Flow resistance over a gravel bed: Its consequence on initial sediment movement

Abstract

The first part concerns itself with the friction factor of a gravel bed. Velocity distributions are measured in a gravel-bed flume having large slopes of 0.2<S_o (%)<2 and total water depths of 7<D(cm)<23. Two uniform gravel sizes of d_s=2.35 cm and d_s=1.35 cm are investigated. It is shown that : (i) the velocity distribution (see Fig.1) can be described by the logarithmic law, eqn (2) (see Fig.2a) in the inner region and by a parabolic law, eqn (4) (see Fig.2b) in the outer region; (ii) the friction velocities are reasonably equal to the ones computed from the energy slope; (iii) the position of the reference level, y_o, can be established. The flow-resistance relations, eqns (6) and (6a), were researched and rendered : (i) the numerical constants, Br (see Fig.3) and $\bar B$r, depend upon the relative roughness (see Fig.4); (ii) where 3 zones can be identified; (iii) zone 1 being for small relative roughness with $\bar B$r≈6.25, proposed by Keulegan (1938); (iv) zone 3 being for large relative roughness with $\bar B$r≈3.25, proposed by Graf (1984). Two independent laboratory experiments and one set of field data (see Fig.6) are used to demonstrate the validity of the proposed flow-resistance relation.

The second part deals with the consequence of the above-developed flow-resistance relation on the initiation of grain movement on the bed. The results for steep-sloped and gravel-bed channels do not seem to agree with the well-accepted Shields diagram (see Fig.8). The understanding of the hydrodynamics of the turbulent flow over rough surfaces, expressed with the flow resistance, eqn (6a), and an appropriate constant, $\bar B$r (see Fig.4), help to explain the deviation from the Shields diagram if relative roughness are of importance, i.e. : (d_s/D)>0.04. Data, now available in the literature, are used (see Fig.10) to present in a simple way for the determination of initial sediment movement.