Uncovering triadic interaction relationships latent in Mode A behind a circular cylinder

Coherence between multiple low-frequency components latent in the flow fields characterizes the nonlinear aspects of fluid dynamics. This study reveals the existance of the distinct frequency components and their interaction relation of the classical Mode A of the cylinder wake. Primaries are one-third of the Karman vortex shedding frequency (third-subharmonic) and bubble pumping, known as the previous study. However, when the spanwise domain size in numerical simulations is sufficiently large, their interaction is obscured by the presence of numerous frequency components. To address this, we introduce a process in which distinct frequency components gradually emerge by starting with a small spanwise domain size and then gradually increasing it from 3.3D to 4.7D, where D represents the diameter of the cylinder. From 3.3D to 3.5D, only the vortex shedding frequency harmonics are present. Third-subharmonic frequency appeared ranging from 3.5D to 3.7D. Bispectral mode decomposition reveals that the harmonics of the third-subharmonic frequency govern the flow in this domain size. The bubble pumping is emergence in the flow fields between 3.7D and 3.8D. The frequency component after this emergence is not only the harmonics of bubble pumping and periodic nature is disrupt. Nonlinear interactions between bubble pumping, the Karman vortex, and the third-subharmonic component complicate the temporal behavior of the flow field. Utilizing the constraint of the spanwise domain size, our approach effectively reveals the interaction relationship between frequency components inherent a flow field with a significant number of frequency components.