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POTENTIAL EFFECTS OF TRANSLATORY WAVES ON ESTIMATION OF PEAK FLOWS By H. W. Hjalmarson,' Member, ASCE, and J. V. Phillips' I I--~-...- ABSTRACT: During the afternoon of August 19, 1971, an intense thunderstonn a few miles southwest of Wildeup, Arizona, produced one of the largest known flood peaks for a 49,2,square.km drainage basin, Initial computations of the peak. discharge assumed stable flow conditions and a four.section slope area measurement indicated that discharge was 2,082 m'ls, Recent findings based on free,surface instability characteristics at the site suggest that gravitational forces exceeded boundary retarding forces, and flow in the wide sand channel was unstable, Computations for roll or translatory waves indicate that waves crashed into the highway bridge at velocities of as much as 12.5 mls. The close agreement of free surface instability results, translatory wave computations, estimates of the steady flow on which the translatory waves traveled, and an eyewitne'ss account of the translatory waves suggest the total peak discharge could have been 2,742 m'ls or 32% greater than the published discharge. The occurrence of translatory waves in natural channels may be more common than pre- viously thought, and instability criteria should be considered for hydraulic analysis of flow in steep smooth channels. INTRODUCTION The purposes of this report are to (I) Reexamine the peak discharge for the flood of August 19, 1971, in Bronco Creek by using free surface instability criteria and translatory wave techniques; (2) discuss the regional implications and potential hazards of translatory waves in stream channels; and (3) share the practical experience associated with this investigation. Previous Investigations On the afternoon of August 19, 1971, an intense thunder- stonn produced an extreme floodflow on Bronco Creek near Wildeup, Arizona, A four,section slope area estimate of the peak discharge, made by the U,S. Geological Survey (USGS), yielded 2,082 mJls (Adridge 1972), This peak discharge, which is one of the largest known flood peaks in the world for a 49,2 km' drainage basin (Costa 1987), has been reex- amined by several investigators (H, W. Hjalmarson, hydrolo, gist, USGS, written communication, 1971; Carmody 1980; House and Pearthree 1995), Eyewitness Account The writers recently obtained a detailed account of the flood from Ernest Fancher, an employee of the Arizona Deparbnent of Transportation (ADOT) facility at Wildeup, Arizona, who observed floodwaves overtopping the U,S, Highway 93 bridge at Bronco Creek on the afternoon of August 19, 1971. Fanch, er's observations were briefly documented in an ADOT mem- orandum (E, I. lencsok, senior hydraulics designer, ADOT, written communication, 1971). Pancher's account (Ernest Fancher, oral communication, 1994, 1995) is summarized as follows: About every 4 to 5 minutes, a wave exJending bank to bank would move rapidly downstream. The largest waves were 4-5 ft. (1.22-1.52 m) high and would pound over the bridge, The largest waves seen 400-500 yards (366-457 'Consulting Hydro" HC75 Box 3558, Camp Verde, AZ B6322, 2Hydro. U.S. Geological Survey, WRD, 1545 W. University Drive, Tempe, AZ B52BL Note. Discussion open until November I, 1997. To extend the closing date one month, a written request must be filed with the ASeE Manager of Journals. The manuscript for this technical note was submitted for review and possible publication on January 17, 1995. This technical note is part of the Journal of Hydraulic Engineering, Vol. 123, No.6, June, 1997, @ASCE, ISSN 0733,9429/9710006-0571-05751$4,00 + $.50 per page. Technical Note No. 9968. m) upstream would take about 30-45 secoods to reach the bridge, The water passed uoder the bridge at a great veloc- ity until a wave would hit The waves occurred for about 2 hours, and wave heights decreased in size later in the flood, Fearing failure, the bridge was closed to traffic for about 2 hours until the waves ended, DESCRIPTION OF STUDY AREA Channelcharacteristics in Bronco Creek (Fig, I) specifically related to the fonnation and propagation of the pulsating trans- latory waves are (I) The sand channels are wide and flat with a general rectangular shape; (2) the channel roughness de- creases below the paleoflood sites; (3) the channel width-depth ratio changes from about 7-12 in the bedrock channels to about 15-50 in the sand channels; and (4) the grade changes from about 5% at the bedrock channels to a rather uniform 3% where the channel beds are sand, ANALYSIS OF REPORTED WAVES Free Surface Instability Flow stability techniques were applied at Bronco Creek to detennine if (I) Formation of waves in the slope area reach was possible; and (2) if formation of the waves over the re, ported duration of about 2 h was possible, Koloseus and Dav- idian (1966) defined conditions under which flow in open channels is classified as either stable or unstable. Where chan- nels are steep and smooth, gravitational effects can exceed boundary resistance, and stable flow can give way to unstable flow, Stability criteria were developed on the basis of a dynamic equation of motion for gradually varied flow and an equation of continuity, A complete description of the development of the stability criteria and associated assumptions is given by Koloseus and Davidian (1966), Flow is classified as unstable if the Froude number (F) is greater than the stable Froude number (Fs) and Fs = {["if ~ "- '"'1- "'"'^' .,"t (1) where f = dimensionless resistance coefficient; and equals JOURNAl. OF HYDRAULIC ENGINEERING I JUNE 1997/571