FLOOD10252

• County: Statewide
• Basin: Statewide
• Title: Critical Flow Constrains Flow Hydraulics in Mobile-Bed Streams: A New Hypothesis
• Date: 2/1/1997
• Prepared For: Corvallis Ooregon
• Prepared By: USFWS
• Floodplain - Doc Type: Educational/Technical/Reference Information

904

CHANSON: COMMENTARY

F1_A.xJs

" dI'" RunTr2 4
(Po) 1.75 Fr = 1.25
3.50 d,jW = 0.2116
.. 1.5
..
3.00 . Q
i .. 1.25
250 . 1'''"'.-1
a ~ ..
.' ----l0-
a , OShear(1lW",O,2S)
2,00 .. OShear(71W",rUj
.. ...,Vdc (7JW=l1 OS4)
. a 0.75
].50 A<I"'C(1IW=O_2~)
a lJ.,V,f((7Jw..,n5)
a 0.5
].00 - a
a a a
. a a
0.50 0.25
.
. a C a
......----.----.---,-!I~~ .
000 0
IJ7 13' 14' 143 '" 147 14' 151 153 !l/de
Fl _b.xls

" did, Runrr2 I
,Po) 1.75 Fr= US
.. d/W=O.286
35 ..
i 1.5
..
. .
i .. 1.25
a .. ~-_.-..
2.5 ! .. .Shcar(,JW=l1,0461
OShc:lr ('!W:fI 25)
a .. OShcar(71W=O.5)
~
~ a AJI<lc(,^V=O.OJIi)
. 0.75 A<.Vdc{7.I'N"O.25)
a
1.5 lJ.dldc(,JW=O.51
------------- -
C 0,5
. . C c
a a 0.25
0,5 a
. a
. .
0 0
144 146 148 150 152 ]54 156 158 </d,

Figure 1. Bed shear stress along an undular hydraulic jump, (a) Flow conditions: Fr = 1,25, dJW =
0,286, W ~ 0,25 m (Run TI2_ 4), (b) Flow conditions: Fr = 1.35, dJW = 0,286, W = 0,25 m (Run
TT2_1),

function of the dimensionless distance x/dc. where x is the
.- distance from the channel intake and d(. is the critical flow
depth. On the same graph, the dimensionless flow depth elide
is shown also.
The discussers' data show large fluctuations of bed shear
~tress in the crosswise and longitudinal directions. Typically,
the bed shear is minimum below the wave crests and maximum
underneath the wave troughs. The results are similar to the
findings of lma; and Nakagawa [1992]. .
The results have direct implications to natural mobile-hed
channels. Considering a flat movahle-bed stream, an undular
flow might take place during a flood event or in an estuary
during a period of the tide. Below the free-surface undulations,
the movahle hed hecomes suhjected to an nonuniform bound-
ary shear stress distrihution (Figure 1), and, as a result, erosion
may take place underneath the wave troughs while accretion
occurs hclow the wave crests. Altogether the conditions are
Ll\'nrahlc for the development of standing-wave bed forms (in
phase with the free-surface standing waves).

Note further that the boundary shear stress is consistently
smaller near the wall (hlack squares in Figure I) than on the
channel centerline (white squares in Figure 1). Hence sedi-
ment motion is likely to be more intense near the channel
centerline than next to the banks.

4, Discussion

Gran/'s [1997) hypothesis and the corollary that "Hssumplinn
of critical flow would essentially repl<lce the standard flow
rcsist<lnce equations" might not he an ultimate m:hicvcmcnt.
Even if the limiting state of rnobile.bed flows is critical How,
can the flow conditions he predicted ,-lccurately?
The disclIsser docs not think so. Indeed the present disclIs-
sion has highlighted some aspects of lhe cOOlrlexily of undular
flows. Figure I highlights that the houndary shear stress distri-
hution along undular How (in a fixed-hed cllilnnel) is affc<.:teu
by large changes in hoth the lateral and longitudinal Jirt.'clion....
In Figure 1 the bed shear stresses fluctuate hy 1 order of