Proper Orthogonal Decomposition Modes Research Articles

A closure mechanism for screech coupling in rectangular twin jets

The twin-jet configuration allows two different scenarios to close the screech feedback. For each jet, there is one loop involving disturbances which originate in that jet and arrive at its own receptivity point in phase (self-excitation). The other loop is associated with free-stream acoustic waves that radiate from the other jet, reinforcing the self-excited screech (cross-excitation). In this work, the role of the free-stream acoustic mode and the guided-jet mode as a closure mechanism for twin rectangular jet screech is explored by identifying eligible points of return for each path, where upstream waves propagating from such a point arrive at the receptivity location with an appropriate phase relation. Screech tones generated by these jets are found to be intermittent with an out-of-phase coupling as a dominant coupling mode. The instantaneous phase difference between the twin jets computed by the Hilbert transform suggests that a competition between out-of-phase and in-phase coupling is responsible for the intermittency. To model wave components of the screech feedback while ensuring perfect phase locking, an ensemble average of leading spectral proper orthogonal decomposition modes is obtained from several segments of large-eddy simulation data that correspond to periods of invariant phase difference between the two jets. Each mode is then extracted by retaining relevant wavenumber components produced via a streamwise Fourier transform. Spatial cross-correlation analysis of the resulting modes shows that most of the identified points of return for the cross-excitation are synchronised with the guided jet mode self-excitation, supporting that it is preferred in closing rectangular twin-jet screech coupling.

Compressed neural networks for reduced order modeling

Reduced order modeling (ROM) techniques, such as proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD), have been widely used to analyze stationary flows. Neural networks such as autoencoders are effective to reduce the dimension of non-stationary flow, but their larger storage requirements compared to POD and DMD compromise the expectations on ROM. The present work aims at compressing the autoencoder model via two distinctively different approaches, i.e., pruning and singular value decomposition (SVD). The developed algorithm is then applied to reconstruct the flow fields of typical stationary (i.e., a laminar cylinder flow and two turbulent channel flows) and non-stationary (i.e., a laminar co-rotating vortex pair) examples. It is shown that pruning and SVD reduce the size of the autoencoder network to 6% and 3% for the two simple laminar cases (or 18% and 13%, 20%, and 10% for the two complex turbulent channel flow cases), respectively, with approximately the same order of accuracy. Therefore, the proposed autoencoders optimized by the network pruning and SVD lead to effective ROM of both stationary and non-stationary flows although they require more iterations to converge than conventional methods.

A linear filter regularization for POD-based reduced-order models of the quasi-geostrophic equations

We propose a regularization for reduced-order models (ROMs) of the quasi-geostrophic equations (QGE) to increase accuracy when the proper orthogonal decomposition (POD) modes retained to construct the reduced basis are insufficient to describe the system dynamics. Our regularization is based on the so-called BV-α model, which modifies the nonlinear term in the QGE and adds a linear differential filter for the vorticity. To show the effectiveness of the BV-α model for ROM closure, we compare the results computed by a POD-Galerkin ROM with and without regularization for the classical double-gyre wind forcing benchmark. Our numerical results show that the solution computed by the regularized ROM is more accurate, even when the retained POD modes account for a small percentage of the eigenvalue energy. Additionally, we show that, although computationally more expensive than the ROM with no regularization, the regularized ROM is still a competitive alternative to full-order simulations of the QGE.

Ensemble learning model for effective thermal simulation of multi-core CPUs

An ensemble data-learning approach based on proper orthogonal decomposition (POD) and Galerkin projection (EnPOD-GP) is proposed for thermal simulations of multi-core CPUs to improve training efficiency and the model accuracy for a previously developed global POD-GP method (GPOD-GP). GPOD-GP generates one set of basis functions (or POD modes) to account for thermal behavior in response to variations in dynamic power maps (PMs) in the entire chip, which is computationally intensive to cover possible variations of all power sources. EnPOD-GP however acquires multiple sets of POD modes to significantly improve training efficiency and effectiveness, and its simulation accuracy is independent of any dynamic PM. Compared to finite element simulation, both GPOD-GP and EnPOD-GP offer a computational speedup over 3 orders of magnitude. For a processor with a small number of cores, GPOD-GP provides a more efficient approach. When high accuracy is desired and/or a processor with more cores is involved, EnPOD-GP is more preferable in terms of training effort and simulation accuracy and efficiency. Additionally, the error resulting from EnPOD-GP can be precisely predicted for any random spatiotemporal power excitation.

