Asymptotic Study of Flows Induced by Oscillations of Cylindrical Bodies

Abstract

Hydrodynamic flows induced by translational oscillations of cylindrical bodies of various cross-sectional shapes are studied. The motion of fluid around oscillating bodies is described using the system of Navier–Stokes equations written in a generalized curvilinear coordinate system. Transition to a given body shape is implemented using a conformal mapping. The problem is solved using the method of successive asymptotic expansions under the assumption that the oscillation amplitudes are small. In each asymptotic approximation, the subproblems are solved numerically using the finite-difference method. Based on the results of the work, estimates of the hydrodynamic effect are obtained, the applicability of the high-frequency asymptotic approximation is estimated, and secondary stationary flows near cylinders are studied, in particular, the occurrence of directed stationary flows near an oscillating asymmetric body is considered with reference to the Joukowski airfoil.