|
<br />"...
<br />I "
<br />" \ ~ WAVE ENVELOPE
<br />, Y (0,.01+ OW)
<br />, \
<br />, \
<br />, \
<br />, Ow \
<br />, \
<br />, \
<br />, \
<br />, \
<br />, \
<br />, \
<br />, \
<br />, \
<br />, \
<br />, \
<br />, \
<br />
<br />2 3
<br />FLOW DURATION, IN HOURS
<br />FIG. 2. Estimated Hydrograp!ls for Gradually snd Rapidly Varlad Flow lor Bronco Crssk nasr Wlldsup, Arlzons; Wsve EnvelOpe De-
<br />picts Instantsnsous Dlschsrge for Approxlmlll8ly 30 1l'snsletory Wev.. et 4- to 5-MIn Intervels Overriding B..e Discharge on Basis 01
<br />Fancher's Report
<br />
<br />3,000
<br />
<br />~ 2,500
<br />~
<br />a:
<br />w
<br />Q.
<br />ll!
<br />~
<br />::Ii
<br />o
<br />ill
<br />::>
<br />(,)
<br />;!;
<br />
<br />2,000
<br />
<br />1,500
<br />
<br />ui 1,000
<br />Ii!
<br />c
<br />:z:
<br />fA
<br />is 500
<br />
<br />o
<br />o
<br />
<br />'1
<br />
<br />marson, hydrologist, USGS, written communication, 1971);
<br />and (3) at the slope area site indicate wave formation and
<br />growth in a downstream direction (Fig, I), Waves most likely
<br />were fanned and continued to propagate in the smoother wider
<br />sand channel reaches downstream from the boulder and bed-
<br />rock channels,
<br />
<br />Design Implications
<br />
<br />Translatory waves can develop in steep channels of super-
<br />critical slope and therefore are a concern to the designer of
<br />engineered structures on these channels, Should pulsating flow
<br />occur in a channel designed for stable flow, the channel ca,
<br />pacity may be inadequate at a discharge that is much smaller
<br />than the design flow, For example, the flood of July 9, 1988,
<br />was adequately conveyed through a highway culvert at Al-
<br />buquerque, New Mexico, until pulsating waves at least 1 m
<br />high crashed into the headwall and splashed onto the roadway
<br />and on passing automobiles (film on file at the Albuquerque
<br />Metropolitan Arroyo Flood Control Authority), Another ex-
<br />ample is the Tonopah Canal, part of the Central Arizona
<br />Project, has produced pulsating translatory waves that ex-
<br />ceeded design capacity for the channel. Holmes (1936) de-
<br />scribes an example of large translatory waves that decreased
<br />a channel's capacity to convey flow by a factor of 7-8 when
<br />compared to the theoretical capacity for stable flow compu-
<br />tations, Also, the U,S, Highway 93 bridge over Bronco Creek
<br />was not designed for unstable flow conditions (translatory
<br />waves); however, results presented in this note suggest waves
<br />are possible in the reach upstream from the bridge for flow
<br />rates as low as 142 m'/s, The design capacity of U,S, Highway
<br />93 bridge is 481 m'/s, As witnessed by Fancher, the base dis-
<br />charge was adequately conveyed through the bridge opening
<br />until the waves approached at high velocities and broke over
<br />the bridge,
<br />
<br />SUMMARY AND CONCLUSIONS
<br />
<br />Application of free-surface instability criteria developed by
<br />Koloseus and Davidian (1966) show that, at n = 0,030, roll
<br />
<br />574/ JOURNAL OF HYDRAULIC ENGINEERING / JUNE 1997
<br />
<br />,---
<br />
<br />0, TOTAL INSTANTANEOUS
<br />DISCHARGE
<br />01 BASE OISCHARGE FOR
<br />DURATION OF FLOW
<br />OW INSTANTANEOUS WAVE
<br />OISCHARGE
<br />
<br />NOTE: Volume of runoff __
<br />wI1h Ow Is .._ .. be &bout one
<br />percent of total \tOlume of runoff.
<br />0/,0, during mOlt of lIowdurodon,
<br />
<br />4
<br />
<br />5
<br />
<br />waves were possible for a wide range of discharge. The com-
<br />puted instantaneous peak discharge of 2,740 m'/s is comprised
<br />of Q,~. = 799 m'/s and Q.mu = 1,943 m'/s, The value of
<br />Q'mu is from estimates by Carmody (1980) and House and
<br />Pearthree (1995), The use of the standard step method, on the
<br />basis of Manning's equation, produced values of D, and V"
<br />The value of Q._ is obtained from the product of cross-
<br />section area and velocity of the largest waves compured using
<br />the equation by Brater and King (1954) for a large translatory
<br />wave, The results of these hydraulic computations, including
<br />the duration of the wave occurrences, the wave velocity, and
<br />the wave height are in close agreement with the observations
<br />of Ernest Fancher,
<br />Pulsating flow is a matter of concern in the design of en-
<br />gineered structures on steep channels. If potentially hazardous
<br />translatory waves occur at high stages in a channel designed
<br />for stable flow, the capacity of the channel may be inadequate,
<br />Roll waves and pulsating flow possibly are more common than
<br />previously thought and may have been overlooked in deter,
<br />mining peak-flow rates for some floods, Application of
<br />translatory wave teclmiques needs verification by additional
<br />experiments. observations. and research.
<br />
<br />ACKNOWLEDGMENTS
<br />
<br />This report is funded in part by the Flood Control District of Maricopa
<br />County. The writers also wish to thank Ernest Fancher, retired from
<br />ADOT. for his patience in allowing us to record his detailed eyewitness
<br />account of the flood.
<br />
<br />APPENDIX. REFERENCES
<br />
<br />Aldridge. B. N. (1972). "Investigation of floods from small drainage
<br />basins in Arizona." Proc., 21st Annu. Conj. on Roads and Streets.
<br />University of Arizona, Tucson. Ariz., 107-126.
<br />Belcher. J. (1976). "Ocotillo digs out-Flood leaves town battered but
<br />undefeated," Los Angeles Times, (Sept 12), 1.
<br />Brater, E. F" and King, H, W, (1954), Handbook of hydraulics, McGraw,
<br />Hill Book Co., Inc.. New York.
<br />Brock, R. B. (1969). "Development of roll-wave trains in open chan-
<br />nels," J, Hydr. Engrg" ASeE. 95(4),1401-1427,
<br />
|