Title: Uncovering triadic interaction relationships latent in Mode A behind a circular cylinder Show Chinese title

Title: 揭示圆柱后模态A中存在的三元交互关系

Abstract: 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. Show Chinese abstract

Abstract: 流场中多个低频成分之间的相干性表征了流体力学的非线性特性。 本研究揭示了圆柱尾流经典模式A中存在的不同频率成分及其相互作用关系。 主要频率成分包括三分之一的卡门涡脱落频率（三倍次谐波）和气泡泵动，这与先前的研究一致。 然而，在数值模拟中，当展向域尺寸足够大时，它们的相互作用会被众多频率成分所掩盖。 为了解决这一问题，我们引入了一种逐步扩展展向域尺寸的过程，从较小的尺寸开始，逐渐将其从3.3D增加到4.7D，其中D表示圆柱直径。 从3.3D到3.5D，仅存在涡脱落频率的谐波。 三倍次谐波频率出现在3.5D到3.7D之间。 双谱模态分解表明，在此尺寸范围内，三倍次谐波频率的谐波主导着流场。 气泡泵动在3.7D到3.8D的流场中显现。 在这之后出现的频率成分不仅包括气泡泵动的谐波，而且其周期性行为被破坏。 气泡泵动、卡门涡和三倍次谐波成分之间的非线性相互作用使流场的时间行为变得复杂。 通过限制展向域尺寸，我们的方法有效地揭示了具有大量频率成分的流场中固有频率成分之间的相互作用关系。