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 = (1,93g^0,5D^1,5S^0,5)/d₉₀,

and Zimmermann (2010)-ZIM: 

v = 2,3g^0,5D^1,2d₈₄^-0,72S^0,72,  

logarithmic relation of Lee and Fergusson (2002) with introduced roughness parameter by Jarrett (1990)-LFJ:

√(1/f) = 0,35R^0,33.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/n_totR^0,67.S^0,5; 1/n_r = 23,2/⁶√d₉₀; n_r/n_tot = 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, n_r 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. 59–71.

Rickenmann, D., (2005): Geschiebetransport bei steilen Gefällen. Mitteilung 190 der Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie, ETH Zurich, p. 107–119.

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.