Estimation of flow resistance in gravel‐bedded rivers: A physical explanation of the multiplier of roughness length

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Abstract
The need to estimate velocity and discharge indirectly in gravel‐bedded rivers is a commonly‐encountered problem. Semilogarithmic friction equations are used to estimate mean velocity using a friction factor obtained from depth and grain size information. Although such equations have a semi‐theoretical basis, in natural gravel‐bed channels, an empirical constant (6.8 or 3.5) has to be introduced to scale‐up the characteristic grain size (D50 or D84) to represent the effective roughness length. In this paper, two contrasting approaches are used to suggest that the multiplier of characteristic grain size is attributable to the effect of small‐scale form resistance, reflecting the occurrence of microtopographic bedforms in gravel‐bedded environments. First, spatial elevation dependence in short, detailed bed profiles from a single gravel‐bedded river is investigated using semivariogram and zero‐crossing analyses. This leads to objective identification of two discrete scales of bed roughness, associated with grain and microtopographic roughness elements. Second, the autocorrelation structure of the three‐dimensional near‐bed velocity field is examined to identify regularities associated with eddy shedding and energy losses from larger grains and microtopographic bedforms. Apart from improving the capacity to determine friction factors for velocity and discharge estimation, the findings have implications in general for the initial motion of gravelly bed material.