Multiple modes of vortex-induced vibration of a sphere

In this work, we discover the existence of multiple modes, of vortex-induced vibration of a tethered sphere in a free stream. In addition to the first two modes, defined as Modes I and II, and found originally by Govardhan & Williamson (1997), we find the existence of an unexpected Mode III at much higher normalized velocities (U*). This third mode, involving large-amplitude and remarkably periodic vibrations, was discovered by changing our focus fi om "light", or buoyant, tethered spheres in a water facility (where relative density, m* < 1), to "heavy" spheres in wind tunnel facilities (where m* much greater than 1). In this manner, we are able to achieve a very wide range of normalized velocities, U* = 0 - 300, and investigate a wide range of masses, m* = 0.1 - 1000. The first two modes might be identified as analogies to the 2S and 2P modes for an excited cylinder (Williamson & Roshko 1988), and can be associated with a lock-in of the vortex formation frequency with the natural frequency. These modes of sphere dynamics occur within the velocity regime U* similar to 5 - 10. However, our Mode III occurs over a broad range of high velocity (U* similar to 20 - 40), where the body dynamics cannot be synchronised with the principal vortex formation frequency. At extremely high velocities (U* > 100), we find yet another mode of vibration that persists to at least U* > 300, which we define as Mode IV, but in this case the unsteady oscillations are characterized by intermittent bursts of vibration. Regarding the periodic Mode III, it cannot be explained by classical "lock-in" of the principal vortex shedding and body motion, and one is left with a tantalizing question: What causes this unexpected periodic high-speed mode of vortex-induced vibration? (C) 2001 Academic Press.