A three-dimensional multilayer shallow water approach to study polydisperse sedimentation and sediment transport in a viscous fluid is presented. The fluid is assumed be loaded with finely dispersed solid particles that belong to a finite number of species that differ in density and size. The model formulation allows one to recover the global mass and linear momentum balance laws of the mixture. The model incorporates compressibility of the sediment and viscosity of the mixture through a viscous stress tensor. As a consequence of a dimensional analysis applied to the global mass conservation and linear momentum balance equations, the horizontal components of the compression term and the horizontal terms of the viscous stress tensor may be neglected. This results in a final model that is vertically consistent with the classical one-dimensional vertical model. Numerical simulations illustrate the coupled solids volume fraction and flow fields in various scenarios and the effect of the compressibility and viscosity terms. Various bottom topographies give rise to recirculation of the fluid and high solids volume fractions on the bottom.

提出了一种三维多层浅水方法，用于研究粘性流体中的多分散沉降和泥沙输送。假定流体中负载有细分散的固体颗粒，这些颗粒属于有限数量的密度和大小不同的物质。该模型公式使人们可以恢复混合物的整体质量和线性动量平衡定律。该模型通过粘性应力张量结合了沉积物的可压缩性和混合物的粘度。由于对整体质量守恒方程和线性动量平衡方程进行了尺寸分析，因此可以忽略压缩项的水平分量和粘性应力张量的水平项。这导致最终模型与经典的一维垂直模型在垂直方向上保持一致。数值模拟说明了在各种情况下耦合的固体体积分数和流场以及可压缩性和粘度项的影响。各种底部地形会导致底部流体和高固体分馏分的再循环。