Interaction of a vortex pair with a flexible plate in an ideal quiescent fluid

Abstract

The coupled interaction of a cantilevered Kirchhoff–Love plate with two vortex filaments of equal and opposite circulation in an infinite incompressible, inviscid, and irrotational fluid domain is investigated. The vortices initially advect toward the cantilevered plate, which is oriented perpendicular to the direction of propagation of the vortex pair and undergoes cylindrical bending. As the pair approaches the plate, the pressure field induced by the vortices deflects the plate and initiates vibration of the structure. The vibration of the structure, in turn, alters the path of the two vortices. The level of interaction depends on the vortex circulation and on the ratio of the plate inertia to the fluid inertia, termed the mass ratio. In general, the vortices tend to pass around the plate and eventually advect away from the plate, albeit with a modified trajectory, which depends on the strength of the fluid and structure coupling. The energy imparted to the plate increases with increasing vortex circulation and decreasing mass ratio. The findings of this study provide an initial framework for assessing the energy that can be imparted to a plate for energy harvesting purposes by coherent fluid structures in the absence of viscous effects.