|
<br />
<br />~. -.r!-_
<br />
<br />/"'>- .,.-= ---.
<br />.,' .fJ'OJtco.'.-r- C'~ej''-..,.~ ...
<br />.././ .:.-1...........-
<br />(. ---.J-.- ...
<br />) Ir-~v'~? ;0'"
<br />/: ..' ""W..~ 1'./ f
<br />0/ ) /-/ "'~.
<br />rf' . _r- l'
<br />) /" rf:r
<br />. J ~<.f
<br />'/,-'
<br />
<br />EXPLANATION
<br />
<br />WATERSHED BOUNDARY
<br />SUB-BASIN BOUNDARY
<br />
<br />A
<br />o
<br />a
<br />
<br />BEDROCK CHANNEL
<br />SAND CHANNEL
<br />SLOPE-AREA MEASUREt.ENT sITe
<br />CONVEYANCE-SLOPEsrrE
<br />PALEOFLOOO srrE (Hou.. and Pearthree 1994)
<br />
<br />r'
<br />
<br />il
<br />I
<br />o
<br />
<br />---
<br />
<br />2 MILES
<br />I
<br />
<br />I
<br />2 KILOMETERS
<br />
<br />FIG. 1. Bronco Creek Weterahed Showing Subbaaln Boundarlea, Locstlon 01 Slope-Area MBBSurement Site, Locatlona of Convey-
<br />anca-6lope and Paleoflood Sit... and Bedrock and Sand-Channel Reachaa
<br />
<br />8TlpVl
<br />
<br />where T = average boundary shear equals pgRS; p = mass
<br />density of the fluid; B = width of channel; D, = depth of flow
<br />measured nonnalto the channel floor; BID, = channel aspect
<br />ratio; VI = average velocity; g = acceleration of gravity; R =
<br />hydraulic radius or depth of flow for wide, shallow rectangular
<br />channels; and S = slope of the energy gradient. The Froude
<br />number is
<br />
<br />F = V/(gD, cos a)'a
<br />
<br />where a = channel slope in degrees.
<br />In general, for wide, flat, and steep channels, unstable flow
<br />conditions exist for F greater than about 1.6 (Koloseus and
<br />Davidian 1966). Equations (1), (2), and (3) were applied to
<br />cross sections 3 and 4 of the slope area measurement. Base
<br />discharges (flow preceding or beneath the waves, Q,) that
<br />ranged from 142 m'/s (arbitrarily selected) to 1,076 m'ls were
<br />used for free-surface instability computations to determine the
<br />possible duration of ~bIe ..tlpw,and roll wave development
<br />[Note: Manning's roughness coefficient (n) values selected for
<br />the original slope area were questioned at the time of the office
<br />review; therefore, n values of 0.030 and 0.040 are used for the
<br />analyses in this report]. Values of V, and D, were determined
<br />from base discharge computations in the slope area reach using
<br />the original survey data and the standard step method (Shear-
<br />man 1990). Computed Fs for all discharges and n values
<br />ranged from about 1.60 to 1.65. All average values of F/Fs
<br />for n = 0.040 are less than I, and flow is considered stable.
<br />Conversely, all average values of F/F s for n = 0.030 are
<br />greater than I, and flow is considered unstable. The data in-
<br />dicate that roll waves are possible at this site for flow rates as
<br />small as 142 mJ/s. Fancher's report of waves for about 2 h is
<br />supported by the computed unstable flow conditions for a wide
<br />range of discharge using n = 0.030.
<br />
<br />Wave Celerity
<br />
<br />The often used and rather elementary equation developed
<br />by Brater and King (1954) for wave velocity and celerity was
<br />
<br />5721 JOURNAL OF HYDRAULIC ENGINEERING 1 JUNE 1997
<br />
<br />(2)
<br />
<br />considered appropriate for the reported flood and channel con-
<br />ditions. The equation, which was developed for large abrupt
<br />waves in rectangular channels, was derived using momentum
<br />considerations where celerity was a function of force differ-
<br />ences associated with the weight of water at the vertical wave
<br />fronL The Brater and King formula for a frictionless positive
<br />surge wave is
<br />
<br />V. = c + V, or (4a)
<br />
<br />(3)
<br />
<br />V. = [(gD,IW,)(D, + D,)]1n + V, (4b)
<br />
<br />where V... = velocity of the wave, in m1s; c = celerity, in m1s;
<br />V, = velocity of water preceding the wave, in mls; g = accel-
<br />eration of gravity, in mls'; D, = depth of water preceding the
<br />wave, in m; and D, = depth of water following the wave front,
<br />in m.
<br />The static effect of the water weight difference at the wave
<br />front is considered; however. the effects of channel slope and
<br />roughness, atmospheric resistance and increased fluid viscosity
<br />and mass density from the transported suspended sediment are ~..#
<br />neglected. Other possible effects of transported sediment, su~
<br />as lowering of the Fs (frowbridge 1987) also are negleefed.
<br />
<br />Discharge Computations
<br />
<br />The method of determining the discharge of pulsating flow
<br />requires (1) Computation of the discharge in the overriding
<br />waves; and (2) computation of flow in the shallow depth, or
<br />overrun. part of flow (Rantz et aI. 1982). The sum of the two
<br />discharges is the total discharge. Thompson (1968) assumed
<br />steady uniform-flow conditions for the water preceding the
<br />waves (base discharge), and Manning's equation was used to
<br />compute V,. For analysis of the peak discharge for the Bronco
<br />Creek flood, a base discharge (Q,...J of 799 m'ls (Carmody
<br />1980; House and Pearthree 1994) was used with an n of 0.030
<br />and 0.040 for computations of assumed steady uniform flow
<br />preceding the wave. The computations to obtain values of D1
<br />and Vi for Qlmax were made using Manning's equation in the
<br />standard step method (Shearman 1990) with channel~ and sec-
<br />
|