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8 - Scaling Theory

Published online by Cambridge University Press:  24 November 2022

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

Empirical equations of downstream hydraulic geometry, entailing width, depth, velocity, and bed slope, can be derived using the scaling theory. The theory employs the momentum equation, a flow resistance formula, and continuity equation for gradually varied open channel flow. The scaling equations are expressed as power functions of water discharge and bed sediment size, and are applicable to alluvial, ice, and bedrock channels. These equations are valid for any value of water discharge as opposed to just mean or bank-full values that are used in empirical equations. This chapter discusses the use of scaling theory for the derivation of downstream hydraulic geometry. The scaling theory-based hydraulic geometry equations are also compared with those derived using the regime theory, threshold theory, and stability index theory, and the equations are found to be consistent.

Type
Chapter
Information
Handbook of Hydraulic Geometry
Theories and Advances
, pp. 245 - 260
Publisher: Cambridge University Press
Print publication year: 2022

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References

Ashmore, P. E. (1991). Channel morphology and bed load pulses in braided, gravel-bed streams. Geographical Annals, Vol. 73A, pp. 3752.Google Scholar
Ashmore, P. E. (2001). Braiding phenomena: Statics and kinetics. In: Gravel-Bed Rivers V, edited by Mosley, M. P., pp. 95114, New Zealand Hydrological Society, Wellington.Google Scholar
Bennett, J. P. (1978). One-dimensional surface water transport modeling. U.S. Geological Survey National Training Center, Video Series No. 2500, tapes 10–14, Denver, CO.Google Scholar
Bennett, J. P. and Nordin, C. F. (1977). Simulation of sediment transport and armoring. Hydrological Sciences Bulletin, Vol. 22, No. 4, pp. 555560.CrossRefGoogle Scholar
Bray, D. I. (1979). Estimating average velocity in gravel-bed rivers. Journal of Hydraulics Division, ASCE, Vol. 105, pp. 11031122.CrossRefGoogle Scholar
Davies, L. H. (1974). Problems posed by new town development with particular to Milton Keynes. Paper no. 2 in: Proceedings of Research Colloquium on Rainfall, Runoff and Surface Water Drainage of Urban Catchments, Department of Civil Engineering, Bristol University.Google Scholar
Griffiths, G. A. (1979). Rigid boundary flow resistance of gravel rivers. Ministry of Works Development, Christchurch, Water and Soil Division, Report WS 127, pp. 20.Google Scholar
Griffiths, G. A. (1980). Downstream hydraulic geometry of some New Zealand gravel bed rivers. Journal of Hydrology (N.Z.), Vol. 18., pp. 106108.Google Scholar
Griffiths, G. A. (1981). Stable-channel design in gravel bed rivers. Journal of Hydrology, Vol. 52, pp. 291308.CrossRefGoogle Scholar
Griffiths, G. A. (2003). Downstream hydraulic geometry and similitude. Water Resources Research, Vol. 39, No. 4, 1094, doi:10.1029/2002WR001488.Google Scholar
Guy, H. P., Simons, D. B., and Richardson, E. V. (1966). Summary of Alluvial Channel Data from Flume Experiments, 1956–61. US Government Printing Office.CrossRefGoogle Scholar
Henderson, F. M. (1966). Open Channel Flow. Macmillan, New York.Google Scholar
Kellerhals, H. (1967). Stable channel with gravel paved beds, Journal of Waterways and Harbors Division, ASCE, Vol. 93, pp. 6384.Google Scholar
Lacey, G. (1930). Stable channels in alluvium. Proceedings, Institution of Civil Engineers, Vol. 229, No. 1930, pp. 259292.Google Scholar
Laursen, E. M. (1958). Sediment-transport mechanics in stable-channel design. Transactions of American Society of Civil Engineers, Vol. 123, pp. 195203.CrossRefGoogle Scholar
Leopold, L. B., and Maddock, T. (1953). The hydraulic geometry of stream channels and some physiographic implications. U.S. Geological Survey Professional Paper 252, p. 57.Google Scholar
Little, W. C. and Mayer, P. G. (1976). Stability of channel beds by armoring. Journal of Hydraulics Division, ASCE, Vol. 102, pp. 16471661.CrossRefGoogle Scholar
Parker, G. (1979). Hydraulic geometry of active gravel rivers. Journal of Hydraulics Division, ASCE, Vol. 105, pp. 11851201.Google Scholar
Shields, A. (1936). Application of Similarity Principles and Turbulence Research to Bed-Load Movement. (Translated from German), California Institute of Technology, Pasadena.Google Scholar
Yalin, M. S. (1971). Theory of Hydraulic Models. pp. 266, Macmillan, New York.CrossRefGoogle Scholar
Yang, C. T. (1996). Sediment Transport: Theory and Practice. McGraw-Hill Book Company, New York.Google Scholar

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  • Scaling Theory
  • Vijay P. Singh, Texas A & M University
  • Book: Handbook of Hydraulic Geometry
  • Online publication: 24 November 2022
  • Chapter DOI: https://doi.org/10.1017/9781009222136.009
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  • Scaling Theory
  • Vijay P. Singh, Texas A & M University
  • Book: Handbook of Hydraulic Geometry
  • Online publication: 24 November 2022
  • Chapter DOI: https://doi.org/10.1017/9781009222136.009
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.

  • Scaling Theory
  • Vijay P. Singh, Texas A & M University
  • Book: Handbook of Hydraulic Geometry
  • Online publication: 24 November 2022
  • Chapter DOI: https://doi.org/10.1017/9781009222136.009
Available formats
×