Asymptotic Modeling of Viscous Fluid Flows Near Oscillating Cylindrical Bodies

In this paper, we study viscous fluid flows induced by vibrations of cylindrical bodies with different cross-sectional shapes. Hydrodynamics is described using the Navier-Stokes equation, the solution of which is carried out using the method of successive asymptotic expansions. The problem is solved in a generalized curvilinear coordinate system, given by a conformal mapping of the exterior profile of an oscillating body onto the exterior of a circle, which makes it possible to study the motion of a cylindrical body with an arbitrary section profile. Within the framework of the study, the hydrodynamic influence on cylindrical bodies of various cross-sectional shapes is analyzed, the structure of flows induced by oscillations is described and the applicability of the constructed asymptotic is studied.