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99 _""G . tvE)l.SlJREDWATERSlJRFACE 97 c;o,<.,PUTEO\IVl,TER SURfACE """ 1CCO 1500 HORIZONTAl D<STANCE(ft) 2lID FIGURE 5. Comparison of energy grade line and computed water-surface elevations with measured water-surface elevation~ at a discharge of about 1,200 cis in the right branch channel, RM 16.5, Yampa River. elevations and flow distributions that were close to the surveyed and gaged values. The chute channel was modeled assuming weir flow at the chute channel entrance; data from stream gaging of the chute chan- nel provided a cross-sectional shape for these calculations. As shown on the site location map (Fig- ure 2), the river downstream of the study reach narrows considerably and makes a sharp turn to the right. The ratio of radius of curvature to width for this bend is ap- proximately 3.2, based on measurements from the USGS Quadrangle map (Tanks Peak). Energy loss through the bend re- duces the local energy gradient at the bend entrance, creating a backwater condition in the upstream channel. The energy loss through the bend increases with increas- ing discharge, which causes the energy gradient at the bend entrance to decrease with increasing discharge. For purposes of verifying the model, it was assumed that the energy gradient at the bend entrance would be approximately 0.2% (the average bed slope of the river in this area and the approximate energy slope at the time of the 1991 survey) at flows less than about 1,200 cfs. To account for the increased en- ergy loss through the bend at higher dis- charges, the energy gradient at this loca- tion was reduced progressively from 0.2% at 1,200 cfs to 0.15% at 20,000 cfs. The change in energy gradient with discharge was approximated using the relationships between energy loss, bend geometry, and velocity discussed in Henderson (1966). The computed water-surface elevations at a discharge of 1,207 cfs using the above- 2SOO stated assumptions compared well with the measured values, with a maximum differ- ence of about 0.16 ft in the split flow reach around the bar (Figure 5). The computed elevations at the two most upstream cross sections were approximately 0.4 ft lower than the measured values. Review of the available held data did not reveal the cause of this discrepancy, but these cross sections are located in the pool upstream of the primary bar and are not signihcant in the following analyses. As a further check, the hydraulic model results showed a flow dis- tribution among the left, right, and chute channels that was nearly identical to the measured distribution. Model runs were made for discharges ranging from 500 to 20,000 cfs. The results indicated that the primary bar is entirely inundated at a discharge greater than 10,000 cfs, thereby eliminating the split-flow con- dition. Field observations of high-water marks during the site visit corroborated the model results. The 1991 peak discharge was about 9,700 cfs and it was evident that the highest elevations of the midchannel bar (Figure 3) had not been submerged during the 1991 runoff season. Because the analysis was primarily concerned with the hydraulic and incipient motion conditions in the split-flow channels, subsequent analyses concentrated on discharges up to 10,000 cfs. The hydraulic analysis is based on a one- dimensional solution to a multidimension- al hydraulic problem, and as such, local velocities and shear stress can vary signif- icantl y from the cross-section averages predicted by the HEC-2 model. However, the present analysis clearly dehnes the variations in hydraulic energy that occur over a range of discharges at various lo- cations at the spawning bar. Incipient Motion Analysis The critical particle size (Dc; particle size that is on the verge of motion) for the range of discharges modeled was estimated using Shields's (1936) relation: Ie = '*cbs - ')')D (1) where Ie is the critical shear stress, I*c is the dimensionless critical shear stress, ')', is the unit weight of sediment (-165 Ibl ft3), ')' is the unit weight of water (62.4 Ib/fe), M.D. Harvey et al. 121 I I~