At-a-station hydraulic geometry relations, 1: Theoretical development

Hydrological Processes

Volumn 22, Issue 2, 2008, Pages 189-215

  Singh, Vijay P ^a   Zhang, L ^a  

^a Texas A and M University   (United States)

Author keywords

Energy dissipation rate; Exponents; Hydraulic geometry; Principle of maximum entropy; Resistance equations; Stream power; Theory of minimum variance; Tractive force theory; Weighting factors

Indexed keywords

BOUNDARY CONDITIONS; DISCHARGE (FLUID MECHANICS); FLOW VELOCITY; FRICTION; RIVERS;

HYDRAULIC GEOMETRY; WEIGHTING FACTOR;

HYDRAULICS;

BOUNDARY CONDITIONS; DISCHARGE (FLUID MECHANICS); FLOW VELOCITY; FRICTION; HYDRAULICS; RIVERS;

BOUNDARY CONDITION; CHANNEL HYDRAULICS; DISCHARGE; ENERGY DISSIPATION; FLOW VELOCITY; GEOMETRY; MAXIMUM ENTROPY ANALYSIS; RIVER CHANNEL; STREAMFLOW; TEMPORAL VARIATION; THEORETICAL STUDY;

EID: 38549108647     PISSN: 08856087     EISSN: 10991085     Source Type: Journal    
DOI: 10.1002/hyp.6411     Document Type: Article

References (57)

