Flow Around a Tethered Body: The Effect of Tether Length

The tethered cylinder may be considered an extension of the more familiar (and widely studied) freely oscillating cylinder. In particular, assuming that the tether does not provide significant mechanical damping it directly extends the work of Khalak and Williamson (1999), Govardhan and Williamson (2000) and Govardhan and Williamson (2003). In particular, as with a lightly damped oscillating cylinder, the tethered cylinder system exhibits a critical mass ratio, below which large amplitude oscillations are observed (Ryan et al. 2007). This critical mass ratio is observed to vary as a function of tether length. As part of their work, Ryan et al. (2007) observed a peak in maximum oscillation amplitude (for the particular case of m * = 0.2) at a tether length ratio of L * ≈ 2.0. However, no explanation for this local maximum was presented therein. This paper explores the reasons for this local peak, in addition to describing the structures in the wake of the cylinder as a function of tether length. Figure 1 describes the geometry of the problem. A cylinder is attached to a mass-less, inflexible tether who’s length may be described as the length ratio, L * = L/D; Where L is the length of the tether, and D is the diameter of the cylinder. An additional controlling parameter is the cylinder mass ratio, m*, defined as the ratio of the density of the cylinder to that of the working fluid. The equation of motion for the system may be written as ( ),* * DLFDLTJ osc=+ φφ (1) where J is the moment of inertia of the tethered body system, T is the tension within the tether, Fosc describes the fluid force acting to oscillate the body and φ describes the angular oscillation of the system about the mean layover angle θ. Details of the system may be found in Ryan et al. (2007). In particular, the moment of inertia is defined exactly a