【摘要】 运用自组织理论和方法建立河湾的演化方程 .结合 Fokker- Planck方程解析解的性质与Langevin方程的动力学特征 ,推断河湾演变的基本规律如对称破缺、形态转变、演变趋势及速度等 .然后根据数学模型与理论分析结果 ,研究长江洲湾 ,下荆江尺八口、上车湾、碾子湾等实际河湾演变的自组织规律及其稳定性特征。理论推导结果与实际观测资料基本一致更多还原

【Abstract】 The evolution equations of river bends are proposed by using the self-organized theory and method which are the Fokker-Planck equation and the Langevin equation. And the qualitative achievements, such as the evolution laws of river bends, symmetry damaged, form transition, and developing trend,are got by detailed analysis of analytic solution of the Fokker-Planck and the Langevin equations and it’s dynamic inferences Finally, we analyze the evolution features of some really river bends The theoretical results tally with the observed results更多还原