Characterization and low-order representation of the vortex meandering motion in upswept afterbody wakes

Vortex meandering is often characterized by seemingly stochastic motions of the vortex core. An elucidation of the underlying mechanisms of core movement aids not only in characterizing the meandering phenomenon but also forms a starting point to guide flow control techniques. This paper investigates the complex motion of longitudinal vortices behind an abstracted cargo aircraft fuselage. In contrast to wingtip vortices that arise in relative isolation, in this case the large aft region upsweep generates a meandering counter-rotating vortex pair that retains its coherence for long distances downstream. High-resolution spatio-temporal datasets obtained from large-eddy simulation of a cylindrical fuselage with longitudinally aligned axis and a sharp-edged base are used for this purpose. The circulation of each vortex in the pair initially increases immediately after formation and asymptotes to a near constant value downstream. Although the time-mean form of the vortices becomes nearly axisymmetric, the transient disorganized motions include time-local regions of opposite vorticity. The complicated meandering motion is decomposed using proper-orthogonal decomposition (POD) modes as primary building blocks. The first two modes constitute a mutually orthogonal |m|=1 elliptic pair, accounting for about 35% of the total energy; individually these modes account for the displacement of vortex cores along straight lines whose slopes coincide with their respective dipole axes. The wake outside of the immediate vicinity of the base displays low-rank behavior, in that the number of modes required to reproduce the flow to a given degree of accuracy diminishes rapidly. Beyond two fuselage (cylinder) diameters downstream, the two leading POD modes can reconstruct the dominant meandering motion and spatial structure in the LES data with less than 15% error using a suitable loss measure.

Dual-Orthogonal-Plane Particle Image Velocimetry Measurement of the Turbulent Flow in the Channel Head of a Large-Scale Steam Generator Mockup

Abstract In this work, a large-scale mockup of a compact complex system integrating a steam generator (SG) and a reactor coolant pump (RCP) is considered. The three-dimensional turbulent flow in the steam generator channel head (SGCH) is measured in detail. Dual-orthogonal-plane particle image velocimetry (PIV) is employed to extract high-resolution flow information in two orthogonal planes. Two separate measurements are first made to see the three-dimensional time-mean flow dynamics and the statistical quantities in the two planes. These measurements highlight two distinct flow phenomena: jet arrays and massive turbulent separation bubbles (TSBs). These patterns are attributed to mass flow redistribution in the U-shaped tubes. Proper orthogonal decomposition (POD) identifies the first POD mode as corresponding to the TSB breathing-like motion, which significantly intensifies the side view streamwise velocity fluctuations, leading to them reaching 370% of the local mean velocity. To examine the unsteady behavior of massively separated regions, the dual-orthogonal-plane PIV system is then synchronized to simultaneously measure variations in the flow fields, and the missing data due to illumination interference are reconstructed using gappy POD. The synchronized analysis reveals a direct relationship between the low-frequency fluctuations in the side and front views. These fluctuations are in phase across both views, indicating a synchronized behavior that spans the entire field. This large-scale low-frequency breathing motion has critical implications for numerical simulations and sheds light on the unsteady behavior of the RCP system within the SGCH.

Reduced-order modeling of conjugate heat transfer in lithium-ion batteries

Reduced-order modeling (ROM) techniques involving physics are gaining importance due to their ability to generate physically meaningful results swiftly and accurately. They are finding applications in design and optimization and in digital twins where real-time results are required. The proper orthogonal decomposition (POD)-Galerkin ROM based on finite volume discretization methodology is utilized here for solving a high-dimensional system in a reduced dimensional space in which the reduced basis is spanned by the POD modes. The reduced-order equations are obtained by projecting the discretized form of the full-order model (FOM) equations onto the reduced basis which eliminates the need for boundary control techniques. The proposed methodology is demonstrated for transient conjugate heat transfer (CHT) in an electric vehicle battery. The POD modes are computed using simulation data for three Reynolds numbers and the ROM is evaluated for transient analysis of temperature from initial state to steady state for seven Reynolds numbers. The ROM predictions are fairly accurate both in the interpolated and the extrapolated regions with significant computational speed-up. Five modes are sufficient for constructing the fluid and battery temperature ROM solution. The ROM computational speed-up obtained with 5 modes is approximately 4–7.4 times compared to the FOM. The proposed methodology is generic and can be readily applied for any engineering system involving CHT.

