FUNDAMENTALLY DISCRETE STOCHASTIC-MODEL FOR WIND RIPPLE DYNAMICS

We present a discrete, stochastic model for wind formed ripples in san d, which are observed to increase in size through mergers and seemingl y approach an asymptotic spatial scale. The model is shown to predict (1) a logarithmic increase in pattern scale with time, (2) a proportio nality between the microscopic discrete scale (sand grain diameter) an d the macroscopic pattern scale (ripple height), and (3) a lack of sca le separation. The implications are that growth and apparent stabiliza tion of scale both can be explained by a single mechanism, and that th e evolution of wind ripples and other physical systems of this type ca nnot be modeled by either deterministic methods or spatial continuum m ethods.