Wednesday 13 February 2013

Computed stream velocity in Carpathian headwater streams of the flysch belt


Four equations originally developed for high-gradient channels with steep slopes and high hydraulic roughness, were selected to test their suitability in local channels. Power relations of Rickenmann et al. (2006)-RIC
v = (1,93g0,5D1,5S0,5)/d90,
and Zimmermann (2010)-ZIM
v = 2,3g0,5D1,2d84-0,72S0,72,  
logarithmic relation of Lee and Fergusson (2002) with introduced roughness parameter by Jarrett (1990)-LFJ:
√(1/f) = 0,35R0,33.S-0,38,
and a classic Manning approach with divided roughness parameter in to the grain and form resistance (Rickenmann, 2005; Wong and Parker, 2006)-MAN
v = 1/ntotR0,67.S0,5; 1/nr = 23,2/6√d90; nr/ntot = 0,092S-0,35(D/d90)0,33.  
D means hydraulic depth (m), f is Darcy-Weisbach friction factor, g corresponds to 9.81m.s-2, nr is grain roughness parameter (grain resistance).

We taken bankfull parameters and grain-size distributions from a variety of local channels (n=93), where alluvial and semi-alluvial channel-reach morphologies were accounted (i.e., pool-riffles, rapids, step-rapids, step-pools, cascades and bedrock-cascades). Table 1 shows computed values during bankfull stage for some typical channel-reaches of the studied region. All evaluated channel-reaches are illustrated by Figure 1 together with normalised parameters of the channel roughness, channel gradient and stream velocity.

Table 1.
Stream
Morphology
S
[m/m]
D/d90
[m/m]
ZIM
[m.s-1]
RIC
[m.s-1]
LFJ
[m.s-1]
MAN
[m.s-1]
Libotínský potok
pool-riffle
0.03
2.69
0.67
1.35
0.54
0.90
Veřmiřovský potok
rapid
0.04
2.21
0.80
1.48
0.73
1.02
Velký Škaredý p.
rapid
0.06
3.67
2.01
3.60
0.95
1.55
Malá Ráztoka
step-rapid
0.06
1.26
0.79
0.95
0.65
0.74
Dížená
step-rapid
0.07
1.85
0.87
1.25
0.52
0.79
Vsetínská Bečva
step-pool
0.07
2.09
1.12
1.60
0.58
0.89
Rybský potok
step-pool
0.07
2.53
1.36
2.14
0.67
1.05
Kněhyňka
cascade
0.22
1.03
1.88
1.52
0.74
0.78
Velký Škaredý p.
cascade
0.32
3.11
6.42
7.29
1.16
1.81
Velký Škaredý p.
bedrock-casc.
0.53
2.99
7.14
8.21
1.09
1.79

Fig. 1

As Fig. 1 and Tab. 1 documented, we computed a wide range of stream velocities in local high gradient channels and so, there cannot be recommended a single equation valid for all evaluated cases. Power relationships (RIC and ZIM) highly overestimate velocities in steep narrow channels with relatively fine bed sediments. In world-wide literature, stream velocities in steep channels are usually lower than 2 m.s-1. Logarithmic relationship LFJ systematically underestimates velocities even on higher slopes >0.1 m/m. Combined Manning relatioship MAN calculates relatively uniform values for all reaches. Thus there is a possibility of underestimating on higher channel gradients and on the other hand, some overestimating on moderate slopes. Nevertheless, for stepped-bed morphologies with some lower roughness, this equation can be appropriate. For pool-riffles and rapids we recommend some of power-law equation. Probably relationship derived by Rickenmann RIC is more suitable due to the fact, that relationship by Zimmermann ZIM was tested only in a laboratory flume. We hope that one day we will do some direct measurement of stream velocities in local high-gradient channels to test and verify our conclusios.  

Jarrett, R.D., (1990): Hydrologic and hydraulic research in mountain rivers. Water Resoures Bulletin 26 (3), p. 419–429. 
Lee, A. J., Ferguson, R.I., (2002): Velocity and flow resistance in step-pool streams. Geomorphology 46, p. 5971.
Rickenmann, D., (2005): Geschiebetransport bei steilen Gefällen. Mitteilung 190 der Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie, ETH Zurich, p. 107119.
Rickenmann, D., Chiari, M., Friedl, K., (2006): SETRAC - A sediment routing model for steep torrent channels. In Ferreira, R., Leal, E.A.J., Cardoso, A. (Eds.): River Flow 2006, Vol. 1, p. 843–852. London, Taylor & Francis.
Wong, M., Parker, G., (2006): Reanalysis and correction of bed-load relation of Meyer-Peter and Müller using their own database. Journal of Hydraulic Engineering 132, 1159 doi:10.1061/(ASCE)0733-9429(2006)132:11(1159).
Zimmermann, A., (2010): Flow resistance in steep streams: An experimental study. Water Resources Research 46, W09536, doi:10.1029/2009WR007913.