Co-existence of A and B modes in the cylinder wake at [formula omitted

Abstract

We address the issue of co-existence of the modes A and B in the infinite cylinder wake after the onset of three-dimensionality. To distinguish them from each other we use the opposite symmetry of their time Fourier modes obtained by integrating the periodic flow field over one vortex shedding period. As argued in a recent paper, a relatively significant spanwise period of the simulation has to be considered to obtain a realistic simulation of the infinite spanwise geometry. This spanwise period of the simulation is taken equal to 10πd, d standing for the cylinder diameter, which amounts to 8 times the linearly preferred wavelength. In this numerical configuration the 3D state is found fully chaotic and stable down to the Reynolds number (Re) of 170. The obtained asymptotic state is analyzed to evidence the fingerprint of either of the modes A and B by time Fourier analysis. The results show the presence of both modes, which allows us to conclude that the mode B is excited simultaneously with the onset of mode A by non-linear couplings and that the progressive emergence of the mode B, described by Williamson as an “energy transfer” from frequencies associated to mode to those of mode B, observed experimentally to start from Re=220, occurs actually along the whole discontinuous branch of the Williamson Strouhal vs. Reynolds number curve. This explains why a bifurcation giving rise to the mode B has never been observed.