The stability of a uniform flow above an erodible bed composed of a bimodal mixture of sediments is investigated by means of linear analysis. Results show that, for any given set of the flow and sediment parameters, two distinct modes of instability arise, each one characterized by its own wave speed, growth rate and longitudinal wavelength, each one involving spatial variations of both grain size density and bed elevation. Although at a linear level no information on the amplitude of the perturbations is gathered, the analysis of the eigenvectors associated with the two modes of instability allows for an easy classification in terms of the relative amplitudes of the perturbations of bed elevation and size density. One eigenvalue is shown to be associated with the modifications of bed forms induced by the presence of the heterogeneous mixture, such as the local accumulation of finer and coarser material along the unit wavelength, the other with the formation of the low-amplitude sorting waves known as bedload sheets. In the present unidirectional shallow-water framework, only the sorting wave is found to be unstable, since dunes and antidunes, the relevant bed forms for this case, require a more refined rotational flow model in order to become unstable. On the other hand, the simple flow model adopted allows for the formulation of an algebraic eigenvalue problem that can be solved analytically, allowing for a deep insight into the mechanisms that drive both instabilities.

中文翻译：

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单向浅水流中的分选和底波

通过线性分析研究了由沉积物双峰混合物组成的易蚀床上方均匀流动的稳定性。结果表明，对于任何给定的流量和沉积物参数，会出现两种不同的不稳定模式，每种模式都有自己的波速、增长速率和纵向波长，每一种都涉及粒度密度和床高的空间变化. 尽管在线性水平上没有收集关于扰动幅度的信息，但对与两种不稳定模式相关的特征向量的分析允许根据床高和尺寸密度扰动的相对幅度进行轻松分类。一个特征值被证明与由非均相混合物的存在引起的床形态的改变有关，如沿单位波长局部堆积较细和较粗的物质，另一种是形成低振幅分选波，称为床载片。在目前的单向浅水框架中，只有分选波是不稳定的，因为沙丘和反沙丘，这种情况下的相关河床形式，需要更精细的旋转流模型才能变得不稳定。另一方面，采用的简单流模型允许制定可以通过分析解决的代数特征值问题，从而深入了解导致两种不稳定性的机制。在目前的单向浅水框架中，只有分选波是不稳定的，因为沙丘和反沙丘，这种情况下的相关河床形式，需要更精细的旋转流模型才能变得不稳定。另一方面，采用的简单流模型允许制定可以通过分析解决的代数特征值问题，从而深入了解导致两种不稳定性的机制。在目前的单向浅水框架中，只有分选波是不稳定的，因为沙丘和反沙丘，这种情况下的相关河床形式，需要更精细的旋转流模型才能变得不稳定。另一方面，采用的简单流模型允许制定可以通过分析解决的代数特征值问题，从而深入了解导致两种不稳定性的机制。