泥沙起动研究的伊辛和重整化群方法探讨

Approaches of Ising and Renormalization Group to Study the Incipient Motion of Sediment

为探讨泥沙起动的物理机制和临界概率,把泥沙起动作为一种临界现象,与连续相变进行类比,应用临界现象、连续相变和重整化群的原理和方法建立了泥沙成片起动的二维伊辛模型和二维重整化群模型及算法。通过综合分析得到泥沙成片起动的一个临界概率,其阈值约为0.42,该值与已有实验和观测结果基本接近。把泥沙运动力学和分形动力学相结合探讨了床面起动的物理机制。研究结果表明:床面整体起动和DLA(受限制的扩散凝聚)集团的分形生长有类似的物理机制,对阈值小于0.5就能引起床面整体起动给出了一个物理诠释。该新思想和新方法的引入对探讨推移质整体启动这类复杂现象是有所裨益的。

In the aim of exploring the physical mechanisms and critical probability of sediment＇ s incipient motion, the incipient motion is regarded as a critical phenomenon and is compared with continuous phase transition. Two-di- mensional Ising model and renormalization group model as well as algorithm of sediment are established based on the principle and method of critical phenomena, continuous phase transition and renormalization group. By compre- hensive analysis, a critical probability of sediment＇ s incipient motion is obtained （ the threshold is about 0.42 ） which is approximate with the results of experiments and observations. In association with sediment movement me- chanics and fractal dynamics, the physical mechanism of bed surface starting is discussed. The results show that the integral incipient motion of bed surface have similar physical mechanism with fractal growth DLA group. It gives a physical interpretation to the integral incipient motion of bed surface with a threshold less than 0.5.