Numerical Analysis on the Generation of Equilibrium Aeolian Sedimentary Bed-Forms From Random Surfaces

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.