Unsteady Boussinesq-type flow equations for gradually-eroded beds: application to dike breaches
Unsteady Boussinesq-type flow equations for gradually-eroded beds: application to dike breaches
复制标题
逐渐侵蚀层的非稳态 Boussinesq 型流动方程：在堤坝决口中的应用
DOI：
10.1080/00221686.2012.739579
复制
发表时间：
2013
影响因子：
2.3
通讯作者：
W. Hager
中科院分区：
文献类型：
--
作者：
O. Castro;W. Hager
漫顶溃堤是指在弯曲河床上的非恒定流，由于冲刷作用而不断发生变形。水面和河床剖面上的曲率和坡度表明，浅水方程可能不适合用于建模目的。考虑垂直惯性效应的Boussinesq方程给出了下一阶的数学近似。本文建立了弯曲可蚀床的新型非定常流动方程。利用Boussinesq型闭合，给出了垂直速度、压力分布和动量函数的表达式。这取决于与水流深度的时间和空间导数有关的两个参数，即底部高程和平均流速。将模型方程与以前的非定常Boussinesq型模型进行了比较，表明新的公式是对可侵蚀床的推广。Boussinesq系数使用在VAW，ETH进行的选定实验进行了进一步研究。
Dike breach due to overtopping involves unsteady flow over a curved bed continuously deforming in time due to erosion. The curvatures and slopes on the water surface and the bed profiles indicate that the shallow-water-equations may be inappropriate for modelling purposes. The next degree of mathematical approximation is given by the Boussinesq equations accounting for vertical inertia effects. Herein novel unsteady flow equations for a curved erodible bed are developed. Using a Boussinesq-type closure, expressions for the vertical velocity, the pressure distribution and the momentum function are presented. These depend on two parameters relating to the temporal and spatial derivatives of the flow depth, namely bottom elevation and average flow velocity. The model equations are compared with previous unsteady Boussinesq-type models, indicating that the novel formulation is a generalization for erodible beds. The Boussinesq coefficients are further investigated using selected experiments conducted at VAW, ETH.