This work is a study into the unsteady behaviour of aeolian sediment transport. A one-dimensional and a two-dimensional numerical model were developed in order to investigate the temporal behaviour of transport rate as well its spatial distribution. The numerical model of McEwan (1991) for steady state saltation served as a starting point in the development phase. Both models presented in this thesis are capable of simulating temporary varying winds. In addition, the two-dimensional model allows the relaxation of the assumption of streamwise homogeneous flow. The one-dimensional model was tested against results for steady state predicted by previous models. Further tests showed that the discretisation time step size Δ<I>t</I> has an influence on the model's temporal behaviour. The reason for this is the better coupling of the wind-sand system when a smaller Δ<I>t</I> is used. The implications of bed area choice on the statistical accuracy of predicted transport rate was demonstrated. In the one-dimensional case the grain cloud's total forward momentum equals transport rate, which is independent of model geometry. The initial over-shoot reported by previous investigators was found not to appear for simulation heights small than 50 to 60cm. This is due to the fast propagation of the grains' influence (momentum exchange) upward in the flow and the immediate deceleration of the wind. Confirmation of these findings comes from reports of experiments conducted in differently sized wind tunnels. Different types of wind velocity variations were investigated. The transport rate's response depends on the amplitude and frequency of the wind fluctuations. At frequencies higher than <I>f </I>≈ 0.5Hz the transport rate was found not to respond to the wind changes.

The formation of aeolian ripples has been modeled, quite successfully, using discrete approaches like cellular automaton models. Numerical analysis of continuum models to obtain similar success in modeling ripple evolution, however, has not been studied extensively. A numerical model based on continuum theories expedites calculations, as opposed to discrete approaches which model trajectory of each and every sand grain, and are hence relatively more economical. The numerical analysis strives to contribute to the field of study of aeolian ripple migration by an extensive comparison and discussion of modeled ripple evolution results with those of a particular laboratory based wind-tunnel experiment. This research also endeavors to under- stand the physics behind ripple generation and what parameters to be modified to account for multiple grain sizes. Incorporation of multiple grain sizes would enable us to study the stratigraphy of the generated bed-forms. To obtain smoother and realistic ripple surfaces, a sixth-order compact finite difference numerical scheme is used for spatial derivates and fourth-order Runge-Kutta scheme for time derivates. The boundary conditions incorporated are periodic and the initial condition employed to generate ripple is a rough sand surface. The numerical model is applied to study the effect of varying the angle, at which the sand bed gets impacted by sand grains, on the evolution of ripples. Ripples are analyzed qualitatively and quantitatively by considering the contribution of processes involved in the evolution process. The ripple profiles and the time taken to reach equilibrium state, obtained by numerical experiments, are in close agreement with the ones obtained by the wind-tunnel experiment.