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r, tion'geometry values from the original slope area measure- ment. The high water marks and cross sections of the channel from the original survey are assumed to define the crest of the wave that produced the peak discharge and the channel ge' ometry at that time, Wave heights were determined by sub, tracting the computed water surface elevations (D,) from the surveyed flood mark elevations (D,), Instantaneous discharge of the largest waves (Q._) was computed as the product of the cross-sectional area of the waves and the corresponding velocity (V._) using the equation by Brater and King (1954), For the average conditions at the cross sections and using a roughness coefficient of 0,030, the average wave height of 1.37 m [Table I, column (2)] is the same as the average height of the largest waves observed by Fancher, The computed wave velocity [Table I, column (6)] for these conditions, using the equation by Brater and King (1954), is also in close agreement with Fancher's observations. This close agreement suggests the total instantaneous peak discharge may have been 2,740 m'ls or 32% more than the published discharge of 2,082 m'ls [Table I, column (7)], An estimated hydrograph for Q, and an "envelope" hydro' graph for total instantaneous peak discharge were determined (Fig, 2), The wave envelope depicts the instantaneous wave discharge for approximately 30 translatory waves at 4-5,min intervals for about 2 h on the basis of Fancher's account, Nearly all of the runoff volume is depicted by the hydrograph for Q, because the wave envelope depicts only the instanta- neous discharge for approximately 30 waves, and total wave volume was estimated to be about I % of the total runoff, The hydrograph and wave envelope (Fig, 2) are intended to rep- resent only the general runoff and wave conditions for the flood as reported by Fancher and were developed from both discharge and flow instability computations, '1 I I I ANALYSIS Supercritical Flow and Translatory Waves Reports of pulsating waves in steep flood channels and lab- oratory flumes are fairly common and have been documented by Holmes (1936), Thompson (1968), Brock (1969), Foley and Vanoni (1977), and Kranenburg (1992), How common are supercritical flow and translatory waves in natural channels? McGee (1897), Glancy and Harmsen (1975), Belcher (1976), Phillips and Hjalmarson (1996), and Hjalmarson (1987) doc- umented eyewiiness accounts of possible translatory waves (supercritical flow) in natural channels, Perhaps the occurrence of pulsating flow in natural channels is more common than indicated because (I) The potential for observations has been small because of the sparse population in the areas where many steep wide channels are found; (2) the cause of walls of water in arid lands has been erroneously attributed to intra- event damming and breaching (Schick and Lekach 1989); and (3) the waves have not been clearly recognized by hydraulic engineers involved in the collection and analysis of flood-peak discharge data who have assumed that the flow was gradually varied and stable, For example, the observation of waves in the channel up' stream from U,S, Highway 93 bridge was mentioned to the original USGS survey crew immediately following the Bronco Creek flood but was not considered in the computation of peak discharge, Another example is the catastrophic flood of Sep- tember 14, 1974, in Eldorado Canyon, Nevada, which killed at least nine people and destroyed many homes, vehicles, and boats (Glancy and Harmsen 1975), The flood had a computed peak discharge of 2,152 m'ls, a drainage area of 53,3 kIn , and similar to the Bronco Creek flood, the highwater marks in the slope area reach may have been produced by translatory waves (Glancy and Harmsen 1975), Following are some statements by observers of flow in the steep sand channel of Eldorado Canyon: "," a 6-8 ft-high (1.83-2.44 m) approaching wall. . ." and ", . . initial wave followed by several wavelike surges. . ." McGee (1897) documents his eyewitness account of a sheet- flood wave on the western piedmont slopes of the Tortolita Mountains north of Tucson, Arizona. According to McGee, the floodwater spread beyond the confines of a channel at "race-horse speeds" with a wall of water 15 - 30 cm high, and within the flood, transverse waves formed breakers, The trans- verse waves may have been similar to the reflected waves reported by Thompson (1968) for wave development in su' percritical flow. The steep incised channels of some alluvial fans with slopes of about 3% or greater in the southwestern United Stales are possible sites for the formation of potentially hazardous waves. Wave Development The translatory waves in Bronco Creek may have been formed where the channel bed changes gradually from bedrock to sand (Fig, 1) because, according to Koloseus and Davidian (1966), the degree of flow stability is inversely proportional to the channel width-depth ratio and directly proportional to channel roughness, Peak discharge estimates at (I) The paleo- flood sites of 750 m'ls (House and Pearthree 1995); (2) the channel conveyance'slope sites of 1,082 m'ls (H. W. Hjal- TABLE 1. Results of Slope Ares snd Wsve Computstlonslor Flood 01 August, 19, 1971, In Bronco Cresk Total instantaneous Cross-section Wavs hslght Q,~ Vt",.1C QWfl'llllC Vwrnax- peak discharge number (m) (m'/s) (mls) (m'/s) (mls) (m'ls) (1) (2) (3) (4) (5) (6) (7) (a) n = 0,030 Average 3-4 10,06 2.739b Average 3-4 1.37 799 6,60 1,943 12,51 2,742' (b) n = 0.040 Average 3-4 7,64 2,082b Average 3-4 1.13 799 5,47 1,433 11.05 2,232' (c) Average of Ernest Fancher's observations 1.37 I I 11.33 Note: [Q....,., maximum base discharge; Vi....,.. mean velocity of the maximum base discharge; Q......,., instantaneous discharge of the largest waves; V..mu, average velocity of the largest waves. Dashes indicate no data. -Computed using (4) except for Fancher's observations. bComputed using slope area method. CComputed using translatory wave techniques. JOURNAL OF HYDRAULIC ENGINEERtNG I JUNE 1997/573