Book contents
- Handbook of Hydraulic Geometry
- Handbook of Hydraulic Geometry
- Copyright page
- Dedication
- Contents
- Preface
- Acknowledgments
- 1Introduction
- 2Governing Equations
- 3Regime Theory
- 4Leopold–Maddock (LM) Theory
- 5Theory of Minimum Variance
- 6Dimensional Principles
- 7Hydrodynamic Theory
- 8Scaling Theory
- 9Tractive Force Theory
- 10Thermodynamic Theory
- 11Similarity Principle
- 12Channel Mobility Theory
- 13Maximum Sediment Discharge and Froude Number Hypothesis
- 14Principle of Minimum Froude Number
- 15Hypothesis of Maximum Friction Factor
- 16Maximum Flow Efficiency Hypothesis
- 17Principle of Least Action
- 18Theory of Minimum Energy Dissipation Rate
- 19Entropy Theory
- 20Minimum Energy Dissipation and Maximum Entropy Theory
- 21Theory of Stream Power
- 22Regional Hydraulic Geometry
- Index
- References
7 - Hydrodynamic Theory
Published online by Cambridge University Press: 24 November 2022
Book contents
- Handbook of Hydraulic Geometry
- Handbook of Hydraulic Geometry
- Copyright page
- Dedication
- Contents
- Preface
- Acknowledgments
- 1Introduction
- 2Governing Equations
- 3Regime Theory
- 4Leopold–Maddock (LM) Theory
- 5Theory of Minimum Variance
- 6Dimensional Principles
- 7Hydrodynamic Theory
- 8Scaling Theory
- 9Tractive Force Theory
- 10Thermodynamic Theory
- 11Similarity Principle
- 12Channel Mobility Theory
- 13Maximum Sediment Discharge and Froude Number Hypothesis
- 14Principle of Minimum Froude Number
- 15Hypothesis of Maximum Friction Factor
- 16Maximum Flow Efficiency Hypothesis
- 17Principle of Least Action
- 18Theory of Minimum Energy Dissipation Rate
- 19Entropy Theory
- 20Minimum Energy Dissipation and Maximum Entropy Theory
- 21Theory of Stream Power
- 22Regional Hydraulic Geometry
- Index
- References
Summary
Several hydrodynamic theories have been employed for deriving downstream hydraulic geometry relations of width, depth, velocity, and slope in terms of flow discharge. Five theories, the Smith theory, the Julien-Wargadalam (JW) theory, the Parker theory, the Griffiths theory, and the Ackers theory, are discussed in this chapter. These theories employ different forms of the continuity equation, friction equation, and transport equations. The Smith hydrodynamic theory also uses a morphological relation, whereas the JW theory uses an angle between transversal and downstream shear stress components, and the Parker theory uses a depth function.
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- Handbook of Hydraulic GeometryTheories and Advances, pp. 210 - 244Publisher: Cambridge University PressPrint publication year: 2022
References
Ackers, P. (1964). Experiments on small streams in alluvium. Journal of the Hydraulics Division, Proc. ASCE, Vol. 90, No. HY4, pp. 1-37.CrossRefGoogle Scholar
Afzalimehr, H., Abdolhosseini, M., and Singh, V. P. (2010). Hydraulic geometry relations for stable channel design. Journal of Hydrologic Engineering, Vol. 15, No. 10, pp. 859–864.CrossRefGoogle Scholar
Bagnold, R. A. (1956). The flow of cohesionless grains in fluids. Philosophical Transactions, Royal Society of London, Series A, Vol. 249, No. 964, pp. 235–297.Google Scholar
Bray, D. L. (1973). Regime relations for Alberta gravel bed river. In: Fluvial Processes and Sedimentation, Proceedings of Hydrology Symposium held at University for Alberta, Edmonton, Thorn Press, Limited, Ottawa.Google Scholar
Chang, H. H. (1980). Geometry of gravel stream. Journal of the Hydraulics Division, ASCE, Vol. 106, No HY9, pp. 1443–1456.Google Scholar
Chang, H. H. (1988). Fluvial Processes in River Engineering. John Wiley & Sons, New York.Google Scholar
Charlton, F. G., Brown, P. M., and Benson, R. W. (1978). The hydraulic geometry of some gravel rivers in Britain. Report IT 180, Hydraulic Research Station, Wallingford.Google Scholar
Davies, T. R. H. and Sutherland, A. J. (1983). Extremal hypotheses for river behavior. Water Resources Research, Vol. 19, No.1, pp. 141–148.CrossRefGoogle Scholar
