非均匀介质中的对流不稳定性：亚临界圆柱尾流中的脉冲响应

Forecasting subcritical cylinder wakes with Fourier Neural Operators

We apply Fourier neural operators (FNOs), a state-of-the-art operator learning technique, to forecast the temporal evolution of experimentally measured velocity fields. FNOs are a recently developed machine learning method capable of approximating solution operators to systems of partial differential equations through data alone. The learned FNO solution operator can be evaluated in milliseconds, potentially enabling faster-than-real-time modeling for predictive flow control in physical systems. Here we use FNOs to predict how physical fluid flows evolve in time, training with particle image v…

On Some Modal Implications of the Dynamic Mode Decomposition Through the Lens of a Subcritical Prism Wake

The Dynamic Mode Decomposition (DMD) is a Koopman-based algorithm that straightforwardly isolates individual mechanisms from the compound morphology of direct measurement. However, many may be perplexed by the messages the DMD structures carry. This work investigates the modal implications of the DMD/Koopman modes through the prototypical subcritical free-shear flow over a square prism. It selected and analysed the fluid mechanics and phenomenology of the ten most dominant modes. The results showed that the reduced-order description is morphologically accurate and physically insightful. Mode 1…

Phase-synchronization properties of laminar cylinder wake for periodic external forcings

We investigate the synchronization properties of the two-dimensional periodic flow over a circular cylinder using the principles of phase-reduction theory. The influence of harmonic external forcings on the wake dynamics, and the possible synchronization of the vortex shedding behind the cylinder to these forcings, is determined by evaluating the phase response of the system to weak impulse perturbations. These horizontal and vertical perturbations are added at different phase values over a period, in order to develop a linear one-dimensional model with respect to the limit cycle that describe…

Phase-locking of laminar wake to periodic vibrations of a circular cylinder

Phase synchronization between the vortex shedding behind a two-dimensional circular cylinder and its vibrations is investigated using the phase-reduction analysis. Leveraging this approach enables the development of a one-dimensional, linear model with respect to the limit-cycle attractor of the laminar wake, which accurately describes the phase dynamics of the high-dimensional, nonlinear fluid flow and its response to rotational, transverse and longitudinal vibrations of the cylinder. This phase-based model is derived by assessing the phase-response and sensitivity of the wake dynamics to imp…

第一个$R_{cr}$作为二维定常尾流中卷吸长度的可能量度

The first $R_{cr}$ as a possible measure of the entrainment length in a 2D steady wake

在距产生尾流的物体固定距离处，只有当距离接近20个物体尺度时，才能看到卷吸随雷诺数（$R$）增加。这种增加水平高达雷诺数接近临界值的第一不稳定性的发病。在所考虑的$R$范围内（即[20 - 100]），对于所有定常尾流，在几乎相同的距离处观察到夹带几乎消失，这表明超临界定常尾流具有与亚临界尾流相同的夹带长度。据观察，该距离等于等于临界雷诺数（$\sim 47$）的值的物体长度的数量，如大量的实验结果汇编所示。{\it A fortiori}这些发现，我们建议解释非定常分岔作为一个过程，允许一个平滑的增加-重新分布的卷吸沿尾流根据对流的重量在扩散。已使用Navier-Stokes速度场的匹配渐近展开[Tordella和Belan，{\it Physics of Fluids}，15（2003）]确定了沿稳定尾流的卷吸变化，该展开建立在包括卷吸过程产生的横向速度匹配的标准上。

The Linear-Time-Invariance Notion of the Koopman Analysis-Part 2: Physical Interpretations of Invariant Koopman Modes and Phenomenological Revelations

This serial work presents a Linear-Time-Invariance (LTI) notion to the Koopman analysis, finding consistent and physically meaningful Koopman modes and addressing a long-standing problem of fluid-structure interactions: deterministically relating the fluid and structure. Part 1 (Li et al., 2022) developed the Koopman-LTI architecture and applied it to a pedagogical prism wake. By the systematic procedure, the LTI generated a sampling-independent Koopman linearization that captured all the recurring dynamics, finding six corresponding, orthogonal, and in-synch fluid excitation-structure respons…