Author(s): R. Fernandez Luque; R. Van Beek

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Abstract: Results are presented of a series of experiments in which were measured: the mean critical bed shear stress at SHIELDS' grain-movement condition and at the initiation of non-ceasing scour, the rate of bedload transport, the average particle velocity, the rate of deposition, and the average length of individual steps of saltating bed-load particles, in water, as a function of the time-mean bed shear stress. These experiments were performed in a closed rectangular flow channel at different slopes of the bed surface and using five different bed materials (two sands, gravel, magnetite and walnut grains). Comparing the threshold drag acting at different downward slopes of the bed surface (0°, 12°, 18° and 22°) a surprisingly large critical-drag angle of 47° was found. The initiation of non-ceasing scour of a loose granular bed was studied experimentally behind a consolidated bed of the same material as the loose bed. The corresponding instantaneous threshold drag was about three times larger than the threshold drag acting at SHIELDS' grain movement condition. The rate of bed-load transport measured as a function of the mean bed-shear stress satisfies a generalised MEYER-PETER and MULLER formula (1948), also at various downward slopes of the bed surface, as investigated up to 22°. The rate of particle deposition was found to be proportional to the rate of bed-load transport, and the average length of individual particle steps was found to be a constant. This implies that the probability of a bed-load particle being deposited when striking the bed surface is independent of the flow rate within the experimental range. This result contradicts EINSTEIN'S theory of bed-load transport (1950). Close examination of the motion of saltating bed-load particles revealed that these particles are transported almost in suspension for the greater part of their trajectory. The average transport velocity of the suspended particles was found to be equal to the average fluid velocity calculated for a turbulent flow without a bed load, at about three particle diameters above the bed surface, minus a constant. The constant was proportional to the critical shear velocity at SHIELDS' grain-movement condition. This can be explained by considering that the turbulent shear flow must exert a lift force on the suspended particles that is practically equal to their submerged weight. Combining the MEYER-PETER and MULLER formula for the rate of bed-load transport and the abovementioned expression for the average transport velocity of the bed-load particles shows that the areal bed-load concentration increases linearly with increasing bed-shear stress. This contradicts KALINSKE'S theory (1947). Calculation of the average reduction in fluid shear at the bed surface due to the bed load, using empirical relations for the transfer of momentum of bed-load particles to the bed surface by intergranular collisions and for the areal bed-load concentration, reveals that at low transport rates this reduction is very small. The critical shear stress required to erode the topmost grains of the bed surface must therefore increase with increasing bed shear stress. It was also found that the average reduction in fluid shear due to the bed load increases so rapidly with increasing bed-shear stress that a higher transport rates the remaining fluid shear will nowhere exceed the threshold drag corresponding to the initiation of “non-ceasing“ scour.

DOI: https://doi.org/10.1080/00221687609499677

Year: 1976