

@mastersthesis {6797,
	title = {Stream erosion and its relation to drainage networks and landscape evolution - a summary},
	year = {1996},
	note = {U083058},
	school = {University of Cambridge (United Kingdom)},
	type = {phdPh.{D}.},
	address = {Ann Arbor},
	abstract = {Using basic hydro-dynamics, a model for the erosion of a landscape by streamflow is developed and used in a numerical simulation. The observation is made that the drainage network on the landscape enters an equilibrium state in which there are no lakes present, the network is steady and the field of heights is of separable variable form. The steady state drainage networks compare favourably with both natural network and networks produced by simulations performed by other workers.Two scaling laws, one between modified slope and throughput and the other between height and time, are derived analytically for the steady state and successfully verified by simulation. A detailed investigation of the sensitivity of the model to the initial conditions and the effect of varying the operating parameters is then undertaken, and the results are discussed.Following this, the principle of minimum energy expenditure is outlined. The modified slope-area law derived earlier is shown to be the condition for a functional L to be stationary, subject to the constraints of water conservation. This implies that stream erosion evolves landscapes into a steady state characterised by an optimum value of L, thus providing a theoretical basis for the principle of minimum energy expenditure. The nature of the stationary point is studied, using both analytical and numerical methods. The framework for a model in which the drainage network can optimise itself with regard to channel shape, as well as the arrangement of channels, is then established. A suitable functional is found, which gives rise to a scaling relation between width and throughput of the same form as that observed in the field. The difficulties involved in deriving an erosion law to complement this functional are then discussed.Finally, the model is extended to include first non-uniform boundary conditions and then a non-local erosion law, and the extra dynamics this incorporates are qualitatively examined.},
	keywords = {(UMI)AAIU083058, 0388:Hydrologic sciences, Bibliographies, Earth sciences, Hydrologic sciences, Psychology{\textendash}Abstracting, Statistics},
	url = {http://search.proquest.com/docview/301520962?accountid=14270},
	author = {Sinclair, K}
}
