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首页> 外文会议>International Conference on Fluvial Hydraulics Vol.2, Sep 4-6, 2002, Louvain-LA-Neuve, Belgium >Weakly nonlinear stability analysis of dune formation
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Weakly nonlinear stability analysis of dune formation

机译：沙丘形成的弱非线性稳定性分析

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摘要

The transition process of dune formation is known to show a hysteresis that the Froude number at which dunes disappear with increasing discharge is larger than the Froude number at which dunes reappear with decreasing discharge. In this study, a weakly nonlinear stability analysis is performed in order to provide a theoretical explanation for the hysteresis observed in the dune transition. The growth rate expansion method with the aid of the multiple scale expansion technique is used to derive a nonlinear amplitude equation, the Landau equation, from two-dimensional Reynolds equations and the Exner equation for sediment conservation with five boundary conditions at the water and bed surfaces. The results show that the first Landau constant is positive in the range of parameters employed in this analysis; thus, the transition from dune-covered to flat beds corresponds to the subcritical bifurcation. This implies that there is a great possibility that the hysteresis is caused by the subcritical bifurcation.
机译：已知沙丘形成的过渡过程显示出滞后现象，沙丘随着流量增加而消失的弗洛德数大于沙丘随着流量减少而重新出现的弗洛德数。在这项研究中，进行了弱非线性稳定性分析，以便为沙丘过渡中观察到的滞后现象提供理论解释。利用多尺度扩展技术的增长率扩展方法，从二维Reynolds方程和Exner方程推导出非线性振幅方程，Landau方程，用于在水和床面具有五个边界条件的沉积物保护。结果表明，在此分析中使用的参数范围内，第一个Landau常数为正。因此，从沙丘覆盖到平床的过渡对应于亚临界分叉。这意味着磁滞很可能是由亚临界分叉引起的。

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