Geomorphology describes the shaping of the Earth's surface by the action of wind, water and ice. The formation of aeolian dunes, and the particular varieties such as barchan dunes, seif dunes and star dunes is due to the erosive action of wind on sand, and the dunes are formed as the result of an instability. Particularly challenging features of the modelling are the parameterisation of turbulent shear flow over a hill, the description of separated flow adjoining the slip face, and the nonlinear evolution of the sand slope under differing wind regimes.
Overland flow of rainwater over sediments leads to the formation of small furrows called rills, and eventually, over geologic time, streams and then rivers form. The network of channels which thus form constitutes a dendritic pattern which efficiently drains a catchment area. Similar branching patterns occur in ice sheets, cave systems, and in the lungs and arteries. The initial formation of channels is associated with an erosional instability which is described by the Smith/Bretherton model of 1972, but the finite amplitude of solutions of this model, and their possible rôle in the formation of fractal drainage patterns remains as a major challenge.
Sediment is washed down from mountains into alluvial plains, from where the rivers which scour the landscape empty their load into the oceans. The sediments are washed by storms and wave action to the edge of the continental shelf at a depth of some 200 metres, where they spill down the continental slope, forming fast moving submarine turbidity currents, which erode huge canyons. These canyons extend out for up to a thousand kilometres from the continental margin, forming branched networks, whose origin is not well understood.