Engineers, Vol. 27, pp. 1647.CrossRefGoogle Scholar
Lacey, G. (1958). Flow in alluvial channels with sandy stable beds. Proceedings of the Institution of Civil Engineers, Vol. 9, Discussion 11, pp. 145164.Google Scholar
Leopold, L. B. and Maddock, T. (1953). The hydraulic geometry of stream channels and some physiographic implications. Geological Professional Paper, 252, U.S. Government Printing Office, Washington, DC.CrossRefGoogle Scholar
Nanson, G. C. and Huang, H. Q. (2017). Self-adjustment in rivers: Evidence for least action as the primary control of alluvial channel form and process. Earth Surface Processes and Landforms, Vol. 42, No. 4, pp. 575594.CrossRefGoogle Scholar
Ohara, N. and Yamatani, K. (2019). Theoretical stable hydraulic section based on the principle of least action. Scientific Reports, Vol. 9, 7957, https://doi.org/10.1038/s41598–019-44347-4.CrossRefGoogle ScholarPubMed
Rhoads, B. L. (1991). A continuously varying parameter model of downstream hydraulic geometry. Water Resources Research, Vol. 27, No. 8, pp. 1865-–1872.Google Scholar
Riley, W. F. and Sturges, L. D. (1993). Engineering Mechanics-Statics. John Wiley & Sons, New York.Google Scholar

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  • Principle of Least Action
  • Vijay P. Singh, Texas A & M University
  • Book: Handbook of Hydraulic Geometry
  • Online publication: 24 November 2022
  • Chapter DOI: https://doi.org/10.1017/9781009222136.018
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  • Principle of Least Action
  • Vijay P. Singh, Texas A & M University
  • Book: Handbook of Hydraulic Geometry
  • Online publication: 24 November 2022
  • Chapter DOI: https://doi.org/10.1017/9781009222136.018
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Principle of Least Action
  • Vijay P. Singh, Texas A & M University
  • Book: Handbook of Hydraulic Geometry
  • Online publication: 24 November 2022
  • Chapter DOI: https://doi.org/10.1017/9781009222136.018
Available formats
×