This study uses the boundary perturbation method to investigate the motion of a slightly distorted circular cylinder around another circular one. An approximate complex velocity potential is derived by means of successive images. The hydrodynamic interaction between these cylinders is computed based on the dynamical equations of motion. In a relative coordinate system moving with the uniform stream, the kinetic energy of the fluid is expressed as a function of fifteen added masses. Approximate analytical solutions of added masses in series form are obtained and applied to determine the trajectories of a slightly distorted circular cylinder around a fixed circular cylinder. Numerical results show that the initial configuration of the slightly distorted circular cylinder has a decisive influence on the development of its subsequent rotational motion.
Accurate prediction of the motion of a body moving around another in an unbounded fluid and determination of the hydrodynamic interaction between them have a variety of applications to the polar and offshore engineering. For example, when an ice floe moves near an offshore structure, the hydrodynamic interaction between these bodies becomes significant. Therefore, in the design of an offshore drilling platlbrm in the arctic region, engineers may have to consider the motion of drifting ice floes, conveyed by a stream, around the platform, and to predict whether the drifting body would collide with the platform. In practical cases, the Reynolds number based on the characteristic size of the offshore structure is usually large, the potential-flow theory would provide a good approximation of physical situations (Wu and Landweber, 1960) and the effect due to the fluid viscosity may be dealt with separately (Mofison et al., 1950; Sarpkaya and Isaacson, 1981). The problem of two parallel circular cylinders translating in an unbounded fluid was first considered by Hicks (1879).