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Scaling behaviour in models of river networks and landscape evolution


Research objectives and content
Scaling Behaviour in Models of River Networks and Landscape Evolution. Abstract The
proposal is focussed on dynamical models of landscape evolution and of the related fractal properties of river networks. The main research objectives are: 1. To extend the models to take account of landscape heterogeneity; 2. To relate to network structure the response of a drainage basin to fluctuations in precipitation and other perturbations; 3. To interpret the work in the context of wider questions such as how fractals arise and why scale free structures are ubiquitus in nature. Experimental analyses of river networks have shown clear evidence of fractal behaviour characterized by power laws and the absence of a well-defined length scale. Scaling concepts like universality and finite size scaling, analogous to those developed in conventional critical phenomena, have been successfully applied to models of river networks. Networks minimizing the rate of energy dissipation have been found to have striking similarities with those observed in Nature. Remarkably, these optimal networks have been shown to be related to those arising from an independently formulated continuum theory of landscape evolution. However most of this work has been done within the unrealistic assumption that the landscape has no spatial variation of its material properties - to be remedied in this proposal.
Training content (objective, benefit and expected impact)
Advance research career of applicant; Use of new techniques, particularly addressing the relationship between optimisation models and dynamical ones; Experience of wider range of physics-based research in Dr Ball's group in Cambridge; Opportunity for some informal experience of supervising graduate students and possibly also undergraduates.
Links with industry / industrial relevance (22)
The response of drainage basins to rainfall perturbations is critical to management of flooding risk.
Evolution of river network structure over geological time is of considerable interest to the oil industry in modelling the resulting oil reservoir structures.


Gibbet Hill Road
United Kingdom