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.

Seagrass deformation affects fluid instability and tracer exchange in canopy flow

“…This study builds on previous work by Singh et al [2016] and Wong et al [2020] in analyzing the dynamics of flow through a submerged seagrass canopy and its resultant instabilities. Although monami is manifested in the grass motion, the drag exerted by the vegetation on the flow is central to the instability, and the resulting flow structures persist in laboratory experiments even when deformable grass is replaced by rigid dowels Nepf, 2002, 2006].…”

“…Most previous simplified models fall into one of two categories: models of flow over a specified set of rigid obstacles [Ghisalberti and Nepf, 2004;Singh et al, 2016], or models where grass deformation can occur, but does not change the flow profile [Luhar and Nepf, 2011]. Fewer models [Wong et al, 2020] emphasize the coupling between grass deformation and flow, and our study is unique as it presents numerical simulations of the coupled system and uses them to study monami.…”

“…Singh et al [2016] proposed the seagrass effect on the fluid to be modeled as a continuum drag acting perpendicular to the blade, proportional to the number of stems per unit area, and established the dependence between viscous effects and flow instabilities by performing a linear stability analysis of flows through an array of rigid beams. Wong et al [2020] expanded this model to account for flexible beams, derived the coupled equations of motion and relevant dimensionless groups, and performed a stability analysis to investigate conditions for the onset of instabilities.…”

Multiple-scales analysis of wave evolution in the presence of rigid vegetation

“…In particular, we shall require accurate computations of the wave amplitude, typically much smaller than the wavelength and within a much larger domain. Here, we shall summarise the main details of the implementation; a more complete summary can be found in Wong et al (2020) and Appendix B.…”

“…However, we note that it is impractical to monitor the contributions of individual plants. Instead, following the analysis in Wong, Trinh & Chapman (2020), we consider a simpler averaged model in which the canopy is an effective medium that contributes a bulk volumetric drag.…”