Asymptotic Investigation of Hydrodynamic Forces Acting on an Oscillating Cylinder at Finite Streaming Reynolds Numbers

Abstract

The paper is devoted to the study of the problem of high-frequency low-amplitude harmonic oscillations of a circular cylinder in a viscous incompressible fluid. The study develops the classical method of successive asymptotic expansions of a solution into internal and outer, steady and oscillating components in terms of a small parameter. The case of finite streaming Reynolds numbers is considered. Using the original method for calculation of the hydrodynamic force components from external flow characteristics, analytical expressions for four terms of the force expansion were found. The obtained results allow to evaluate not only a linear response to perturbations of flow caused by oscillations of the cylinder, but also the effect of the non-linear interaction of harmonics in the boundary layer.