Shear-induced instabilities of flows through submerged vegetation

Abstract

We consider the instabilities of flows through a submerged canopy, and show how the full governing equations of the fluid-structure interactions can be reduced to a compact framework that captures many key features of vegetative flow. By modelling the canopy as a collection of homogeneous elastic beams, we predict the steady configuration of the plants in response to a unidirectional flow. This treatment couples the beam equations in the canopy to the fluid momentum equations. Our linear stability analysis suggests new insights into the development of instabilities at the surface of the vegetative region. In particular, we show that shear at the top of the canopy is a dominant factor in determining the onset of instabilities known as monami. Based on numerical and asymptotic analysis of the generalised eigenvalue problem, the system is shown to be stable if the canopy is sufficiently sparse or if the plants are sufficiently flexible.