Fluid flow through vegetation

This thesis is concerned with the mechanical aspects of fluid-vegetation interaction in coastal flows and their resultant instabilities. Specifically, we consider the evolution of periodic waves as they propagate through vegetated domains, and the emergence of monami – the progressive, synchronous oscillation of submerged vegetation under sufficiently strong flows. We divide our analysis between rigid and flexible vegetative canopies. These new predictions and physical insights will be applicable in the analysis of a diverse range of industrial and environmental applications involving fluid-vegetation interactions. In the case of rigid vegetation, using the method of multiple scales, we derive the evolution of small-amplitude waves propagating over a varying substrate fully covered with vegetation. In particular, we give time-averaged predictions for both the amplitude and the wavelength of the waves as functions of the distance of propagation. We then extend this analysis to include the situations of (i) combined current-wave flows and (ii) shallow-water waves through vegetation. For the case of combined current-wave flows, we demonstrate the manner in which the surface waves vary as a function of the current, and also how the current remains unaffected by the evolving wave. For shallow-water waves, we explore how cnoidal waves, nonlinear periodic solutions of the Korteweg-de Vries equation, evolve on horizontal substrates. For all of the flows considered above on rigid vegetation, their evolutions are only drag-dependent and hence independent of added mass and virtual buoyancy. In the case of flexible vegetation, we propose a model where the plants are described by elastic cantilever beams. Our first analysis concerns the propagation of small-amplitude waves. Compared to the case of rigid vegetation, the fluid will load and deform each vegetative structure. This deformation, in turn, must affect the flow. Although the flow and the beam dynamics have to be determined simultaneously, we show that when the wavelength is sufficiently small, such quantities are asymptotically decoupled -- this allows us to first determine the local beam dynamics before evaluating the momentum loss in the macroscopic flow. In contrast to rigid vegetation, we find that added mass and virtual buoyancy play a role. Finally, we focus on understanding the mechanisms and critical conditions for triggering monami. We treat the current as unidirectional and solve for the steady configurations of the flow and the deflected canopy. Our stability analysis predicts that monami is induced by shear along the top of the canopy. Meanwhile, monami can be suppressed if the canopy is sufficiently sparse or if there is sufficient inertia in the system.