Asymptotic theory of the oscillatory motion of a cylindrical body in a fluid

This work investigates the hydrodynamics of a rigid cylindrical body with an arbitrary cross-section undergoing arbitrary translational oscillations in a viscous incompressible fluid. An asymptotic solution is derived analytically in a high-frequency, small-amplitude approximation, using a generalised curvilinear non-inertial coordinate system. The solution yields analytical expressions for the three components of the hydrodynamic force: the added mass, the Basset force and the viscous drag. These general dependencies are used to analyse the hydrodynamic loads on various oscillating cylinders, including an elliptical cylinder, a symmetric Zhukovsky aerofoil, a rounded polygonal profile (defined as a hypotrochoid) and a rectangular cylinder. For sharp-edged bodies, limitations are discussed. The range of applicability of the developed theory is assessed by comparing its predictions with numerical simulations and experimental data. The appendix provides formulas for calculating the hydrodynamic force coefficients in the Morison form for bodies of different shapes.