Limits to scale invariance in alluvial rivers

Abstract

Assumptions about fluvial processes and process–form relations are made in general models and in many site‐specific applications. Many standard assumptions about reach‐scale flow resistance, bed‐material entrainment thresholds and transport rates, and downstream hydraulic geometry involve one or other of two types of scale invariance: a parameter (e.g. critical Shields number) has the same value in all rivers, or doubling one variable causes a fixed proportional change in another variable in all circumstances (e.g. power‐law hydraulic geometry). However, rivers vary greatly in size, gradient, and bed material, and many geomorphologists regard particular types of river as distinctive. This review examines the tension between universal scaling assumptions and perceived distinctions between different types of river. It identifies limits to scale invariance and departures from simple scaling, and illustrates them using large data sets spanning a wide range of conditions. Scaling considerations and data analysis support the commonly made distinction between coarse‐bed and fine‐bed reaches, whose different transport regimes can be traced to the different settling‐velocity scalings for coarse and fine grains. They also help identify two end‐member sub‐types: steep shallow coarse‐bed ‘torrents’ with distinctive flow‐resistance scaling and increased entrainment threshold, and very large, low‐gradient ‘mega rivers’ with predominantly suspended load, subdued secondary circulation, and extensive backwater conditions. © 2020 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd

An experimental investigation of turbulent free-surface flows over a steep permeable bed

“…Various equations have thus been developed specifically to deal with flow resistance in steep streams by proposing new power-law equations adjusted on steep-stream data (Rickenmann 2016), but because of the wide range of temporal and spatial scales associated with these streams, flow resistance data are scattered, and no unique scaling law emerges from them. There is thus growing evidence that steep streams exhibit no scale invariance (Ferguson 2021), and thus, faced with this failure of scale invariance, we need to dig down into the issue of spatial scales by looking into their flow dynamics at a mesoscopic scale (that is, at the bed roughness scale).…”

Quasi‐Universal Length Scale of River Anabranches

“…From this standpoint, several works (e.g., Chadwick et al., 2019; Chatanantavet et al., 2012; Jerolmack & Swenson, 2007) indicated that the distance between avulsion nodes and the shoreline in lowland deltas scales with the backwater length. The latter is defined as the distance over which, depending on flow conditions, the water surface exhibits a drawdown or a steepening (Lamb et al., 2012; Paola & Mohrig, 1996) set by a downstream standing body of water (e.g., lake, sea, or dam reservoirs) or a channel confluence (Ferguson, 2021; Meade et al., 1991; Ragno et al., 2021; Samuels, 1989).…”

Experiments on Gravel‐Sand Transitions: Examination of Washload Deposition

“…Gravel exhaustion GSTs form where gravel supply downstream of a mountain range decreases through selective deposition, where deposition of the coarsest fraction is promoted through the generation of accommodation (e.g., subsidence, consolidation of sediment). Once gravel is exhausted from the supply, a break in water surface slope develops as sand bed rivers require lesser gradient to transport the incoming sand supply than gravel bed rives (e.g., Ferguson, 2021; Lane, 1954; Parker et al., 2007). Other GSTs have been found to coincide with backwater limits upstream of local base level controls where a rapid decline in transport capacity of the river exists (e.g., Frings, 2011; Sambrook Smith & Ferguson, 1995).…”