风成沙波纹的数值模拟及稳定性分析

Numerical Modeling and Stability Analysis of Aeolian Sand Ripples

本文基于颗粒的质量守恒原理,考虑了沙粒的跃移、溅移和蠕移运动,建立了风成沙波纹的非线性积分微分演化方程,并进而通过尺度变换得到了近似的微分方程。数值求解该微分方程,得到了与野外观测相一致的沙波纹斑图,同时再现了沙波纹生成、合并的非线性行为,为进一步风成地貌形成演化的理论分析提供了一种可行的数学物理方法。

A continuous mathematical model is introduced to simulate the aeolian sand ripples.The model takes into accounts the saltation,reptation and surface creep of sand.The numerical modeling results show that it can be capable of demonstrating some important features of aeolian sand ripples,such as formation,coarsening and saturation of ripple growth for homogeneous sand in nature.Linear stability analysis of the full model and the results of numerical simulation are presented as well.In conclusion,the development of the aeolian sand ripples is an example of self-organizing system in the desert.The implication of this model show that the evolution of aeolian sand ripples and stabilization of scale can be explained by a single spatial continuum method.