Aquatic vegetation in fluvial systems is often characterized by spatial patterning of the plant patches. To investigate the conditions for the formation of vegetation patches, we explore the stability of a uniform flow over a non-erodible bed with a uniform vegetation cover of submerged plants. The flow model consists of the two-dimensional shallow water and continuity equations. The hydrodynamic equations are coupled firstly to the classic formulation for vegetation dynamics, and secondly to a modified version of the equation. The revised relationship for vegetation dynamics accounts for the influence of removal, transport, and resettlement of propagules on the growth rate of aquatic vegetation. Linear stability analysis of the eco-hydrodynamic problem is performed by enforcing the quasi-steady approximation. We obtain a dispersion relation disclosing the growth rate and the migration rate of the perturbations of vegetation density as a function of the wavenumber and the relevant flow and vegetation parameters. The present theory predicts the onset of vegetation patterns and includes an adequate wavelength selection mechanism. While uprooting initially reduces plant density, the analysis demonstrates that resettled propagules after removal are fundamental for further plant population increases and the development of vegetation patterns. The proposed framework is then validated against data available in the literature. Additionally, the presence of an upper threshold in terms of vegetation density, above which uniform vegetation cover is stable, might explain the absence of any spatial pattern and thus the extremely dense vegetation cover induced by climate change and invasive species in altered ecosystems.

中文翻译：

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河流淹没植被格局稳定性分析

河流系统中的水生植被通常以植物斑块的空间模式为特征。为了研究植被斑块的形成条件，我们探索了在具有均匀植被覆盖的沉水植物的不可侵蚀床上的均匀流动的稳定性。流动模型由二维浅水和连续性方程组成。水动力方程首先与植被动力学的经典公式相结合，其次与方程的修改版本相结合。修正后的植被动态关系解释了繁殖体的迁移、迁移和重新安置对水生植被生长速率的影响。生态水动力问题的线性稳定性分析是通过强制执行准稳态近似来进行的。我们获得了一个离散关系，该关系揭示了植被密度扰动的生长速率和迁移速率作为波数和相关流量和植被参数的函数。本理论预测植被模式的开始，并包括适当的波长选择机制。虽然连根拔起最初会降低植物密度，但分析表明，移除后重新安置的繁殖体对于植物种群的进一步增加和植被模式的发展至关重要。然后根据文献中可用的数据验证所提出的框架。此外，在植被密度方面存在一个上限，高于该上限的均匀植被覆盖是稳定的，