ABSTRACT

Equilibrium theory, evolution and least action principle; factors determining self-adjustment in geomorphology and Earth’s fluvial stratigraphic record

  
- Gerald C. Nanson University of Wollongong NSW 2519 gnanson@uow.edu.au 
- He Qing Huang Chinese Academy Sciences, Beijing China

A fascinating characteristic of alluvial rivers is that they self-adjust. If a channel is too wide it narrows, too steep it meanders or braids, too fast and it roughens its boundary. In short, rivers evolve to minimise their action, but how do they ‘know’ to do this? Until recently no universal agreement for a philosophical or scientific methodological framework has been proposed to guide the study of fluvial geomorphology. Least action principle (LAP) provides a new paradigm for river research by identifying the attractor state controlling river channel evolution. It is the theoretical basis of variational mechanics and is exemplified in rivers in the form of maximum flow efficiency (MFE), linking major advances in theoretical physics to fluvial geomorphology, hydraulic engineering and sedimentology. LAP explains that alluvial rivers self-adjust (evolve) towards an optimum state whereby they do the work imposed upon them by transporting their sediment load using the least amount of energy (i.e. they adopt MFE). Because of Earth’s continuing tectonics and abundant runoff, most rivers are significantly overpowered. They create dynamic-equilibrium forms to shed excess energy and maximise their stability. A few are underpowered and adjust their form to conserve energy, disperse and deposit excess sediment and remain relatively stable. Very few rivers occupy the ‘Goldilocks zone’ where the valley and energy gradients are equal. Some examples of this last type are illustrated from the ancient, barely-eroding surface of the arid Australian continent. Bedforms in rivers are of two types; those that create roughness to consume surplus energy and those that minimise roughness and store surplus load. LAP explains profound biases in Earth’s surviving stratigraphic record. Meanders are an energy-shedding mechanism and sequester little sediment; all known sequences are <50m thick. In contrast, low-energy braided and anabranching systems have no excess energy so dominate Earth’s stratigraphic record by sequestering sediment piles over a kilometre in thickness and up to several hundred kilometres wide. LAP provides a universal, rational explanation for why alluvial rivers strategically evolve to change their width/depth ratios, planforms, bedforms and erosion or deposition to achieve stable equilibrium in response to changing externally-imposed sediment loads and energy conditions.