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 Lz 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 Lz 3.5D , only the vortex-shedding frequency harmonics are present. One-third of the vortex-shedding frequency component appeared in Lz 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 Lz 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.