A test of equilibrium theory and a demonstration of its practical application for predicting the morphodynamics of the Yangtze River

Abstract

Taking the width/depth ratio of a river channel as an independent variable, a variational analysis of basic flow relationships shows that alluvial‐channel flow adjusts channel geometry to achieve stationary equilibrium when the condition of maximum flow efficiency (MFE) is satisfied. As a test of the veracity of MFE and to examine if this theory of self‐adjusting channel morphodynamics can be practically applied to large river systems, this study examines the degree of correspondence between theoretically determined equilibrium channel geometries and actual measurements along the middle and lower Yangtze River. Using four different forms of the Meyer‐Peter and Müller bedload relation and relations of flow continuity and resistance we show that the Meyer‐Peter and Müller bedload relation modified on the basis of MFE theory predicts channel dimensions most accurately when applied to the middle and lower Yangtze River. This provides convincing evidence supporting MFE equilibrium theory. Copyright © 2014 John Wiley & Sons, Ltd.

The morphometric variation of islands in the middle and lower Yangtze River: A variational analytical explanation

“…Where it is a single channel, the Yangtze River along the study reach is some 1100 to 2200 m wide with depths averaging about 12 to 22 m. In such a wide and relatively shallow river the character of the banks play a very minor role in determining what is a self-adjusting alluvial channel morphology dominated by the primary drivers of flow continuity, flow resistance, and bedload transport Nanson, 2000, 2002;Huang et al, 2014). This situation is in contrast to much smaller rivers where cohesive vegetated banks can have a profound influence on bank strength and hence channel form (Nanson and Huang, 1999;Millar, 2000;Parker et al, 2007;Eaton and Giles, 2009).…”

“…Firstly, in contrast to a variety of empirical assumptions embedded in the development of previous formulae, the Huang formula is based on a theoretical relationship exhibited when the complex interactions reach a stationary equilibrium state among the three essential components of a river (channel geometry, bedload transport, and flow resistance; Huang and Chang, 2006). Secondly, the Huang formula yields bedload transport rates highly consistent with experimental observations and provides a higher level of prediction for channel geometry of rivers, including very large rivers such as the middle and lower Yangtze River where suspended sediment represents nearly 90% of the total sediment load (Huang et al, 2014).…”

Seasonal variation of river and tide energy in the Yangtze estuary, China

“…Field studies have produced some evidence compatible with the assumptions that have allowed some selective testing of these concepts (Langbein, ; Yang, ; Cherkauer, ). Subsequently, there are further developments (Rodríguez‐Iturbe et al ., 1992; Dun and Townend, ; Lanzoni and Seminara, ; Savenije, ; Kleidon et al ., ; Huang et al ., ) and criticisms (Davy and Davies, ; Griffiths, ) of the arguments surrounding the concept of minimum work and uniform energy dissipation. The criticisms mostly focus on: whether it is legitimate to use an analogue to apply the thermodynamic principle to stream counterparts.…”

“…Some recent work has examined the hydraulic geometry of the middle–lower Yangtze (Huang et al ., ) and demonstrated that equilibrium geometry (width/depth ratios) is consistent with conditions of minimum energy slope equivalent to maximum sediment transport. They attributed the deviation of theoretical predictions from observed equilibrium state to tidal influence.…”

“…(i) whether it is legitimate to use an analogue to apply the thermodynamic principle to stream counterparts. Although Kleidon et al (2013) have since made clear that this is simply a function of how work is defined; and (ii) the compatibility with observations when combining these extremal hypotheses with conventional sediment transport and flow resistance equations, although recent work by Huang et al (2014) demonstrated the applicability of these concepts to the fluvial reaches of the Yangtze.…”