Aquatic vegetation is ubiquitous in lowland rivers, and it is typically present in the shape of spatial self-organized patches of biomass. In this work, we mathematically define the threshold conditions for the incipient formation of self-organized vegetated patterns in the shape of central or multiple row patches. The analysis is carried out through a linear stability analysis whereby the 2D eco-hydrodynamic model is linearized and the growth rate of small-scale perturbations is evaluated considering a basic state represented by an initially uniformly vegetated and straight channel having a certain aspect ratio and Froude number. Results illustrate that, for given vegetation properties, instability arises when both the Froude number and the aspect ratio are higher than a given threshold; in this case, self-organization occurs, and spatial patterns of patches will develop according to the wavelength associated to the maximum growth rate. Moreover, instability and self-organization take place when the undisturbed vegetation density is lower than upper bound; this suggests that densely vegetated channels, as in the case of rivers populated by invasive species, will not experience the formation of any spatial patterns.

水生植被在低地河流中普遍存在，并且通常以空间自组织的生物质斑块的形式存在。在这项工作中，我们在数学上定义了初始形成中央或多行斑块形状的自组织植被模式的阈值条件。该分析是通过线性稳定性分析进行的，其中二维生态水动力模型被线性化，并且考虑由具有一定纵横比的初始均匀植被和直通道表示的基本状态和 Froude 来评估小尺度扰动的增长率数字。结果表明，对于给定的植被特性，当弗劳德数和纵横比均高于给定阈值时，会出现不稳定性；在这种情况下，发生自组织，斑块的空间模式将根据与最大生长速率相关的波长而发展。此外，当原状植被密度低于上限时，会发生不稳定和自组织；这表明植被茂密的渠道，例如入侵物种居住的河流，不会经历任何空间模式的形成。