Dou, G. R. (1964). Hydraulic geometry of plain alluvial rivers and tidal river mouth. Journal of Hydraulic Engineering (in Chinese), No. 2, pp. 1–13.Google Scholar
Einstein, H. A. (1942). Formulas for transportation of bed-load. Transactions, ASCE, Vol. 107, pp. 561–575.Google Scholar
Einstein, H. A. and Chien, N. (1954). Similarity of distorted river models with unstable beds. Proceedings, ASCE, Vol. 80, No. 566, p. 21.Google Scholar
Engelund, F. and Hansen, E. (1967). A Monograph of Sediment Transport in Alluvial Streams. Copenhagen, Teknisk Forlag, 62 p. 62.Google Scholar
Ferguson, R. I. (1986). Hydraulic and hydraulic geometry. Progress in Physical Geography, Vol. 0, pp. 1–31.Google Scholar
Griffiths, G. A. (1979). Recent sedimentation history of the Waimakariri River. Journal of Hydrology (New Zealand), Vol. 18, No. 1, pp. 6–28.Google Scholar
Griffiths, G. A. (1980). Hydraulic geometry relationships of some New Zealand gravel bed rivers. Journal of Hydrology (New Zealand), Vol. 19, No. 2, pp. 106–118.Google Scholar
Griffiths, G. A. (1981). Stable channel design in gravel bed rivers. Journal of Hydrology, Vol. 52, pp. 291–396.CrossRefGoogle Scholar
Hager, W. H. (1996). Discussion of “Alluvial channel geometry: theory and applications,” by Julien, P. Y. and Wargadalam, J.. Journal of Hydraulic Engineering, Vol. 122, No. 12, p. 750. AGoogle Scholar
Hey, R. D. (1979). Dynamic process-response Julien del of river channel development. Earth Surface Processes, Vol. 4, pp. 59-–72.Google Scholar
Hey, R. D. and Thorne, C. R. (1986). Stable channels with gravel beds. Journal of Hydraulic Engineering, Vol. 112, No. 6, pp. 671–689.CrossRefGoogle Scholar
Huang, H. Q. (1996). Discussion of “Alluvial channel geometry: theory and applications,” by Julien, P. Y. and Wargadalam, J.. Journal of Hydraulic Engineering, Vol. 122, No. 12, pp. 750–751.Google Scholar
Huang, H. Q. and Warner, R. F. (1995). The multivariate control of hydraulic geometry: a causal investigation in terms of boundary shear distribution. Earth Surface Processes and Landforms, Vol. 20, No. 2, pp. 115–130.CrossRefGoogle Scholar
Inglis, C. C. (1946). Meanders and their bearing in river training. Maritime Paper No. 7, Institution of Civil Engineers, London.Google Scholar
Julien, P. Y. (1988). Downstream Hydraulic Geometry of Noncohesive Alluvial Channels. International Conference on River Regime, John Wiley & Sons, New York, pp. 9–18.Google Scholar
Julien, P. Y. (2014). Downstream hydraulic geometry of alluvial rivers. Proceedings of a Symposium on Sediment Dynamics from the Summit to the Sea, held in New Orleans, December 11–14, IAHS Publication 367, pp. 3–11.Google Scholar
Julien, P. Y. and Wargadalam, J. (1995). Alluvial channel geometry: Theory and applications. Journal of Hydraulic Engineering, Vol. 121, No. 4, pp. 312–325.CrossRefGoogle Scholar
Kalinske, A. A. (1947). Movement of sediment as bed load in rivers. Transactions, American Geophysical Union, Vol. 28, pp. 615–620.Google Scholar
Kellerhals, R. (1967). Stable channels with gravel-paved beds. Journal of the Waterways and Harbors Division, ASCE, Vol. 93, No. WW1, pp. 63–84.Google Scholar
Keulegan, G. H. (1938). Laws of turbulent flow in open channels. Gaithersburg, MD: National Bureau of Standards, Vol. 21, pp. 707–741Google Scholar
Lacey, G. (1957–1958). Flow in alluvial channels with sandy mobile beds. Proceedings, Institution of Civil Engineers, Vol. 9, pp. 145–164, London.Google Scholar
Lane, E. W., Lin, P. N. and Liu, H. K. (1959). The most efficient stable channel for comparatively clean water in non-cohesive material. Report CER59HKLS, Colorado State University, Fort Collins.Google Scholar
Langbein, W. B. (1964). Geometry of river channels. Journal of the Hydraulics Division, ASCE, Vol. 90, No. HY2, pp. 301–311.Google Scholar
