On the stability of interacting flapping plates

The motion of several plates in an inviscid and incompressible fluid is studied numerically, the general motivation being to understand the hydrodynamic interactions in schooling and flocking behavior in animal collectives. We consider two to four plates initially placed in-line, one behind the other, separated by a specified distance d0, and move each in the vertical direction with a prescribed oscillatory motion. This yields horizontal plate motion due to their self-induced thrust and the fluid drag forces. The plates are observed to approach an equilibrium distance between each other that depends on d0, with the front plate moving practically the same as a single plate. In this talk we address the stability of these equilibria. We find that the equilibria lose stability as either the number of plates increases, or the oscillation amplitude decreases. A simple mechanism is implemented and shown to successfully stabilize the motion. The stabilization has a remarkable impact on the regularity of the vortex pattern in the wake.