This study considered a 2-D numerical simulation with LES modeling of a sinusoidal oscillatory flow heading at different directions from an imposed uniform flow. The numerical simulation considered the time-dependent, 2-D, incompressible Navier-Stokes equations in polar coordinates using primitive variables with a combined spatial approximation of the central differencing scheme and the Fourier spectral method. A newly implemented combination of Dirichlet and spatial Convective Projection boundary conditions is proposed to assure traveling waves, from the time-dependent flow structures formed at the cylinder surface, to be convected undisturbed outside the flow field.

It is found that the drag and inertia coefficients of the wavy flow are reduced with the increased strength of the imposed uniform flow as long as the wavy flow is parallel to the uniform flow. The change in the heading angle of the wavy flow from that of the imposed uniform flow affects the trend behavior of these coefficients in an unpredictable manner which requires further investigation. Another important result is that the heading angle has no observable effect on the trend of drag and inertia coefficients as the Keulegan Carpenter number changes. A minor exception is observed when the heading angle is between 0 (deg) and 90 (deg) due to the complicated dominance between the two flow types on the behavior of the flow field structures that can lead to negative values of drag coefficients.

Finally, the major effect of the heading angle is restricted in being a magnifier of the transverse force acting on the cylinder surface and in reducing the sensitivity of the inline force on the Keulegan Carpenter number as the strength of the imposed uniform flow increases.