Uncovering triadic interaction relationships latent in Mode A for the wake of a circular cylinder

This study reveals the presence of frequency components lower than the wake vortex-shedding frequency within the classical Mode A. Primaries are one-third of the vortex-shedding frequency and frequencies corresponding to recirculation bubble pumping, as previously studied. However, when the spanwise domain size $L_z$ in numerical simulations is sufficiently large, their interaction relationship becomes obscured. To clarify the interaction relationship, we introduce a process in which distinct frequency components gradually emerge by starting with a small spanwise domain of $3.3D$ and then increasing it to $4.7D$ , where $D$ represents the diameter of the cylinder. At $L_z \leqslant 3.5D$ , only the vortex-shedding frequency harmonics are present. One-third of the vortex-shedding frequency component appeared in $L_z \geqslant 3.6D$ . Bispectral mode decomposition and energy transfer analysis reveal that the difference interaction between the one-third-shedding frequency and the vortex-shedding frequency component transfers energy to another low-frequency component. The recirculation bubble pumping is evident in the flow fields $L_z \geqslant 3.8D$ . The frequency components after this emergence are not only the harmonics of the lowest-frequency component, and the periodic nature is disrupted, which is marked as a quasi-periodic state. Nonlinear interactions between the lowest-frequency component corresponding to recirculation bubble pumping, primary frequency components such as wake vortex shedding, and approximately one-third of the vortex-shedding frequency complicate the temporal behaviour of the flow field. Utilising the constraint of the spanwise domain size, our approach effectively reveals the interaction relationship among frequency components inherent in a flow field with several coherent spectral components.