1. Allen PM, Arnold JG, Byars BW. 1994. Downstream channel geometry for use of in planning-level models. Water Resources Bulletin 30: 663-671.
2. Blench T. 1952. Regime theory for self-formed sediment hearing channels. Transactions, American Society of Civil Engineers 117: 383-408.
3. Bray RD. 1982. Regime equations for gravel-bed rivers. In Gravel-Bed Rivers, Hey RD, Bathurst JC, Thorne C (eds). John Wiley: New York; 517-544.
4. Brebner A, Wilson KC. 1967. Derivation of the regime equations from relationships for pressurized flow by use of the principle of energy-degradation rate. Proceedings, Institution of Civil Engineers 36: 47-62.
5. Chang HH. 1980. Geometry of gravel stream. Journal of the Hydraulics Division, ASCE 106: 1443-1456.
6. Chang HH. 1988. Fluvial Processes in River Engineering. Wiley: New York.
7. Cheema MN, Marino MA, DeVries JJ. 1997. Stable width of an alluvial channel. Journal of Irrigation and Drainage Engineering 123: 55-61.
8. Colby BR. 1961. The effect of depth of flow on discharge of bed material. United Staes, Geological Survey, Water Supply Paper 1498-D.
9. Davies TRH, Sutherland AJ. 1983. Extrernal hypotheses for river behavior. Water Resources Research 19: 141-148.
10. Deng Z, Zhang K. 1994. Morphologic equations based on the principle of maximum entropy. International Journal of Sediment Research 9: 31-46.
11. Dou GR. 1964. Hydraulic geometry of plain alluvial rivers and tidal river mouth. Journal of Hydraulic Engineering (2): 1-13 (in Chinese).
12. Huang HQ, Nanson GC. 2000. Hydraulic geometry and maximum flow efficiency as products of the principle of least action. Earth Surface Processes and Landforms 25: 1-16.
13. Jaynes ET. 1957. Information theory and statistical mechanics, I. Physical Review 106: 620-630.
14. Judd HE, Peterson DF. 1969. Hydraulics of large bed element channels. Report No. PRWG 17-6, Utah Water Resources Research Laboratory: Logan, Utah.
15. Knighton AD. 1974. Variation in width-discharge relation and some implications for hydraulic geometry. Geological Society of America Bulletin 85: 1069-1076.
16. Knighton AD. 1977. Alternative derivation of the minimum variance hypothesis. Geological Society of America Bulletin 83: 3813-3822.
17. Lane EW. 1955. Design of stable canals. Transactions of the American Society of Civil Engineers 120: 1234-1260.
18. Langbein WB. 1964. Geometry of river channels. Journal of the Hydraulics Division, ASCE 90: 301-311.
19. Leopold LH, Langbein WB. 1962. The concept of entropy in landscape evolution. United States, Geological Survey, Professional Papers 500-A.
20. Leopold LB, Maddock TJ. 1953. Hydraulic geometry of stream channels and some physiographic implications. United States, Geological Survey, Professional Papers 252.
21. Leopold LB, Miller JP. 1956. Ephemeral streams-hydraulic factors and their relation to the drainage net. United States, Geological Survey, Professional Papers 282-A.
22. Lewis LA. 1966. The relations of hydrology and geomorphology in a humid tropical stream basin, the Rio Grande de Manati, Puerto Rico. Dissertation Abstracts 26: 7255.
23. Li RM. 1975. Mathematical modeling of response from small watershed. PhD dissertation, Colorado State University, Fort Collins, CO (unpublished).
24. Maddock T. 1969. The behavior of straight open channels with movable beds. United States, Geological Survey, Professional Papers 622-A.
25. Merigliano MF. 1997. Hydraulic geometry and stream channel behavior: an uncertain link. Journal of the American Water Resources Association 33: 1327-1336.
26. Myrick RM, Leopold LB. 1963. Hydraulic geometry of a small tidal estuary. United States, Geological Survey, Professional Papers 422-B.
27. Nizery A, Braudeau G. 1955. Discussion of 'Design of stable channels,' by E.W. Lane. Transactions of the American Society of Civil Engineers 120: 1266-1269.
28. Park CC. 1977. World-wide variations in hydraulic geometry exponents of stream channels: an analysis and some observations. Journal of Hydrology 33: 133-146.
29. Ramette M. 1980. A theoretical approach on fluvial processes. In Proceedings of International Symposium on River Sedimentation, Theme No. 3, Beijing, China: C16-1-C-16-22.
30. Rhodes DD. 1977. The b- f -m diagram: graphical representation and interpretation of at-a-station hydraulic geometry. American Journal of Science 277: 73-96.
31. Rhodes DD. 1978. World wide variations in hydraulic geometry exponents of stream channels: an analysis and some observations - comments. Journal of Hydrology 33: 133-146.
32. Richards KS. 1973. Hydraulic geometry and channel roughness-a nonlinear system. American Journal of Science 273: 877-896.
33. Richards KS. 1976. Complex width-discharge relations in natural river sections. Geological Society of America Bulletin 87: 199-206.
34. Riley SJ. 1975. The channel shape-grain size relation in eastern Australia and some paleohydrologic implications. Sedimentary Geology 14: 253-258.
35. Riley SJ. 1978. The role of minimum variance theory in defining the regime characteristics of the lower Namoi-Gwydir basin. Water Resources Bulletin 14: 1-11.
36. Rodriguez-Iturbe I, Rinaldo A, Rigon R, Bras RL, Marani A, Ijjasz-Vasquez EJ. 1992. Energy dissipation, runoff production and the three dimensional structure of river basins. Water Resources Research 28: 1095-1103.
37. Schumm SA. 1960. The shape of alluvial channels in relation to sediment type. United States, Geological Survey, Professional Papers 352B: 17-30.
38. Schumm SA. 1968. River adjustment to altered hydrologic regime - Murrumbridgee River and paleo channels, Australia. United States, Geological Survey, Professional Papers 598.
39. Singh VP, Yang CT, Deng ZQ. 2003a. Downstream hydraulic geometry relations: 1. Theoretical development. Water Resources Research 39(12): SWC2-1-SWC2-15.
40. Singh VP, Yang CT, Deng ZQ. 2003b. Downstream hydraulic geometry relations: 1. Calibration and testing. Water Resources Research 39(12): SWC3-1-SWC3-10.
41. Smith TR. 1974. A derivation of the hydraulic geometry of steady-state channels from conservation principles and sediment transport laws. Journal of Geology 82: 98-104.
42. Stall JB, Fok Y-S. 1968. Hydraulic geometry of Illinois streams. University of Illinois Water Resources Center, Research Report No. 15, Urbana-Champaign, Illinois.
43. Stall JB, Yang CT. 1970. Hydraulic geometry of 12 selected stream systems of the United States. University of Illinois Water Resources Research Center, Research Report No. 32, Urbana-Champaign, Illinois.
44. Stebbings J. 1963. The shape of self-formed model alluvial channels. Proceedings of the Institution of Civil Engineers, London 25: 485-510.
45. Virmani JK. 1973. The relationship between channel forming flows and the cross-section shape, slope, and bed materials in large bed element streams. PhD dissertation, Utah State University, Logan, UT (unpublished).
46. White WR, Bettess R, Paris E. 1982. Analytical approach to river regime. Journal of the Hydraulics Division, Proceedings of ASCE, Vol. 108, No. HY10; 1179-1193.
47. Williams GP. 1967. Flume expenments on the transport of a coarse sand. United States, Geological Survey, Professional Papers 562-B.
48. Williams GP. 1978. Hydraulic geometry of river cross-sections - theory of minimum variance. United States, Geological Survey, Professional Papers 1029.
49. Wolman MG. 1955. The natural channel of Brandywine Creek, Pennsylvania. United States, Geological Survey, Professional Papers 271.
50. Wolman MG, Brush LM. 1961. Factors controlling the size and shape of stream channels in coarse noncohesive sands. United States, Geological Survey, Professional Papers 282-G: 183-210.
51. Yalin MS, Da Silva AMF. 1997. On the computation of equilibrium channels in cohesionless alluvium. Journal of Hydroscience and Hydraulic Engineering 15(2): 1-13.
52. Yalin MS, Da Silva AMF. 1999. Regime channels in cohesionless alluvium, Journal of Hydraulic Research 37: 725-742.
53. Yang CT. 1972. Unit stream power and sediment transport. Journal of the Hydraulic Division, ASCE 98: 1805-1826.
54. Yang CT. 1976. Minimum unit stream power and fluvial hydraulics. Journal of the Hydraulics Division, ASCE 102: 919-934.
55. Yang CT. 1986. Dynamic adjustment of rivers, In Proceedings, 3rd International Symposium on River Sedimentation, Jackson, MS; 118-132.
56. Yang CT, Song CCS. 1986. Theory of minimum energy and energy dissipation rate. In Encyclopedia of Fluid Mechanics, Volume 1: Flow Phenomena and Measurement, Cheremisinoff NP (ed.). Gulf Publishing Company: Houston, TX; 353-399.
57. Yang CT, Song CC, Woldenberg MT. 1981. Hydraulic geometry and minimum rate of energy dissipation. Water Resources Research 17: 877-896.