Momiji, Hiroshi; (2001) Mathematical modelling of the dynamics and morphology of aeolian dunes and dune fields. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

The aim of this thesis is to model the dynamics of free sand dunes. In the first part, a new theoretical scheme is presented to model the shape and migration speed of a sand dune at equilibrium. Unlike earlier models it does not require iterative calculations of the interaction between the wind flow and the topography. As the first step, a self-consistent model which describes two- dimensional dune migration is introduced, which is comprised of a grain-scale model of sand deposition in the lee of dune and the assumption of equilibrium. The model gives quantitative relations between sand grain diameter, wind velocity on level ground and dune height. By further incorporating theory based on aerodynamics, the wind-directional profile of barchan dunes can be estimated. The thesis goes on to develop a computer simulation model that describes the three-dimensional morphology and dynamics of an aeolian dune field. Following recent advances, the proposed model is based on an approach using discrete lattice dynamics. In the model, dunes are treated as accumulations of 'sand slabs' on a two-dimensional lattice, whose motion is the result of wind-directional sand transport and avalanching. By incorporating new features, which reflect physically observed mechanisms, the model can simulate dunes whose individual shape and collective patterns are similar to those observed in nature. The model can also quantitatively simulate dune growth and dune migration. Some dune patterns can be explained by the model in terms of seasonally changing wind direction and sand availability (initial sand depth). These two approaches are complimentary. Some results in this thesis may be applicable to the morphology and dynamics observed in subaqueous and other terrestrial bedforms.

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