Fluid–structure–surface interaction of a flexibly mounted pitching and plunging flat plate in proximity to the free surface

This experimental study investigates the fluid–structure–surface interactions of a flexibly mounted rigid plate in axial flow, focusing on flow-induced vibration (FIV) response and vortex dynamics of the system within a reduced velocity range of $U^*=0.29\unicode{x2013}8.73$ , corresponding to a Reynolds number range of $Re=518\unicode{x2013}15\,331$ . The plate, with one and two degrees of freedom (DoFs) for pitching and plunging oscillations, is examined at various submerged heights near the free surface. Results show that the plate exhibits divergence instability at low reduced velocities in both 1DoF and 2DoF systems. As the flow velocity surpasses a critical reduced velocity, periodic limit-cycle oscillations (LCOs) occur, increasing in amplitude until a second critical reduced velocity is reached. Beyond this point, LCOs are suppressed, and the plate experiences an increased static divergence angle with further flow velocity increase. The proximity to the free surface significantly influences the FIV response, with decreasing submerged heights leading to reduced LCO amplitudes and a shift of instabilities to higher reduced velocities. Vortex dynamics are analysed using time-resolved volumetric particle tracking velocimetry and hydrogen bubble flow visualisation. The analysis reveals disruptions in the symmetric flow field near the free surface, causing elongation and fragmentation of vortices in the wake of the plate, as well as vortex coupling. Proper orthogonal decomposition (POD) identifies dominant coherent structures, including leading-edge and trailing-edge vortices, captured in the first and second paired modes. On the other hand, higher POD modes capture the interaction of vortices in the wake and near the free surface.

A local ROM for Rayleigh–Bénard bifurcation problems

This work presents a local reduced-order method for computing bifurcation diagrams in 2D Rayleigh–Bénard convection problems. The proposed method is based on Proper Orthogonal Decomposition, and employs a reduced-order study of the regularity of solutions to detect new solution branches within the bifurcation diagram. The locality of the method is achieved through k-means clustering, and the selection of local problems in the online stage is done in the solution space. All hyperparameters of the reduced method, such as the number of clusters or the number of POD modes, are estimated by deterministic criteria. Furthermore, the offline–online splitting strategy for online calculations is explicitly outlined. The method is applied to a single-parameter problem and a two-parameter problem, showing its ability to rapidly compute bifurcation diagrams with small errors. Compared to a standard approach that samples each branch separately, the local approach produces more accurate results in less computational time.

The reduced-order model of 5 × 5 fuel rod bundles

The fuel rod bundles are the core part of pressurized water reactors (PWRs), and its heat transfer characteristics directly impact the safety of PWRs. A computational fluid dynamics (CFD) model of 5 × 5 fuel rod bundles with a spacer grid is established, and the numerical simulation results are in excellent agreement with the experimental results. Then, the effects of four turbulence models, namely shear stress transport model, standard k–ε model, re-normalization group k–ε model, and realizable k–ε model on the thermal-hydraulic characteristics of the 5 × 5 fuel rod bundles are systematically investigated. Furthermore, two data-driven methods, namely proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD), are used to analyze the flow fields of the 5 × 5 fuel rod bundles. The two methods can extract key modes or features to enhance the comprehension and description of the dynamic behaviors within the flow fields of 5 × 5 fuel rod bundles. Finally, two reduced-order models (ROMs), called the POD-radial basis function neural network surrogate model and DMD method, are constructed, which can enable rapid prediction of the flow fields for 5 × 5 fuel rod bundles with high accuracy. The CFD simulation results presented in this paper can provide valuable insights for studying the thermal-hydraulic characteristics of the 5 × 5 fuel rod bundles. The two ROMs proposed in this paper can significantly reduce the computational costs associated with studying the thermal-hydraulic characteristics of 5 × 5 fuel rod bundles.

