Flow induced by superposed oscillations of a circular cylinder

The temporal development of two-dimensional viscous incompressible flow induced by an impulsively started circular cylinder which performs rotational and recti-linear vibrations is considered. These oscillations are harmonic and superimposed on the constant translational velocity to examine the effect of increase of the perturbation amplitude and of the oscillation frequency on the near-wake structure and the hydrodynamic forces acting on the cylinder. The motion is governed by the Navier-Stokes equations and the method of solution is based on the use of truncated Fourier series representations for the stream function and vorticity in the angular polar coordinate. The Navier-Stokes equations are reduced to ordinary differential equations in the spatial variable and these sets of equations are solved by using finite difference methods, but with the boundary vorticity calculated using integral conditions rather than local finite-difference approximations. Comparisons are made with previous existing results to validate the solution methodology.