Linear stability analysis is used to investigate the behavior of small perturbations of a uniform flow in a straight channel with an erodible bed composed by a unisize sediment. A shallow-water flow model is employed and bedload sediment transport is assumed. The mathematical structure of the linear problem, in terms of the eigenvalues and their associated eigenvectors is explored in detail and information is gathered on the wavespeed and growth rate of the perturbations as a function of their wavelength and of the relevant flow and sediment parameters. Several aspects of the solution are discussed, with particular focus on the behaviour in the transcritical region where the Froude number approaches unity. An approximate solution for the roots of the eigenrelationship is presented, which is not uniformly valid in the transcritical region, leading to the appearance of an unphysical instability. A regular perturbation expansion is then introduced that allows for the elimination of this singularity.

线性稳定性分析用于研究在具有由均匀沉积物组成的可侵蚀床的直通道中均匀流动的小扰动的行为。采用浅水流模型，假设床载泥沙输运。线性问题的数学结构，就特征值及其相关特征向量进行了详细探讨，并收集了关于波速和扰动增长率的信息，作为其波长和相关流量和沉积物参数的函数。讨论了解决方案的几个方面，特别关注弗劳德数接近统一的跨临界区域的行为。给出了特征关系根的近似解，该解在跨临界区域不是一致有效的，导致出现非物理的不稳定。然后引入允许消除这种奇点的规则扰动展开。