FLOOD10252 - Laserfiche WebLink

Home Browse Search

,"-- . :1:;4 GRANT: CRITICAL FLOW CONSTRAINS FLOW HYDRAULICS however, most of their reported values are for storms with low bed load transport rates, where the large boulders that consti- tuted the median grain sizes were not transported. Under these flow conditions the bed may not be adjusting, During storms when the largest boulders were moved. Froude numbers ranged from 1.0 to 1.1. Critical flow therefore appears to be a limiting condition for many mobile bed channels. . The analysis presented is based on consideration of thresh- old channels, that is, those that are near the incipient motion threshold, An upper bound for the relation between Froude numhcr Bnd slope can be derived from an analysis of mobile~ bed channels, on the basis of Parker's [1990] work, Field data from gravel-bed channels suggest that maximum shear stresses in natural mobile-bed channels rarely exceed critical shear stress for the median grain size (D,o) by more than 20-50%, averaging around 40% for gravel-bed streams [Parker, 1982], Then from (4) we have . dS l.4T" = [ (;J - 1] D50 U:\c of the medJ!1n grain $izc require" n Nllghtly ditfcr~nt for- mulation of the resistance equation. Parker {1990] uses a Man- ning-Strickler-type resistance equation rather than the Keule- gan relation given in (3), -"- _ (tt.) 1/6 . - 8,1 k v , where ks is a roughness height given by ks = ADso and A is typically near 6 (G. Parker, written communication, 1995), Combining (2), (7), (8), and (9) gives Fr = XS1/3 where _ (1.4G<,) 113 X - 8,1 ^ and G is the submerged specific gravity of sediment (1.65), With the aforementioned values for A = 6 and 'T:r = 0.03 for active gravel-bed streams, Fr = 3,85S'" This curve shows the same general trend of increasing Froude numher with slope and provides an envelope curve for most of the plotted field data (Figure 4), Recent work by G. Parker (written communication, 1995) demonstrales that for sand-bed streams freely forming braid anahranches and antidunes, shear stresses are typically 20 times <ro For these channels the resistance equation (8) is modified: v .. = 4,8(dID5o)"II V ( 13) Then. by the same analysis and assuming that T~r = 0.06 for sand-hed channels, Fr = 5.1850.11 (14) (7) This equation predicts Froude numbers for active-bed sand channels that are slightly higher than those for gravel channels (Figure 4). Because all of the curves shown in Figure 4 assume steadv quasi-equilibrium flow conditions and rely on empirical esii~ mates of critical parameters, they should be viewed as defining the lower and upper ranges of Froude numbers for competent flows at a given slope. The assumptions and data used to derive these parameters become suspect at slopes much in excess of 0,04, Both the threshold and mohile,hed curves completely break do~n when slopes exceed 0.08 or /110 Rnd Iledlmellt tr"ns~ port undergoes a transition toward dcbris flow [Takahashi, 1987J. The most salient feature of both data and curves pre. sented in Figure 4 is that they all define a similar trend of increasing Froude number with slope and predict flow condi- tions near or slightly above critical for both threshold and active-bed. high-gradient streams. As slope increases above OJJI, flow is constrained to lie near critical for two reasons: firs~, the incipient motion threshold is associated with higher, ncar-critical Froudc numbers; and second, bed form and free surface hydraulic interactions at high Froude numbers will tcnd to produce the oscillatory flow pattern previmudy dc~ scrlhed, restricting the now regime to near-critical. The data clearly show that Froude numbers much in cxcess of t.O are uncommon in mobile-bed channels hut that critical flow itself is common in strcams with gradients above 0.01 (Figure 4). (8) Evidence for Critical Flow in Other Channel Types Although the tendency for streams to adjust channel bed forms to maintain critical flow at competent discharges is most readily illustrated in sand-bed streams. the same phenomenon occurs in many other coarse-bed, high-gradient streams. Most workers consider transverse ribs in gravel.bed channels to he analogous to anti dunes. forming by a similar process of bed deformation and hydraulic-jump development at critical flow [Boothroyd, 1972; G"stavson, 1974; Shaw alld Kellerlwls, 1977; Kosrer, 1978J, Allen [1983J gives an alternative explanation of ribs forming downstream of hydraulic jumps and creating crit- ical overfall weirs; his model also relics on flow oscillating longitudinally around critical. Braided, gravel.bed rivers with slopes in excess of 0.0 I tcnd to maintain critical now in each of their braids over a range of discharges [Fahnestock, 19()3; Sch"mm alld Khan, 1972; Boothroyd alld Ashley, 1975; Ergell- zinger, 1987}. In fact. the pictures and descriptions of upper regime flow in gravel outwash streams provided by Fahnestock are virtually identical to the descriptions of the Oregon beach channels [Fahnestock, 1963, Figurcs 27 and 28}. Step pools are the dominant bed form in boulder-bed. mountain streams [Whittaker alld iaeggi, 1982; Chill, 1989; Grant er ai" 1990; Ergenzillger, 1992; Abrahams et a/" 1995; de long, t 995]. Flume experiments demonstrate that steps form when the Proude number approaches 1.0 and 1"0 barely exceeds 'Tcr for the maximum grain sizes; step spacing varies with the wavelength of standing waves; and pools are scoured down- stream of steps by hydraulic jumps (Figure 5) [lV11illakcr and iaeggi, 1982; Ashida et ai"~ 1984; Grallt alld Miw)'ama, 19911, In step-pool channels the narrow range of discharge values under which steps form, as well as the short time period during which those conditions typically occur. tends to restrict opportunity for repeated cycles of formation and destruction of stcps; in- stcad. steps represcnt disequilibrium bcd forms, preservcd as (9) (10) (11) (12)