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20 - Minimum Energy Dissipation and Maximum Entropy Theory

Published online by Cambridge University Press:  24 November 2022

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

This chapter employs the theory comprising the principle of maximum entropy (POME) and the principle of minimum energy dissipation or its simplified minimum stream power for deriving hydraulic geometry relations. The theory leads to four families of downstream hydraulic geometry relations and eleven families of at-a-station hydraulic geometry relations. The principle of minimum energy dissipation rate states that the spatial variation of the stream power of a channel for a given discharge is accomplished by the spatial variation in channel form (flow depth and channel width) and hydraulic variables, including energy slope, flow velocity, and friction.

Keywords

Principle of maximum entropyweighting factordownsteam hydraulic geomtryminimum stream powerhydraulic geometry relationschannel characteritics
Type
Chapter
Information
Handbook of Hydraulic Geometry
Theories and Advances
 , pp. 491 - 509
Publisher: Cambridge University Press
Print publication year: 2022

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References

Cheema, M. N., Marino, M. A., and DeVries, J. J. (1997). Stable width of an alluvial channel. Journal of Irrigation & Drainage Engineering, Vol. 123, No. 1, pp. 55–61.CrossRefGoogle Scholar
Colby, B. R. (1961). The effect of depth of flow on discharge of bed material. U.S. Geological Survey Water Supply Paper 1498-D, Washington, DC.Google Scholar
Deng, Z. and Zhang, K. (1994). Morphologic equations based on the principle of maximum entropy. International Journal of Sedimentaion Research, Vol. 9, No. 1, pp. 31–46.Google Scholar
Jaynes, E. T. (1957). Information theory and statistical mechanics, I. Physical Review, Vol. 106, pp. 620–630.CrossRefGoogle Scholar
Knighton, A. D. (1974). Variation in width–discharge relation and some implications for hydraulic geometry. Geological Society of America Bulletin, Vol. 85, pp. 1069–1076.2.0.CO;2>CrossRefGoogle Scholar
Langbein, W. B. (1964). Geometry of river channels. Journal of Hydraulics Division, ASCE, Vol. 90, No. HY2, pp. 301–311.Google Scholar
Leopold, L. B. and Maddock, T. J. (1953). Hydraulic geometry of stream channels and some physiographic implications. U.S. Geol. Survey Prof. Paper 252, pp. 55, Washington, DC.Google Scholar
Leopold, L. B. and Wolman, L. B. (1957). River channel patterns: braided, meandering and straight, U.S. Geol. Survey Professional Paper 282-B, U.S. Government Printing Office, Washington, DC.Google Scholar
Maddock, T. (1969). The behavior of straight open channels with movable beds. U.S. Geological Survey Professional Paper 622-A, Washington, DC.Google Scholar
Park, C. C. (1977). World-wide variations in hydraulic geometry exponents of stream channels: An analysis and some observations. Journal of Hydrology, Vol. 33, pp. 133–146.CrossRefGoogle Scholar
Rhodes, D. D. (1977). The b-f-m diagram: Graphical representation and interpretation of at-a-station hydraulic geometry. American Journal of Science, Vol. 277, pp. 73–96.Google Scholar
Riley, S. J. (1978). The role of minimum variance theory in defining the regime characteristics of the lower Namoi-Gwydir basin. Water Resources Bulletin, Vol. 14, pp. 1–11.Google Scholar
Schumm, S. A. (1960). The shape of alluvial channels in relation to sediment type. U.S. Geological Survey Professional Paper 352B, pp. 17–30, Washington, DC.Google Scholar
Schumm, S. A. (1968). River adjustment to altered hydrologic regime-Murrumbridgee River and Paleo channels, Australia. U.S. Geological Survey Professional Paper 598, Washington, DC.Google Scholar
Stall, J. B. and Fok, Y.-S. (1968). Hydraulic geometry of Illinois streams. University of Illinois Water Resources Center, Research Report No. 15, pp. 47, Urbana.Google Scholar
Williams, G. P. (1967). Flume experiments on the transport of a coarse sand, U.S. Geological Survey Professional Paper 562-B, Washington, DC.Google Scholar
Williams, G. P. (1978). Hydraulic geometry of river cross-sections-Theory of minimum variance. U.S. Geological Survey Professional Paper 1029, Washington, DC.Google Scholar
Wolman, M. G. (1955). The natural channel of Brandywine Creek, Pennsylvania. U.S. Geological Survey Professional Paper 271, Washington, DC.Google Scholar
Yang, C. T. (1972). Unit stream power and sediment transport. Journal of Hydraulics Division, ASCE, Vol. 98, No. HY10, pp. 1805–1826.Google Scholar
Yang, C. T. (1986). Dynamic adjustment of rivers. Proceedings of the 3rd International Symposium on River Sedimentation, Jackson, MS, pp. 118–132.Google Scholar
Yang, C. T. (1996), Sediment Transport Theory and Practice, McGraw-Hill Comp., Inc., New York.Google Scholar

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