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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.
Fabio Nobile, Yoshihito Kazashi, Eva Vidlicková