Experiments in Fluids 18 (1995) 153-163 9 Springer-Verlag 1995 Numerical and experimental study of the interaction between a vortex and a circular cylinder R. Verzicco, J. B. Flbr, G. J. F. van Heijst, P. Orlandi dipole Abstract This paper describes a study of the centred collision between a dipolar vortex and a solid circular cylinder. The flow was analysed experimentally by using dye visualizations and streak photography. Flow characteristics such as vorticity fields and the transport of passive tracers were compared with numerical simulations. Observations revealed that thin layers of vorticity, created at the cylinder wall are advected by the primary dipole halves, which, while rolling up into compact patches, give rise to the formation of two new asymmetric dipoles that move away along curved trajectories. The structure of the vorticity distribution inside the dipole, before and after the collision, has been investigated. Both the numerical and the experimental results indicate that the vorticity patches originating from the original primary dipole approximately preserve their original functional relationship co =f(~), while the secondary vorticity patches show a tendency to organize into structures attaining a similar relationship. 1 Introduction The interaction of vortices with a flow boundary is a funda- mental fluid dynamic topic to which much attention has been given in the past, and which still continues to attract the interest of many investigators. The interest in this subject is partially due to practical applications, (e.g. the sound generation by a jet impinging on a wall, the free-surface signature by the trailing vortices of submarines or the behaviour of vortices produced by an aircraft during landing or take-off at an airstrip), and partially in order to gain a better insight in the fundamental dynamics of vorticity in such flow situations. The case of a pair of rectilinear, infinitely long, vortices impinging on a solid flat wall has been widely investigated both Received: 29 July 1993/Accepted: 17 January 1994 R. Verzicco, P. Odandi Dipartimento di Meccanica e Aeronautica, Universit~ di Roma "La Sapienza", I-oo184 Roma, Italia J. B. Fl6r, G. J. F. van Heijst Fluid Dynamics Laboratory; Eindhoven University of Technology, NL-56oo MB Eindhoven, The Netherlands One of us (JBF) gratefully acknowledges financial support by the Foundation for Fundamental Research on Matter (FOM) of the Netherlands Organization for Pure Research (NWO). numerically and experimentally (e.g. Homa et al. 1988; Orlandi, 199o) and it has been found that the generation of secondary vorticity at the wall plays a fundamental role in the evolution of the flow. This vorticity typically organizes into compact structures that interact with the primary vortex and, depending on the Reynolds number, may lead to new structures that are intense enough to migrate away far from the wall. The viscous generation of secondary vorticity at a solid boundary is also responsible for the separation of a wall jet, as was studied experimentally by Lichter et al. (1992). Similar features have been found in the interaction of a vortex dipole with a circular cylinder. In the present study we will not focus on the mechanism producing the secondary vorticity since it does not substantially differ from what occurs on flat walls. This mechanism has been studied experimentally and theoretically by Walker et al. (1987) for a vortex ring impinging on a flat wall. In the case of a circular cylinder, however, the curvature of the boundary and the possible misalignment between dipole and cylinder, add two important parameters that make the dynamics of the flow more complex. Among the experimental studies, that by Voropayev and Afanasyev (1994) proposes an explanation of the interaction in terms of the momentum applied by the cylinder to the flow in a way similar to the interaction between two dipoles of different intensity (van Heijst and F16r, 1989). In a recent numerical study Orlandi (1993) considers a number of cases in which a Lamb dipole interacts with a solid cylinder with either no-slip or free-slip boundary conditions applied to the body. In the latter case the dipole is observed to split, upon which the parts move around the cylinder, meet again at its rear, thus leading to the re-formation of the vortex dipole. It was found that the dipole retains its original shape; scatter plots between vorticity co and stream function ~ confirm that the linear relationship is attained again after the collision. On the other hand, when the no-slip condition is applied the secondary vorticity, generated at the wall, interacts with the primary vortex and leads to the formation of two asymmetric dipolar structures that move along circular trajectories. Although the scatter-plots in this case contain some scatter, the secondary vorticity patches show a dear tendency to attain the linear relationship as well. The principal aim of this study is to gain a better understanding of the physics of the interaction process; particular aspects that will be addressed are the evolution of the vorticity field and the influence of the cylinder diameter in relation to the dipole. It has been found that the smaller the diameter of the cylinder, the higher is the peak vorticity produced at the wall and the more intense are the vorticity 153