Lee, J.-S. and Julien, P. Y. (2006). Downstream hydraulic geometry of alluvial channels. Journal of Hydraulic Engineering, Vol. 132, No. 12, pp. 1347–1352.CrossRefGoogle Scholar
Leopold, L. B. and Maddock, T. J. (1953). Hydraulic geometry of stream channels and some physiographic implications. U. S. Geological Survey Professional Paper 252, p. 55.Google Scholar
Leopold, L. B. and Wolman, M. G. (1957). River channel patterns: braided, meandering and straight. Geological Survey Professional Paper 282-B, pp. 38–85, U.S. Geological Survey, Washington, DC.Google Scholar
Li, R. M., Simons, D. B., and Stevens, M. A. (1976). Morphology of stable streams in small watersheds. Journal of the Hydraulics Division, ASCE, Vol. 102, No. HY8, pp. 1101–1117.CrossRefGoogle Scholar
Mussetter, R. A. (1989). Dynamics of mountain streams. Ph.D. dissertation, Department of Civil Engineering, Colorado State University, Fort Collins.Google Scholar
Parker, G. (1978a). Self-formed rivers with stable banks and mobile bed: Part 1. The sand-silt river. Journal of Fluid Mechanics, Vol. 89, pp. 109–125.Google Scholar
Parker, G. (1978b). Self-formed rivers with stable banks and mobile bed: Part 2. The gravel river. Journal of Fluid Mechanics, Vol. 89, pp. 127–146.Google Scholar
Parker, G. (1979). Hydraulic geometry of active gravel rivers. Journal of the Hydraulics Division, ASCE, Vol. 105, pp. 1185–1201.CrossRefGoogle Scholar
Parker, G., Wilcock, P. R., Paola, C., Dietrich, W. E., and Pitlick, J. (2007). Physical basis for quasi-universal relations describing bankfull hydraulic geometry of single-thread gravel rivers. Journal of Geophysical Research, Vol. 112, F04005, pp. 1–21.Google Scholar
Rozovskii, I. L. (1961). Flow of Water in Bends of Open Channels. Translated by Prushansky, Y., Israel Program for Scientific Translation, Jerusalem, Israel.Google Scholar
Schumm, S. A. (1960). The shape of alluvial channels in relation to sediment type. Professional Paper 352-B, Geological survey, U.S. Department of Interior, Washington, DC.CrossRefGoogle Scholar
Schumm, S. A. and Litchy, R. W. (1964). Time, space and causality in geomorphology. American Journal of Science, Vol. 263, pp. 110–119.Google Scholar
Shin, Y. H. and Julien, P. Y. (2010). Changes in hydraulic geometry of the Hwang River below the Hapheon re-regulation dam, South Korea. International Journal of River Basin Management, Vol. 8, No. 2, pp. 139–150.CrossRefGoogle Scholar
Simons, D. B. and Albertson, M. L. (1960). Uniform water conveyance in alluvial material. Journal of the Hydraulics Division, ASCE, Vol. 86, No. HY5, Proc. Paper 2484, pp. 33–71.Google Scholar
Smith, T. E. (1974). A derivation of the hydraulic geometry of steady-state channels from conservation principles and sediment transport laws. Journal of Geology, Vol. 82, pp. 98–104.Google Scholar
Smith, T. E. and Bretherton, F. P. (1972). Stability and the conservation of mass in drainage basin evolutaion. Water Resources Research, Vol. 8, No. 6, pp. 1506–1524.CrossRefGoogle Scholar
Wargadalam, J. (1993). Hydraulic geometry equations of alluvial channels. Ph.D. dissertation, Colorado State University, Fort Collins.Google Scholar
White, W. R., Bettes, R., and Wang, S. Q. (1986). A study on river regime. Hydraulics Research Station, Wallingford.Google Scholar
White, W. R., Milli, H., and Crabbe, A. D. (1973). Sediment transport: An appraisal of available methods. Hydraulics Research Station, Wallingford.Google Scholar
Williams, G. P. (1978). Hydraulic geometry of river cross-sections- Theory of minimum variance. Professional paper 1029, U.S. Geological Survey, Washington, DC.CrossRefGoogle Scholar
Yang, C. T. (1976). Minimum unit stream power and fluvial hydraulics. Journal of the Hydraulic Division, ASCE, Vol. 102, No. HY7, pp. 919–934.Google Scholar
Yang, C. T. (1984). Unit stream power for gravel. Journal of Hydraulic Engineering, ASCE, Vol. 110, No. 12, pp. 1783–1797.Google Scholar
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