Scale-adaptive simulation of the separated flow past a 90°-inclined prolate spheroid

The separated flow past a 6:1:1 spheroid is numerically investigated by means of the scale-adaptive simulation technique. The Reynolds number based on the free-stream velocity and the diameter at middle-section of the spheroid is located in the subcritical regime, i.e., Re = 3900. In comparison with the circular cylinder at the same Reynolds number, about 35% drag reduction is acquired by the spheroid, and the fluctuations of lift and drag are suppressed effectively. According to the detailed comparison, the satisfactory drag reduction and suppression of fluctuating force obtained by the spheroid are closely associated with the higher base-pressure and lower turbulent fluctuations in the near wake. Abundant contrasts of the different spanwise sections are presented to reveal the mechanism of constrained flow and apex effect of the spheroid. In addition, in order to provide reliable data for testing and developing turbulence models, a large number of turbulence statistics are computed and compared with previous data of the circular cylinder and sphere at comparable Reynolds numbers. Lower Reynolds stress peaks and less vigorous coherent structures indicate that the three-dimensional force and constrained flow caused by the spheroid can lead to the formation of steady shear layer and vortex separation. Furthermore, proper orthogonal decomposition and dynamic mode decomposition are employed to understand the large-scale wake flow structures behind the spheroid. The modal analysis results confirm that the wake of the spheroid is more stable than the circular cylinder, reconfirming the effective flow control.

Data-driven modal analysis of turbulent momentum exchange and heat transfer in composite porous fluid systems

This paper investigates the dynamics governing turbulent momentum exchange and heat transfer between pore flow within porous media and the turbulent flow passing over it. Employing high-fidelity pore-scale large eddy simulation, our investigation explores the fundamental mechanisms driving these phenomena. Modal analysis based on snapshot proper orthogonal decomposition (POD) is employed to quantify the modes of interaction between porous and non-porous regions, providing a comprehensive understanding of the underlying processes. Spatial and temporal modes reveal the existence of localized flow structures at the pore scale, contributing to time-varying patterns of information exchange. At the commencement of the porous block, the mean flow (Mode = 0) from the porous to non-porous region is the dominant mechanism in momentum exchange and heat transfer. This mode facilitates convective heat transfer from the porous to the non-porous region through upward and forward flow movements, showcasing positive flow leakage. In addition to the mean flow, the turbulent flux inherent in alternate POD modes (Mode ≠ 0) plays a substantial role in information propagation, influencing diverse directions. Spatial modes, complemented by statistical analysis, uncover a significant likelihood of observing negative vertical velocity values in the wake of the porous ligaments at the porous-fluid interface, indicative of negative flow leakage. This negative flow leakage precisely corresponds to the local penetration of fluid from the non-porous region into the porous region. Furthermore, our study reveals that information exchange via turbulence fluctuations manifests through complex outward and inward interactions in regions characterized by substantial positive flow leakage. Notably, these regions exhibit a distinct tendency for high-momentum streamwise-oriented flow to migrate outward from the porous region into the non-porous region (outward interactions). Conversely, inward interactions arise in these regions when the instantaneous magnitude of positive flow leakage is smaller than the mean value of positive flow leakage, emphasizing the pulsating nature of positive flow leakage. Finally, the distribution of the Nusselt number highlights that more than 60% of total heat transfer occurs within the initial one-third of the porous block length. Significantly, a notable portion of the porous ligaments experiences insufficient cooling due to positive flow leakage, underlining the critical implications of these findings for the understanding of turbulent momentum exchange and heat transfer in a composite porous-fluid system.

Flow fields prediction for data-driven model of 5 × 5 fuel rod bundles based on POD-RBFNN surrogate model

The fuel rod bundles are a crucial component of nuclear reactors. Research the flow characteristics of the fuel rod bundles can be computationally expensive, despite some progress made in the past few decades. In this paper, the fast prediction of flow fields for 5 × 5 fuel rod bundles is implemented based on a data-driven algorithm. First, a refined model of the 5 × 5 fuel rod bundles with spacer grid is established, and meshes are generated using a hybrid meshes technology. Then, the flow characteristics of the 5 × 5 fuel rod bundles are extensively analyzed using Computational Fluid Dynamics (CFD) methods. A comparison between the CFD results and experimental data reveals a strong agreement, thereby validating our research findings. Subsequently, a reduced-order model (ROM) called the proper orthogonal decomposition (POD)-radial basis function neural network (RBFNN) surrogate model is proposed. the POD algorithm is utilized to extracting the dominant flow modes, and the RBFNN is employed to predict the POD mode coefficients of non-sample points. By linearly combining the predicted POD mode coefficients with the POD modes, rapid prediction of flow fields for non-sample points can be achieved. Compared to the full-scale CFD simulations, it finds that the proposed POD-RBFNN surrogate model not only significantly improved efficiency, but also maintained a high level of predictive accuracy. It is believed that the research results hold important value for CFD calculations within nuclear reactor cores.

