A worldwide correlation for exponential bed particle size variation in subaerial aqueous flows

Abstract

The particle size of the bed sediments in or on many natural streams, alluvial fans, laboratory flumes, irrigation canals and mine waste deltas varies exponentially with distance along the stream. A plot of the available worldwide exponential bed particle size diminution coefficient data against stream length is presented which shows that all the data lie within a single narrow band extending over virtually the whole range of stream lengths and bed sediment particle sizes found on Earth. This correlation applies to both natural and artificial flows with both sand and gravel beds, irrespective of either the solids concentration or whether normal or reverse sorting occurs. This strongly suggests that there are common mechanisms underlying the exponential diminution of bed particles in subaerial aqueous flows of all kinds. Thus existing models of sorting and abrasion applicable to some such flows may be applicable to others. A comparison of exponential laboratory abrasion and field diminution coefficients suggests that abrasion is unlikely to be significant in gravel and sand bed streams shorter than about 10 km to 100 km, and about 500 km, respectively.

The role of sediment in controlling steady-state bedrock channel slope: Implications of the saltation–abrasion incision model

“…The commonly observed downstream fining of grain size is typically treated as an exponential function (e.g. Morris and Williams, 1999), however, many field studies have found good agreement with a power law fining relation (e.g. Brush, 1961;Brierley and Hickin, 1985;Ohmori, 1991).…”

Mine Waste Beach Profile and Flow Resistance Equations

“…It was applied empirically to numerous mine tailings beaches by Abadjiev [33,34] and Williams and Morris [7]. It has also been applied empirically to a large number of subaerial aqueous flows of all kinds [35].…”

“…Morris and Williams [32,35] also compiled independent data from more than one hundred natural streams, canals, laboratory flumes (mine tailings, sand, and gravel), tailings beaches, and coal co-disposal beaches (Fig. 13) that enable b to be evaluated.…”

“…In Figure 13, L may be the length of a beach, canal, or a segment of a stream. The data shown represent flows with bed D ranging from about 0.02 mm to about 4 m. Since the G s of most of the sediments was constant over L, the for mine tailings and other sediments with variable G s were converted to equivalent for sediments with constant G s [35].…”

Downstream trends in sediment size and composition of channel-bed, bar, and bank deposits related to hydrologic and lithologic controls in the Llano River watershed, central Texas, USA

“…Resistant rock units are generally associated with narrower valleys that confine floods, resulting in higher flood peaks and greater unit stream power (Baker and Costa, 1987;Magilligan, 1992). Differential rates and styles of weathering not only dictate the initial size (McPherson, 1971) of detached particles, but also the downstream rate of particle size reduction (Kodama, 1994;Morris and Williams, 1999;MoussaviHarami et al, 2004), thereby indirectly influencing the spatial distribution of sediment.…”