Regime theory and the stability of straight channels with bankfull and overbank flow

Optimal alluvial channel width under a bank stability constraint

“…Based on this inconsistency between the predicted and observed alluvial channel widths, Griffiths and Carson (2000, p. 123) conclude, ''it is thus clear that the notion of 'equilibrium' channels in nature attaining the condition of maximum transport, as sometimes entertained in the past, is invalid.'' We are in agreement with the first quote by Griffiths and Carson, which is also consistent with recent observations by Valentine et al (2001). However, we strongly disagree with the subsequent conclusion in the second quote.…”

“…Their analysis indicates that the observed channel widths of natural rivers in New Zealand are two to four times the width predicted by a rational regime model that applies the maximum sediment transport capacity (MTC) hypothesis. Valentine et al (2001) make similar observations after comparing the channel widths obtained from their laboratory experiments to widths predicted using the MTC model presented by White et al (1982). Based on this inconsistency between the predicted and observed alluvial channel widths, Griffiths and Carson (2000, p. 123) conclude, ''it is thus clear that the notion of 'equilibrium' channels in nature attaining the condition of maximum transport, as sometimes entertained in the past, is invalid.''…”

“…Recent work (Eaton et al, 2004) presents a more physically based explanation for the necessary extremal hypotheses used in rational regime models by relating morphological stability to adjustments of the flow resistance for the fluvial system. In this paper, we address recent criticism that observed channel widths are invariably greater than predicted by rational regime models (Griffiths and Carson, 2000;Valentine et al, 2001;Shields et al, 2003). This criticism is based on optimization models that are not constrained with respect to bank strength.…”

“…This criticism is based on optimization models that are not constrained with respect to bank strength. We believe that the analyses performed by Griffiths and Carson (2000), Valentine et al (2001), and others (Chang, 1979;White et al, 1982) are incomplete because they do not explicitly incorporate the strength of the channel banks relative to the channel bed. Therefore, their regime predictions are inappropriate since they ignore the fundamental constraint of relative bank strength-an issue identified by Griffiths and Carson (2000) as important, but not incorporated into their analytical regime model.…”

Theoretical regime equations for mobile gravel-bed rivers with stable banks

“…Gilbert (1914, p. 134) found the optimum W/D ratio of about 7 in his two complete experiments, which is about two to four times less than is typical of many natural rivers and self-formed sand flume channels. Mathematical optimisation models that do not explicitly consider bank strength (such as Chang (1980) and White et al (1982)) also predict much narrower channels when applied to rivers and experimental channels formed within noncohesive and nonvegetated bank sediments (Simon and Thorne, 1996;Griffiths and Carson, 2000;Valentine et al, 2001). This has prompted criticism that natural rivers do not adjust to an optimum condition, and that optimality theory is invalid (Griffiths and Carson, 2000).…”