angularitycreates an interlocking effect between grains (Komar and Li, 1986). The datacollected at Troutbeck agrees well with the hypothesis as in two out of threeof the size classes equant particles moved further than bladed ones. Although it isapparent size selective transport is occurring from the negative relationship inFigure 2, the scatter in the data could be caused by the presence of equal mobilityat high flows (Lisle, 1995). The competence of a flow increases with dischargedue to the enhanced shear stress, therefore in the most active conditions equalmobility can occur as the largest transported grain size converges with thatavailable on the bed surface (Mao and Lenzi, 2007). It is recognised that partialmobility exists under normal flow conditions, whereby individual particles moveover a static bed, yet complete surface mobilisation can occur at peakdischarges (Ferguson and Ashworth, 1992). In addition, once movement of a largeclast is provoked, finer particles which were trapped beneath are released,thus resulting in the movement of the entire surface layer (Paola and Seal,2010). However, in gravel bed rivers, equal mobility is reserved for highmagnitude, low frequency flow events which could be the cause of scatter inFigure 2. Part 2 – Table 1 displays values of shear stress estimated fromdifferent methods: reach averaged using the du Boys equation, the gradient of velocityprofiles and the approach recommended by Wilcock (1996) which uses the meanvelocity and a single value of bed roughness.
The estimate of shear stress fromthe du Boys equation is considerably larger than the other methods. Du Boys isa reach averaged measure which uses mean water surface slope, average waterdepth, gravity and water density to give an estimate of bed shear stress. Thesimplicity of the hydraulic variables used in the du Boys equation mean it iswidely applied (Ackerman and Hoover, 2001). However, in a gravel-bed river ofmixed grain sizes, hydraulic variables rarely remain spatially and temporallyconstant (Lisle et al. 2000). Instead, due to local grain size and roughnesselements, flow responds instantaneously and thus water depth alterssubstantially over the course of a reach (Afzalimehr and Rennie, 2009).
- Thesis Statement
- Structure and Outline
- Voice and Grammar
Thesensitivity analysis in Table 2 shows that by changing average reach depth ± 1 standard deviation from the mean, the shear stress value changes by ~50%. Therefore, calculations of section averaged shear stress providesubstantially different shear stress values to those calculated at local points,as the equation assumes that flow responds slowly to changes in roughness (Bironet al. 2004). In contrast, theother two methods give a local estimate of bed shear stress at a point (Robert,1997). The Wilcock method uses a single bed roughness observation and velocitymeasurement at 0.4 of the flow depth to calculate shear stress, whereas the standardapproach uses multiple depth averaged velocity measurements. The shear stressvalue estimated from the Wilcock method is considerably lower than thatcalculated from the standard approach. Although there is a time and logistical advantageto the Wilcock method, the collection of velocity measurements throughout thewater column reduces the error associated with a single velocity value (Baueret al.
1992). To analyse the impact of field measurement error on the Wilcockapproach, a sensitivity analysis was undertaken, displayed in Table 3. The analysisshows the reliance of the shear stress estimate on accurate velocity readings,as a 20% change in measured velocity alters the shear stress value by as muchas 44%.
Velocity has a much greater impact on the shear stress than water depthor D84, highlighting the propagation of error in the calculation of shearstress if the single velocity value employed is imprecise. Despite theaccuracy of shear stress estimates from the standard approach due to multiplevelocity values, the technique is limited due to the restricted range of conditionsit can be applied in (Biron et al. 1998). In order to provide precise estimatesof shear stress, the logarithmic profile needs to hold throughout the flowdepth (Petrie et al. 2010). However, in gravel bed rivers, flow is non-uniformowing to the large relative roughness elements which create form drag andturbulent eddies which dominate the flow (Dietrich and Whiting, 1989).
