Boundary conditions for the envelope of canopy interacting with two dimensional laminar flow*

To reveal the mechanisms of collective motions of fibers clamped on a flat wall (i.e., canopy) subjected to fluid flow, boundary conditions at the envelope of canopy are proposed for synchronous and asynchronous motions of fibers, where fibers exhibit identical and individual motions, respectively. By assuming small deflection, the fibers are modeled as rigid bars installed with torsion springs. The effects of fluid forces on the fibers are expressed as the moments of fluid forces through averaging Navier-Stokes equations. The time-development of the envelope for synchronous motion of fibers is represented with mass-spring-damper system driven by the flow over the canopy. As the non-uniformity of fibers' motion is enhanced, the effects of fluid inertia in the wall-normal direction and diffusion of fiber velocities have more important role. The results of the simulations with our models are compared with those of fluid-structure interaction (FSI) simulations, which directly solve the interaction forces between the individual fluid and fibers, to assess the validity of the models. It is remarkable that the grid resolutions have such little influence on the results that one fluid mesh size can be set larger than inter-fibers.