Hydrodynamic instability of vegetated shear flows

Abstract

We examine the genesis of coherent vortices in submerged vegetated flows by means of a linear stability analysis. The mathematical framework is comprised of the conservation equations of fluid mass and momentum. The problem is tackled by imposing normal mode perturbations over an underlying undisturbed flow. We find that the growth rate of perturbations takes maximum magnitude for a specific wavenumber, termed as the critical wavenumber. The critical wavenumber indicates the most favorable wavenumber of coherent vortices emerging in submerged vegetated flows. The critical wavenumber amplifies as the flow Reynolds number, and vegetation height and density augment. The migration velocity of incipient coherent vortices characterizes minimum magnitude for a selected value of the vegetation height. The unstable zone in the stability diagram embarks beyond a critical Reynolds number. The critical Reynolds number designates the onset of coherent vortex appearance in submerged vegetated flows. The predictions of the present study are congruent with the existing theoretical and experimental works.