The flow over a circular cylinder is numerically studied at $\mathrm{Re}=220$ (mode-A instability) by varying the computational domain size in the spanwise direction from $L_z=0$ to $252d$ ($d$ is the cylinder diameter) with a periodic spanwise boundary condition to investigate its effect on the flow structures and mean flow quantities. For a large spanwise domain size ($L_z=252d)$, the instantaneous flow fields reveal large-scale flow structures extending over approximately $45d$ in the spanwise direction (significantly exceeding the characteristics wavelength of $4d$ associated with the mode-A instability), accompanying vortex dislocation and alternating parallel and oblique shedding, whereas parallel shedding is mostly observed for $L_z\le 12d$. The necessity of large spanwise domains to capture these structures is further confirmed through the spanwise wave-number power spectrum and the spanwise two-point correlation of the sectional lift force. Since the vortex shedding phase varies along the spanwise direction at large $L_z$'s, the root-mean-square (rms) lift coefficient decreases towards zero with increasing $L_z$. However, when the sectional lift coefficient is introduced, its rms value converges to a certain value for $L_z\ge 24d$, and other mean flow statistics similarly reach convergence beyond this threshold. We also consider the Reynolds number of $\mathrm{Re}=300$ corresponding to mode-B instability. At this Reynolds number, vortex dislocation and oblique vortex shedding do not occur even at large $L_z$'s, and flow structures and mean flow quantities are accurately obtained for $L_z\ge 6d$.

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• Low Reynolds number flows
• Vortex shedding