Hydraulic geometry and maximum flow efficiency as products of the principle of least action

Huang, He Qing; Nanson, Gerald C.

doi:10.1002/(sici)1096-9837(200001)25:1<1::aid-esp68>3.0.co;2-2

Cited by 173 publications

(146 citation statements)

References 51 publications

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“…Since friction represents energy dissipation into heat, the equivalence between PmE and minimum friction shows, as argued by the Yang group (Yang, 1971(Yang, , 1987Yang and Song, 1979;Yang, 1980, 1982;Yang et al, 1981), that mEDR derived in terms of entropy theory is indeed applicable to open channel flow. However, among the many forms of mEDR that have been previously hypothesized, only those leading to maximum flow efficiency (MFE) (Huang and Nanson, 2000, 2001, mSP and MSTC, can be adopted. The form of mEDR identified here from laws governing open channel flow demonstrates that the principle of minimum entropy production, well developed in non-equilibrium thermodynamics, can also be applied to explain with a velocity field the behaviour of fluids at stationary equilibrium (Stauffer, 2005).…”

Section: Clarifying the Confusion Of Multiple Extremal Hypothesessupporting

confidence: 84%

“…Huang and Nanson, 2000, 2001Huang and Chang, 2006) regard the precise form of the profile as a problem with uncertainty. As a consequence, they advanced an object-orientated variational methodology in the context of fuzzy theory.…”

Section: Advantages Of Fuzzy Objectification and Variational Approachmentioning

confidence: 96%

“…For flow in an open channel, Huang and Nanson (2000, 2001 and Huang et al ( , 2004aHuang et al ( , 2004b have examined the applicability of the LAP and found that, due to the action of gravity, the LAP can be written as the principle of minimum potential energy. For transporting water discharge and sediment load, however, flow needs to have a certain amount of kinetic energy to achieve equilibrium.…”

Section: Extremal Hypotheses In Geomorphologymentioning

confidence: 99%

“…Importantly, this demonstrates that the condition of S f = S fmin or Q s = (Q s ) max is the product of the LAP (Huang and Nanson, 2000, 2001Huang et al, , 2004aHuang et al, , 2004bHuang and Chang, 2006). Hence, the most efficient alluvial channel geometry derived is based on the condition of S f = S fmin or Q s = (Q s ) max and provides a testable case for verifying the applicability of the LAP in alluvial channel flow.…”

Section: Advantages Of Fuzzy Objectification and Variational Approachmentioning

confidence: 99%

“…Consequently, there is almost always a discrepancy between S V and the minimum energy slope S fmin required for transporting an imposed water discharge Q and sediment load Q s in a straight, maximally efficient, single-thread channel. For given Q and Q s from upstream, the river must adjust S fmin as a hydraulic variable, and Huang and Nanson (2000, 2001 showed that S fmin can be determined from the following relationship: Because S V and S fmin are derived from different processes, there are three possibilities: (1) S V = S fmin ; (2) S V > S fmin and (3) S V < S fmin . In the highly unusual situation of S V = S min , the valley gradient is exactly that required to transport the imposed water and sediment.…”

Section: Physical Cause For River-channel Planform Developmentmentioning

confidence: 99%

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Least action principle, equilibrium states, iterative adjustment and the stability of alluvial channels

Nanson

Huang

2007

Earth Surf Processes Landf

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The energy based least action principle (LAP) has proven to be very successful for explaining natural phenomena in both classical and modern physics. This paper briefly reviews its historical development and details how, in three ways, it governs the behaviour and stability of alluvial rivers. First, the LAP embodies the special stationary equilibrium state of motion and so its incorporation with the principle of energy conservation explains why so many optimizing hypotheses have been proposed in fluvial geomorphology. Second, the variational approach underlying the LAP provides a more straightforward and simpler fuzzy-object orientated method for solving river regime problems than do the various complex Newtonian formulations. Third, it is shown that in fluvial systems with surplus energy the surplus can be expended with slope and/or channel geometry adjustments, with the degree of channel geometry adjustment quantified by the dimensionless numbers F for depth dominated adjustment and H for width/depth dominated adjustment. Different planforms are preferred at different energy levels, with H providing a quantitative measure of the flow's efficiency for moving sediment. In rivers with insufficient energy, the interactions of endogenous and exogenous factors are shown to be capable, in certain circumstances, of achieving a stationary equilibrium condition which acts as the attractor state. Importantly, this study describes how iterative changes enable systems to achieve such a stable equilibrium.

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Section: Clarifying the Confusion Of Multiple Extremal Hypothesessupporting

confidence: 84%

Section: Advantages Of Fuzzy Objectification and Variational Approachmentioning

confidence: 96%

Section: Extremal Hypotheses In Geomorphologymentioning

confidence: 99%

Section: Advantages Of Fuzzy Objectification and Variational Approachmentioning

confidence: 99%

Section: Physical Cause For River-channel Planform Developmentmentioning

confidence: 99%

See 3 more Smart Citations

Least action principle, equilibrium states, iterative adjustment and the stability of alluvial channels

Nanson

Huang

2007

Earth Surf Processes Landf

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135

117

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2000

Hydrological Processes

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Catchment‐ and reach‐scale controls on the distribution and expectation of geomorphic channel adjustment

Lisenby

Fryirs

2016

Water Resources Research

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Variability in channel function (behavior) can be assessed by characterizing different forms of adjustment over time. Here, historical channel adjustments in three tributary systems of the Lockyer Valley, Southeast Queensland (SEQ) are analyzed in order to evaluate the range of catchment-and reach-scale controls on channel behavior. Over 300 individual adjustments and 13 forms of adjustment were identified over a $130 year time span. We measured the width-to-depth ratio (W:D), mean stream power (x), and basin area (A) at the location of all observed adjustments. The most common forms of adjustment were avulsions, lateral expansion of the channel, and bend adjustments. The tributary systems behave distinctly different from one another according to statistical comparisons between the W:D, x, and A data for these forms of adjustment. We find that it is possible to develop process domains or typologies for forms of geomorphic adjustment found in the Lockyer Valley. These domains or typologies provide the foundations for synoptic comparisons between catchments and assessing the expectation of channel adjustment (forecasting), which should be included in process-based river management practice.

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Hydraulic geometry and maximum flow efficiency as products of the principle of least action

Cited by 173 publications

References 51 publications

Least action principle, equilibrium states, iterative adjustment and the stability of alluvial channels

Least action principle, equilibrium states, iterative adjustment and the stability of alluvial channels

Current awareness

Catchment‐ and reach‐scale controls on the distribution and expectation of geomorphic channel adjustment

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