Kármán Vortex Street behind a Circular Cylinder by the Series Truncation Method

Semianalytical solutions of the Navier-Stokes equations are presented for two-dimensional, viscous, and incompressible flow past a circular cylinder for Reynolds numbers 100, 200 and 500. The stream and vorticity functions are expanded in a finite Fourier series and then substituted in the Navier-Stokes equations. This leads to a system of coupled parabolic partial differential equations which are solved numerically. In order to excite the flow an asymmetric disturbance in the form of rotation at a constant angular velocity of a cylinder in clockwise and counterclockwise directions is introduced for a short time. This small disturbance very slowly triggers the start of vortex shedding. The flow pattern in the separated region, lift and separation angle oscillate with a definite pattern. The calculated drag, lift, pressure and vorticity distributions around the surface, separation angle and Strouhal number are compared with similar calculations and with available experimental data. Also, a comparison of the calculations has been made for Reynolds number 100 with N = 25 and N = 40.