Theresult of the secondary circulation is a reduction in near-bed velocitiesaround large scale features (Westernbroek, 2006). In contrast to channels whichpossess steady, uniform, subcritical flow, the diverse conditions mean the velocityprofile is non-log linear and does not extend throughout the flow depth(Wilcock, 1988). The absence of a logarithmic vertical velocity profile meansthe equation deriving the shear stress value is only applicable in the near-bedregion; substantially below the free surface but above the influence of individualroughness elements (Smart, 1999). To understand the effect of includingvelocity measurements from a high proportion of the flow depth in thecalculation of shear stress, a sensitivity analysis was undertaken. Velocitymeasurements taken at water depths > 0.2 m and < 0.004 m were excludedfrom the velocity profiles.
The effect on the velocity profile can be seen inFigure 4. Including velocity measurements from the inner and outer regions markedlychanges the shear stress values calculated, thus the standard approach may containa substantial degree of error when calculated using velocity measurements fromthe full flow depth. Moreover,accessing velocity measurements for the near-bed region can prove problematicin the field as the majority of measuring devices are unable to executemeasurements in the vicinity of the bed (Sime et al.
2007). The lack ofmeasurements will substantially affect shear stress estimates, as the absenceof information is in the exact location where the log-law applies (Yu and Tan,2006). The difficulty in obtaining measurements is particularly problematic ina shallow river environment, as the majority of the water depth is dominated bythe deficiency of data (Stone and Hotchkiss, 2007). Hence, for this study,velocity measurements taken in Pod 5 of Troutbeck were used to calculate localshear stress, as the water depth was ~0.
5 m; thedeepest of the pods surveyed. However, the time taken to execute the verticalstack of points, in order to create a velocity profile, can impact the accuracyof the measurements as river discharge is constantly changing (Kim et al. 2000).Due to the fluctuating discharge, successive velocity measurements at differentelevations in the profile become uncorrelated and thus do not reflect values ofvelocity for a given set of conditions (Whiting and Dietrich, 1990).
Rates of bedloadtransport are often estimated by comparing bed shear stress to areference critical shear stress which represents the forcerequired to entrain a particle in the flow (Kirchner et al. 1990). Criticalshear stress is the threshold stress which once surpassed inflicts adequatelift or drag on a certain particle size to overcome the resisting forces and initiatemotion (Wilberg and Smith, 1987). Shields’ (1936) criterion is widely appliedin the calculation of critical shear stress, which uses gravity, sedimentdensity, particle size and a constant to estimate a value of critical shearstress (Hager and Oliveto, 2002). The constant summarises particle shape andarrangement, as well as flow properties (Buffington and Montgomery, 1997). AlthoughShields suggested a value of 0.06 for the constant, other experiments,including Gordon et al.
(2004), predicted a value as low as 0.04. Table 4displays the varying values of critical shear stress and water depth requiredto move particles of b-axis 8 mm to 256 mm, calculated using the valuessuggested.
The results show that there is a substantial difference between thetwo critical shear stress estimates for particles of the same size. The uncertaintycan be explained as Shields’ (1936) experiment was based on particles ofuniform size, shape and packing and therefore pivot angle and protrusion(Buffington, 1999). Thus, Shields’ identified criterion is based on a singlerepresentative grain size, namely the D50 (Mueller et al.2005). However, gravel bed rivers are highly variable, displaying a wide rangeof particle sizes which do not correspond to the median of the sediment (Hey,1979). Moreover, as discussed in Part 1, the effects of grain protrusion and differingpivot angles are prominent within gravel bed rivers (Powell, 1998).
Althoughthe simple linear relationship inferred by Shield is applicable for the D50 of sediment, which suggests critical shear stress increaseswith particle size, the theoretical idea is not valid in all settings (Behesthtiand Ataie-Ashitani, 2008). Instead, movement of bedload in gravel bed rivers isnot only a function of absolute particle size but it is also dependent on thepacking, pivot angle and relative grain sizes on the bed, as well as otherfactors not discussed in this report, such as channel curvature.