FLOOD06873

• County: Statewide
• Basin: Statewide
• Title: Hydraulic Engineering volume 1
• Date: 1/1/1994
• Prepared By: American Society of Civil Engineers
• Floodplain - Doc Type: Educational/Technical/Reference Information

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At-A-Site Mountain River Flow Resistance Variation

James C Bathurst1

Abstract

At-a-site variation in flow resistance is examined in the light of
observations of an S-shaped velocity profile at relative submerg~n('es (dIDI',4)
reater than 1. Factors controlling the development of the p~orlle (slop~ ~nd
~ed material size distribution) are found also to arr~t ~he rcsls!an~e. VRnat~on
hut available data are insuffICient to enahle the vanallo~s. for md~vldu~1 SI1~S
to be collapsed into one general relatio~ship. T!'e .famlllar sem~loganthmlc
relationship is found to overr.stimate resistance slgmficantly at high flows.

Introduction

Relatively tittle research has been carried out into t~e now resi~tance
of mountain rivers. characterized by boulder bed matena,l. s~opes 10 the
. I e 05 eN and raf.os of deplh to bed male"al sIze generally
approxlma e rang .. .,'7(' d' .
less than 10 and frequently as low as 1. In particular, flood flow con ItlO~S
which are of most engineering interest) are poorly r.epresented ~y I e
~vailable field data and the applicability of empirically d,enved ~ow resistance
relationships to high flows must therefore be uncertam. 11115 ?aper tak.es
advanta e of the recent advance in understanding of ~hc vertical .veloc~tv
profile i~ mountain rivers to reassess the form of the r~slstance. relat~onshll~
The approach taken is to consider separate at-a-slte relationships an
investigate the means by which they may he cona~sed in!o ,8 single fOf1:U~~~
Com ared with the more traditional method of Simply flttmg a ~UIVC t
ense:ble of data for different sites and flows, this approach provld,es grc~~r
opportunity to incorporate the understanding provided by the vel~IlY pro :~r
research, to account for flow resista~ce pr~esses and to Improve
applicability of Ihe resislanee relalionsh.p al h.gh nows.

~p;i~;i;~i"R-~search Officer. Water ~eso~rce Systems Research Unil.
Department of Civil Engineering. Umverslty of Newcastle upon Tyne.
Newcastle upon Tyne, NEI 7RU, UK

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FLOW RESISTANCE VARIATION

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S-Shaned Vclocilv Profile

Field measurements in the last decade have shown the velocity profile
in mountain rivers to differ subst,antially froUl the familiar semilogarithmic
form (in whkh velocity varies with the logarithm of distancr from the bed).
Tbe main reason is that, in mountain rivers, a significant proportion of the
flow occurs between the larger boulders, i.e, below the surface defining the
overall lops of Ihe bed material. Al low nows all Ihe now is Ihus
characterized, relative submergence is less than 1 and velocities are relatively
low. As Ihe boulders are snbmerged, however, the nnimpeded now above the
boulder tops develops a "skimming" regime with high velocities. A two-zone
velocily profile Ihen forms. laking on an S-shape (e.g., Marchand .1 aI., 1984;
Bathurst, 1988). Assumption of a semilogarithmic profile in such conditions
is likely to underestimate the trut' mean velocity.

Some characteristics of the velocity profile in mountain streams have
been invesligated Iheorelically (e.g., Aguirre-Pe and fuentes, 1990; Wiberg
and Smilh, 1991) bnllhe precise delerminanls of Ihe S-shape have yet 10 he
clarified, However. two limiting conditions may be defined. first, the bed
material should have a notu,"iform size distribution, since only thus is the
physieal spaee provided fot lhe developmenl of the lower now zone belween
Ihe larger boulders. The S-shaped profile is nol observed over uniform
material, at least in flume flows (Balhurst. 1992). Second, neither flow l.one,
of the S-shape should be signifieantly larger Ihan the olher and Ihus domin.le
the profile. This suggests that as relative submergences rise above about 4.
the profile should be increasingly dominated by a semilogarithmic variation
ahove Ihe boulder lops. Limiled field data (Balhursl, 1988) suggesl also Iha.,
the steeper the slope, the lower is the relative submergence at which the S.
shape is apparent.

Flow Resistance Factors and Data

The close relationship between velocity and flow resislance suggests
Ihallhe factors which eonlrollhe s..shaped velocity profile should also affccl
the resistance law, These factors are bed material size distribution, relative
submergence and channel slope, Their effect is studied in fig, I, using
exisling data, by plolting Ihe resislance fnnelion (S/f)" againsl the logarithm
of relative submergence (dIDR~)' where / = the DarcyM Weisbaeh resislal1ce
coefficient; d = mean depth (little different from hydraulic radius in the flows
considered); and DK.4 = Ihe particle size for which 84% of the bed material is
riner, 'The importance of the 84-percentile size of the bed material as the
dominant length scale defining the velocity profile and flow resistance in
mountain rivers bas been observed through theoretical developments (Wiberg
and Smith, 1991) and f,OOl field measnremenlS (Balhursl, 1985).

The format of Fig.. I is chosen 10 illustrate the differences in observed