Envelope boundary conditions for the upper surface of two-dimensional canopy interacting with fluid flow

Boundary conditions at the surface of a layer of flexible fibers (i.e. the canopy envelope) subjected to fluid flow are proposed for uniform and non-uniform motions of the fibers, where the fibers exhibit identical and individual motions, respectively, to understand the mechanisms of the swaying motion of the canopy. By assuming small deflections, the fibers are treated as rigid rods hinged to a flat wall and the effects of the hydrodynamic force on the fibers are expressed with the moment of fluid forces by averaging the Navier–Stokes equations. For the uniformly moving case, displacement of the envelope is represented by a mass-spring-damper system driven by the hydrodynamic force. As the non-uniformity of the canopy behavior enhances, the effects of the diffusion of fiber velocities and fluid inertia along the fiber stems play a more important role in the envelope displacement equation. Numerical simulations of fluid flow are conducted with the envelope displacement models as the boundary conditions at the canopy surface. The validity of the present models is assessed by comparison with the results of fluid–structure interaction (FSI) simulation, which directly solves the interaction between individual fibers and fluid by an immersed boundary method. With the envelope model for non-uniform displacement, the grid convergence of the numerical result is about a first order rate. The comparison of the terms in the envelope model for non-uniform displacement shows that diffusion of fiber velocities dominates the motion of fibers. The applicability of the model is assessed by varying the number density of the fibers.