CHAPTER 3: BANKFULL CHARACTERISTICS OF RIVERS

1. CHAPTER 3: BANKFULL CHARACTERISTICS OF RIVERS Alluvial rivers construct their own channels and floodplains. Channels and floodplains co-evolve over time. Nameless Siberian stream and floodplain. Image courtesy A. Alabyan and A. Sidorchuk. Browns Gulch, Montana

2. THE CONCEPT OF BANKFULL DISCHARGE Let  denote river stage (water surface elevation) [L] and Q denote volume water discharge [L3/T]. In the case of rivers with floodplains,  tends to increase rapidly with increasing Q when all the flow is confined to the channel, but much less rapidly when the flow spills significantly onto the floodplain. The rollover in the curve defines bankfull discharge Qbf. Minnesota River and floodplain, USA, during the record flood of 1965

3. GRAVEL-BED AND SAND-BED RIVERS Rivers (or more specifically river reaches) can also be classified according to the characteristic size of their surface bed sediment, i.e median size Ds50 or geometric mean size Dsg. A river with a characteristic size between 0.0625 and 2 mm can be termed a sand-bed stream. Two such streams are shown below. Jamuna (Brahmaputra) River, Bangladesh. Image courtesy J. Imran. Fly River, Papua New Guinea.

4. GRAVEL-BED AND SAND-BED RIVERS A river with a characteristic surface size in excess of 16 mm can be termed a gravel-bed river. Here the term “gravel” is used loosely to encompass cobble- and boulder-bed streams as well. Three such streams are shown below. Genessee River, New York, USA. Raging River, Washington, USA. Rakaia River, New Zealand

5. GRAVEL-BED AND SAND-BED RIVERS A river with a characteristic surface size between 2 and 16 mm can be termed transitional in terms of grain size. Such streams are much less common than either sand-bed or gravel-bed streams, but can be found readily enough, particularly in basins that produce sediment from weathered granite. An example is shown to the right. Hii River, Japan. Image courtesy H. Takebayashi

6. Sand-bed Gravel-bed Transitional GRAVEL-BED AND SAND-BED RIVERS The diagram to the left shows the frequency of river reaches with various characteristic grain sizes within two sets, one from Alberta, Canada (Kellerhals et al., 1972) and the other from Japan (Yamamoto, 1994; Fujita et al., 1998). Note that most rivers can be classified as either gravel-bed or sand-bed. The basic data for the subsequent plots in this chapter are given in RTe-bookRivers.xls

7. PARAMETERS USED TO CHARACTERIZE BANKFULL CHANNEL GEOMETRY In addition to a bankfull discharge, a reach of an alluvial river with a floodplain also has a characteristic average bankfull channel width and average bankfull channel depth. The following parameters are used to characterize this geometry. Definitions: Qbf = bankfull discharge [L3/T] Bbf = bankfull width [L] Hbf = bankfull depth [L] S = bed slope [1] Ds50 = median surface grain size [L] n = kinematic viscosity of water [L2/T] R = (rs/r – 1) = sediment submerged specific gravity (~ 1.65 for natural sediment) [1] g = gravitational acceleration [L/T2]

8. DIMENSIONLESS PARAMETERS CHARACTERIZING CHANNEL BANKFULL GEOMETRY = dimensionless bankfull discharge = dimensionless bankfull depth = dimensionless bankfull width = bankfull Froude number (dimensionless) = (estimate of) bankfull Shields number (dimensionless) = bankfull Chezy resistance coefficient (dimensionless) = particle Reynolds number (surrogate for grain size: dimensionless)

9. INTERPRETATION OF SOME OF THE DIMENSIONLESS PARAMETERS Bankfull flow velocity Ubf = Qbf/(HbfBbf) Bankfull Froude number characterizes a ratio of momentum force to gravity force. When Froude number Fr < 1 the flow is subcritical, or tranquil: when Fr > 1 the flow is supercritical, or swift. Here where U and H are cross-sectionally-averaged flow velocity and depth, respectively. The relation can be rewritten as so that a high value of Czbf implies a low bed resistance. As explained in Chapter 5, for the case of steady, uniform (normal) flow, the bed shear stress b is given as b = gHS where H = depth. A dimensionless measure of the ability of the flow to mobilize sediment is the Shields number, * = b/(RgD). Here denotes an estimate of value of * for bankfull flow based on a surface median size for D. Since in most cases g = 9.81 m/s2, R  1.65 and   1x10-6 m2/s, Rep50 is a surrogate for median surface grain size ~ Ds503/2.

10. DIMENSIONLESS CHARACTERIZATION OF BANKFULL STREAM GEOMETRY While each river has its own unique characteristics, alluvial rivers show a considerable degree of commonality. This can be made apparent in terms of dimensionless plots of bankfull characteristics. This is illustrated here with several sets of data. Gravel-bed rivers with Ds50 (surface median size) ranging from 27 mm to 157.5 mm from three compendiums are used: Britain (Charlton et al., 1978), Alberta, Canada (Kellerhals et al., 1972) and Idaho, USA (Parker et al., 2003). In addition, a subset of sand-bed streams with Ds50 < 0.5 mm, including single-thread streams and multiple-thread streams, selected from the compendium of Church and Rood (1983) by Parker et al. (1998), are used. The bankfull characteristics of these streams are studied in the following slides. Transitional grain-size streams have been purposely excluded in order to illustrate the similarities and differences between sand-bed and gravel-bed streams. Two of the slides also include, however, data from Japan (Yamamoto, 1994; Fujita et al., 1998), which includes many transitional grain-size streams.

