Symmetry of the flow around a circular cylinder

Abstract

The symmetry of the two-dimensional, viscous, and incompressible flow past a circular cylinder is studied by disturbing impulsively the steady flow at Reynolds number 10, 20, 40, and 100. The propagation of this disturmbance is studied by dividing the stream and vorticity functions into steady and perturbed stream and vorticity functions. The steady stream and vorticity functions are expanded in the finite Fourier sine series. The steady semianalytical solutions are obtained for the symmetrical flow as a limit of the time-dependent equations. The perturbed stream and vorticity functions are expanded in the finite Fourier sine and cosine series and then along with the steady stream and vorticity functions expansions substituted in the Navier-Stokes equations. This leads to a system of coupled parabolic partial differential equations in the coefficient functions of Fourier series which is solved numerically. This system is solved with the initial condition which corresponds to the applied impulsive velocity to the surface of the cylinder in the perpendicular direction of the flow. Asymmetric vortices are observed for the Reynolds number (Re) 40 and a slight oscillation of the trail of almost symmetrical wakes is seen for the Reynolds numbers 20 up to t = 100. The symmetrical standing vortices in the strictest sense are not observed for Re= 10 even up to t= 100. Vortex shedding is observed for Re = 100. For Reynolds number 10, the disturbance is applied continuously up to t = 1, and asymmetric vortices exist up to t = 100. The symmetry of the flow depends on the disturbance level in the flow even at Reynolds number 10.