Multiple modes of vortex-induced vibration of a sphere

In this work, we discover the existence of multiple modes, of vortex-induce d 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-amplitu de and remarkably periodic vibrations, was discovered by changing our focus fi om "light", or buoyant, tethered spheres in a water facility (where rel ative 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 wid e range of normalized velocities, U* = 0 - 300, and investigate a wide rang e of masses, m* = 0.1 - 1000. The first two modes might be identified as an alogies 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 freque ncy with the natural frequency. These modes of sphere dynamics occur within the velocity regime U* similar to 5 - 10. However, our Mode III occurs ove r a broad range of high velocity (U* similar to 20 - 40), where the body dy namics cannot be synchronised with the principal vortex formation frequency . At extremely high velocities (U* > 100), we find yet another mode of vibr ation that persists to at least U* > 300, which we define as Mode IV, but i n this case the unsteady oscillations are characterized by intermittent bur sts of vibration. Regarding the periodic Mode III, it cannot be explained b y classical "lock-in" of the principal vortex shedding and body motion, and one is left with a tantalizing question: What causes this unexpected perio dic high-speed mode of vortex-induced vibration? (C) 2001 Academic Press.