11. DIMENSIONLESS WIDTH VERSUS DIMENSIONLESS DISCHARGE Each of the two stream types plots in a consistent way. The Alberta gravel-bed streams are consistently a little wider than their British counterparts. This may reflect, e.g. differences in vegetation density. This plot, subsequent plots in this chapter and the basic data for them are given in RTe-bookRivers.xls

12. DIMENSIONLESS DEPTH VERSUS DIMENSIONLESS DISCHARGE Again, each of the two stream types plots in a consistent way.

13. BED SLOPE VERSUS DIMENSIONLESS DISCHARGE The relation for slope versus dimensionless bankfull discharge shows general consistency but much more scatter. This probably reflects the fact that much more time is required to change a river’s bed slope than its width or depth; indeed so much time that tectonics becomes a factor in the scatter.

14. BANKFULL FROUDE NUMBER VERSUS BED SLOPE Sand-bed and gravel-bed streams mesh together smoothly in this plot, but the sand-bed streams generally have lower bankfull Froude numbers Fr. All but one of the streams are in the subcritical range (Fr < 1) at bankfull flow. This does not mean that supercritical flow is dynamically impossible in alluvial streams. Rather, the sediment transport capacity is typically so high that alluvium cannot usually be supplied at a fast enough rate. Frbf

15. DIMENSIONLESS CHEZY FRICTION COEFFICIENT VERSUS SLOPE Again, the sand-bed and gravel-bed sets mesh together smoothly, but the resistance coefficient is generally larger in the sand-bed streams. This probably reflects the effect of dunes.

16. DIMENSIONLESS CHEZY FRICTION COEFFICIENT VERSUS DIMENSIONLESS DEPTH The sand-bed and gravel-bed sets plot in different regions, largely because in sand-bed streams resistance is more dependent on bedform characteristics.

17. BANKFULL SHIELDS NUMBER VERSUS DIMENSIONLESS DISCHARGE Gravel-bed streams maintain a bankfull Shields stress that is loosely about 0.05. Sand-bed streams maintain a bankfull Shields stress that is loosely about 1.9.

18. SOME REGRESSION RELATIONS FOR BANKFULL GEOMETRY The regression relations below are based on the same data as those in the previous slides of this chapter.

19. REVIEW FROM CHAPTER 2: MODES OF TRANSPORT OF SEDIMENT Bed material load is that part of the sediment load that exchanges with the bed (and thus contributes to morphodynamics). Wash load is transported through without exchange with the bed. In rivers, material finer than 0.0625 mm (silt and clay) is often approximated as wash load. Bed material load is further subdivided into bedload and suspended load. Bedload: sliding, rolling or saltating just above bed role of turbulence is indirect, ballistic trajectory Suspended load: feels direct dispersive effect of eddies may be wafted high into the water column

20. SHIELDS REGIME DIAGRAM The concepts in this diagram are explained more in Chapter 6. The thick solid line approximately divides the regimes of no motion versus motion (normally as bedload) of Ds50 of the surface material at bankfull flow. The thin solid line plays the same role in regard to significant suspension of the size Ds50 of the surface material.

21. SHIELDS REGIME DIAGRAM WITH DATA FOR GRAVEL-BED AND SAND-BED STREAMS The two stream types plot in very different places: sand-bed streams can normally easily suspend their dominant bed material at bankfull flow: gravel-bed streams normally cannot do so (but do, on the other hand, suspend sand).

22. SHIELDS REGIME DIAGRAM WITH DATA FOR STREAMS WITH VALUES OF D50 BETWEEN 0.5 mm AND 16 mm ADDED The extra data are for the Japanese streams of Yamamoto (1994): the discharge used is a characteristic flood flow that is probably close to bankfull flow, and for the gravel-bed streams, the characteristic D50 is based on a bulk bed material sample rather than a surface sample. The sand-bed Japanese streams plot with the other sand-bed streams; likewise with the gravel-bed streams. The transition between the two types is seen to be smooth, with a paucity of streams in the transitional range.

23. REFERENCES FOR CHAPTER 3 Charlton, F. G., Brown, P. M. and Benson, R. W. , 1978, The hydraulic geometry of some gravel rivers in Britain, Report INT 180, Hydraulics Research Station, Wallingford, England, 48 p. Church, M. and Rood, K., 1983, Catalogue of alluvial river data, Report, Dept, of Geography, University of British Columbia, Vancouver, B. C., Canada. Fujita, K., K. Yamamoto and Y. Akabori, 1998, Evolution mechanisms of the longitudinal bed profiles of major alluvial rivers in Japan and their implications for profile change prediction, Transactions, Japan Society of Civil Engineering, 600(II-44): 37–50 (in Japanese). Kellerhals, R., Neill, C. R. and Bray, D. I., 1972, Hydraulic and geomorphic characteristics of rivers in Alberta, River Engineering and Surface Hydrology Report, Research Council of Alberta, Canada, No. 72-1. Parker, G., Paola, C., Whipple, K. and Mohrig, D., 1998, Alluvial fans formed by channelized fluvial and sheet flow: theory, J. Hydraul. Engrg., 124(10), 1-11. Parker, G., Toro-Escobar, C. M., Ramey, M. and Beck, S., 2003, Effect Of Floodwater Extraction On Mountain Stream Morphology, J. Hydraul. Engrg., 129(11), 885-895. Yamamoto, K., 1994, The Study of Alluvial Rivers, Sankaidou (in Japanese).