Fluid Flow through Vegetation

  • Researcher: Clint Wong
  • Academic Supervisors: Jon Chapman and Philippe Trinh (University of Bath)
  • Industrial Supervisors: Christopher Kees (CHL, USACE) and Aggelos Dimakopoulos (HRW)

Background

The study of fluid flows interacting with vegetative structures presents a significant theoretical and numerical challenge on account of its inherently multi-scale nature. In particular, the velocity profile of the fluid is mechanically coupled with deformation of the vegetation. As a result, the interface between the two is an unknown to the problem. The vegetative layer, more commonly referred to as the canopy, is also challenging to model, due to its heterogeneity and the complex geometry of individual plants within it. For example, a tree has components with length scales that differ in multiple orders of magnitude, from leaves to branches to the trunk. The plants can also grow in a certain way and experience permanent deformation due to the prevailing direction of the flow.

The goal of this project is to develop a compact model that describes the configuration of a water flow over a uniform and submerged vegetative layer. The model should be sufficient to duplicate effects from real-life observations including instabilities. Our insights can then be applied towards flood control, environmental conservation, and energy production. In particular, the Coastal and Hydraulics Laboratory and HR Wallingford are currently working on Proteus, a computational fluid dynamics package and they are interested in refining the modelling framework and identify important features in different types of flow. 

Progress

With techniques of homogenisation, we have derived the bulk properties of the canopy. This allows us to approximate the canopy as a single body that incorporates the effects of individual plants in it. By non-dimensionalising the governing equations, we identify the key dimensionless parameters that govern the configuration. In particular, the system depends on four parameters: the Reynolds number, the ratio between inertial and viscous effects in the flow; the submergence ratio of the canopy, which is the proportion of the water body that is obstructed by the flow; the planting density in the canopy; and the flexibility of each individual plant. 

Our numerical results indicate that in the steady state, for flows with the same Reynolds number, vegetation in the canopy will deflect less as the canopy density increases. Secondly, by analysing the governing equations, our model predicts that the flow to be primarily uniform within the canopy; this is in good agreement with experimental observations. We are currently studying the conditions for unstable waving motion of vegetation (see figure), a phenomenon that is analogous to a gust of wind blowing across a patch of grass. 

Figure 1: Numerical simulation of the unstable waving motion of a submerged canopy. Shown here is the cross-section of a channel from upstream to downstream, with green elements representing individual plants in a canopy and contours representing streamlines of the flow. 

Future Work

When the stability analysis is complete, we will compare our predictions with 3D numerical simulations and field measurements. The plan is then to model the sheltering effect between individual plants for high density planting and extend the analysis to oscillatory flow, which corresponds to wave propagation.