Formation of alternate river bars in submerged vegetated flows

In this paper, we explore the formation of alternate river bars in the presence of submerged vegetation, modelled as uniformly spaced rigid cylinders. We analyse the stability of the erodible bed by coupling the Exner equation for bed evolution with the continuity and momentum equations for the fluid phase. Through linear and weakly nonlinear stability analyses, we predict the equilibrium wavelength and amplitude of vegetated alternate bars. The computational results hinge on two key parameters: the vegetation aspect ratio (vegetation height to diameter ratio) and the vegetation packing density (dimensionless frontal area per unit volume). We present streamwise flow velocity profiles for different vegetation aspect ratios and vegetation packing densities. We find that the equilibrium wavelength decreases with higher vegetation aspect ratio and vegetation packing density. Vegetation reduces the minimum channel aspect ratio required for the braided channel formation and the threshold channel aspect ratio for the alternate bar formation. The equilibrium amplitude increases with vegetation aspect ratio but reduces with vegetation packing density, eventually reaching a constant value. The predicted alternate bar wavelength and amplitude align with field observations in the Arc River, Hooge Raam River, Alpine Rhine River and Isère River.