明渠挟沙水流双层积分模式的双曲性分析

Hyperbolicity analysis of a double layer-averaged model for open-channel sediment-laden flows

将明渠挟沙水流双层积分模式的控制方程系分别作为单一系统和两个降阶的双曲性系统,分析、比较其特征值;结合溃坝挟沙水流和水库挟沙水流等两类典型的强分层挟沙水流,研究其双曲性.分析表明,尽管作为单一系统和两个降阶的系统时,特征值在定量上有差异,但在所涉及的参数域内,双曲性仍然得以保持,并不引发Kelvin-Helmholtz失稳现象.作为应用实例,对水库异重流进行数值模拟研究.结果表明,在所应用的参数范围内,显著增加水库清水泄流量并未导致异重流失稳,且可明显提高排沙比,减少水库泥沙淤积.

Recently we developed a physically enhanced double layer-averaged model for open-channel sediment-laden flow, which properly incorporates inter-layer interactions, sediment transport and morphological evolution. Yet it is hard to solve the whole set of governing equations of the two layers as a single system, the governing equations for each layer are cast into a non-homogeneous hyperbolic system, whilst the inter-layer interactions are represented as source terms as they are generally negligible when compared to inertia and gravitation. The two reduced-order hyperbolic systems of the governing equations for the two layers are solved separately and simultaneously. The performance of the model has been demonstrated for series of observed datasets. However, it remains to be revealed if the hyperbolicity is preserved. The present study analyzes and compares the eigenvalues of the governing equations when cast into a single system and two reduced-order hyperbolic systems respectively. As applied to typical stratified sediment-laden flows concerning dam-break floods over erodible sediment beds and reservoir turbidity currents, the model can preserve hyperbolicity and thus avoid Kelvin-Helmholtz instability although appreciable discrepancies of the eigenvalues of single system and two reduced-order hyperbolic systems are discernible. Computational tests for reservoir turbidity currents reveal that an excessive clear-outflow would keep the turbidity current from being spoiled, and also is conducive to improve sediment flushing efficiency and mitigate reservoir sedimentation.