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Limits to scale invariance in alluvial rivers

Ferguson, Rob

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Rob Ferguson


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.


Ferguson, R. (2021). Limits to scale invariance in alluvial rivers. Earth Surface Processes and Landforms, 46(1), 173-187.

Journal Article Type Article
Acceptance Date Sep 14, 2020
Online Publication Date Oct 9, 2020
Publication Date 2021-01
Deposit Date Oct 14, 2020
Publicly Available Date Oct 14, 2020
Journal Earth Surface Processes and Landforms
Print ISSN 0197-9337
Electronic ISSN 1096-9837
Publisher British Society for Geomorphology
Peer Reviewed Peer Reviewed
Volume 46
Issue 1
Pages 173-187


Published Journal Article (Advance online version) (2.3 Mb)

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Copyright Statement
Advance online version © 2020 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd. This is an open access article under the terms of the Creative Commons Attribution‐NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.

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