Nonlinear Evolution Equations And Stability Analysis Of Aeolian Sand Ripples

Aeolian sand ripples are a common feature in sandy deserts, which has always been a paradigm for the study of granular materials. Its formation, evolution and disappear are closely related to the movement of the air flow characteristics、 the surface morphology and composition of the sand bed. The nonlinearity and the self-organization behaviors of the processes are fundamental issues of various subjects, including physics, mechanics, chemistry, mathematics, biology and ecology. It has extreme significance in science. In the traditional study of the formation, evolution and dynamic characteristics of sand ripples, field observations and wind tunnel experiments are the two main methods. With the development of computer, theoretical modeling and numerical simulation in studying the development of aeolian sand ripples and the whole aeolian sand are getting more and more attentions. Based on the continuous model, this paper studies the formation and evolution, focuses on the model of the evolution, stability analysis and numerical simulation. The main results of this paper are as follows:1. Based on the mass conservation principle of the particles, considering the saltation, reptation and surface creep of sand, the nonlinear integral differential evolution equations of aeolian sand ripples is built, then through the scale transform the approximate differential equation is obtained. Through linear stability analysis, it is proved that the instability of the flat sand bed is determined by the competition of the reptating flux and the creeping flux caused by the gravity. The sand ripple pattern from the numerical solution of differential equations is the same with the field observations, reproducing the nonlinear behavior of the generating and merging. The study provides a viable method of mathematical physics for further theoretical analysis of the aeolian sand ripples. It also develops new ideas for the research on the forms and mechanisms of aeolian landforms in the future.2. A three-dimensional phenomenological model is extended from the two-dimensional aeolian sand ripples model. The general process of formation and evolution are reproduced by the three-dimensional model successfully. The law of the motion of defects is explored, such as terminations and Y-junctures, and it is indicated that the movement of defects (terminations and Y-junctures) in sand ripples is not predictable.