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Sinuosity (P) is a commonly used parameter to describethe degree of meandering in a stream. Sinuosity is defined as theratio of distance measured along the stream (stream length) todistance measured along the valley axis (valley length). Aperfectly straight stream has a sinuosity of unity, while a streamwith a sinuosity of 3 or more would have tortuous meanders.Meander wavelength (L) is the straight line repeating distance forthe meander waveform, as depicted in Figure 3.8, and is twice theinflection point spacing. The meander path length is the streamlength between inflection points. Meander amplitude (A) is thewidth of the meander bends measured perpendicular to the valleyor straight-line axis (Figure 3.8). The ratio of the amplitude tomeander wavelength is generally within the range of 0.5 to 1.5.Meander wavelength and amplitude are primarily dependent onthe water and sediment discharge, but are usually locally modifiedby spatial variation in the erodibility of the material in which thestream is formed. The effects of different bank materials areresponsible for the irregularities found in the alignment of naturalstreams. In rare cases where the material forming the banks ispractically homogeneous, meanders take a form that may beapproximated by a sine-generated curve with a uniform meanderwavelength. The meander belt is formed by and includes all thelocations historically held by a stream due to meanderdevelopment and migration. It should be noted that the width of themeander belt is usually greater than the meander amplitude and, inmany cases, may include all of the active floodplain.Figure 3.8 – Definition Sketchfor Stream Geometry (FISRWG1998)The radius of curvature (r c ) is the radius of the circledefining the centerline curvature of an individual bend measuredbetween the bend entrance and the bend exit (Figure 3.8). Thearc angle (θ) is the angle swept out by the radius of curvature.The radius of curvature to width ratio (r c /w) is a very useful30 Fundamentals of Fluvial Geomorphology and Stream Processes
parameter used in the description and comparison of meanderbehavior, and in particular, bank erosion rates. The radius ofcurvature is dependent on the same factors as the meanderwavelength and width. Meander bends generally develop a r c /w of1.5 to 4.5, with the majority of bends falling in the range of 2 to 3.Nanson and Hickin (1986) examined the influence of r c /w on bendmigration rate and reported that maximum bank erosion ratesoccurred when the stream acquired an r c /w of between 2 and 3.This finding has been supported by many empirical studies, forexample, Thorne (1991). Plots of erosion rate versus r c /w do,however, display wide scatter and Biedenharn et al. (1989)showed that part of this scatter could be explained by variations inthe erodibility of the outer bank material (Figure 3.9).Figure 3.9 – Average AnnualErosion Rate versus r/w forMeander Bends of the RedRiver – Open SymbolsRepresent Free, Alluvial Bendsand Closed Symbols,Constrained Bends (developedfrom diagrams by Biedenharn etal. 1989)River slope is one of the best indicators of the ability of theriver to do morphological work and, in general, rivers with steepslopes are much more active with respect to stream changesachieved through sediment movement, bed scour, bar building,and bank erosion. Slope can be defined in a number of ways,however, leading to inconsistency in the way slope is used torepresent the ability of the river to do morphological work. Ideally,the energy slope should be used when calculating stream power,but the data required are seldom available. In gaged streams, thewater surface slope may be calculated using stage readings atconsecutive gaging stations along the stream. However, manysmall streams are ungaged. In ungaged streams, the thalwegslope is often used to calculate stream power. The thalweg profilenot only provides a reasonable basis for calculation of streampower, but may aid in locating bed controls due to geologicFundamentals of Fluvial Geomorphology and Stream Processes 31
Page 6 and 7: materials. Also, the threshold mobi
Page 8 and 9: ank of a large river. From an engin
Page 10 and 11: eddies in a stream do not scale on
Page 12 and 13: aiding. Braid bars are sediment fea
Page 16 and 17: outcrops, other non-erodible materi
Page 18 and 19: continent (Inglis 1941, 1947, 1949)
Page 20 and 21: instances where the bankfull discha
Page 22 and 23: uses readily available mean daily f
Page 24 and 25: of flows. The results are plotted a
Page 26 and 27: Similarly, in regime theory the con
Page 28 and 29: 3.7 STREAM STABILITY ANDINSTABILITY
Page 30 and 31: It should be noted that the map coo
Page 32 and 33: and slope of the reach are not sign
Page 34 and 35: (a) Bed and Bank InstabilityFigure
Page 36 and 37: the downstream limit of the system
Page 38 and 39: dam, where degradation was expected
Page 40 and 41: Figure 3.13 - Channel PatternClassi
Page 42 and 43: definition of a graded stream in wh
Page 44 and 45: midwestern experience, while Rosgen
Page 46 and 47: Schumm et al. (1981, 1984) and thei
Page 48 and 49: ut at a much reduced rate. The sedi
Page 50 and 51: • integration of results into eng
Page 52: 68 Fundamentals of Fluvial Geomorph

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