On the discrepancies between POD and Fourier modes on aperiodic domains

The application of Fourier analysis in combination with the Proper Orthogonal Decomposition (POD) is investigated. In this approach to turbulence decomposition, which has recently been termed Spectral POD (SPOD), Fourier modes are considered as solutions to the corresponding Fredholm integral equation of the second kind along homogeneous-periodic or homogeneous coordinates. In the present work, the notion that the POD modes formally converge to Fourier modes for increasing domain length is challenged. A family of analytical correlation functions parametrized by the Taylor macro/micro scale ratio (MMSR) is investigated numerically. The results of the analysis indicate that the discrepancy between POD and Fourier modes along locally translationally invariant coordinates is coupled to the MMSR of the flow. Increasing discrepancies are observed for smaller MMSRs, which are characteristic of low Reynolds number flows. The asymptotic convergence rate of the eigenspectrum matches the corresponding convergence rate of the exact analytical Fourier spectrum of the kernel in question, even for extremely small domains and small MMSRs where the corresponding DFT spectra suffer heavily from windowing effects. The Taylor micro scales are consistently underestimated when reconstructed using Fourier modes—failing to converge to the correct value even if all Fourier modes are used—while these are accurately reconstructed using POD modes.

Nonlinear dimensionality reduction then and now: AIMs for dissipative PDEs in the ML era

This study presents a collection of purely data-driven workflows for constructing reduced-order models (ROMs) for distributed dynamical systems. The ROMs we focus on, are data-assisted models inspired by, and templated upon, the theory of Approximate Inertial Manifolds (AIMs); the particular motivation is the so-called post-processing Galerkin method of Garcia-Archilla, Novo and Titi. Its applicability can be extended: the need for accurate truncated Galerkin projections and for deriving closed-formed corrections can be circumvented using machine learning tools. When the right latent variables are not a priori known, we illustrate how autoencoders as well as Diffusion Maps (a manifold learning scheme) can be used to discover good sets of latent variables and test their explainability. The proposed methodology can express the ROMs in terms of (a) theoretical (Fourier coefficients), (b) linear data-driven (POD modes) and/or (c) nonlinear data-driven (Diffusion Maps) coordinates. Both Black-Box and (theoretically-informed and data-corrected) Gray-Box models are described; the necessity for the latter arises when truncated Galerkin projections are so inaccurate as to not be amenable to post-processing. We use the Chafee-Infante reaction-diffusion and the Kuramoto-Sivashinsky dissipative partial differential equations to illustrate and successfully test the overall framework.

A hybrid proper orthogonal decomposition and next generation reservoir computing approach for high-dimensional chaotic prediction: Application to flow-induced vibration of tube bundles.

Chaotic time series prediction is a central science problem in diverse areas, ranging from engineering, economy to nature. Classical chaotic prediction techniques are limited to short-term prediction of low- or moderate-dimensional systems. Chaotic prediction of high-dimensional engineering problems is notoriously challenging. Here, we report a hybrid approach by combining proper orthogonal decomposition (POD) with the recently developed next generation reservoir computing (NGRC) for the chaotic forecasting of high-dimensional systems. The hybrid approach integrates the synergistic features of the POD for model reduction and the high efficiency of NGRC for temporal data analysis, resulting in a new paradigm on data-driven chaotic prediction. We perform the first chaotic prediction of the nonlinear flow-induced vibration (FIV) of loosely supported tube bundles in crossflow. Reducing the FIV of a continuous beam into a 3-degree-of-freedom system using POD modes and training the three time coefficients via a NGRC network with three layers, the hybrid approach can predict time series of a weakly chaotic system with root mean square prediction error less than 1% to 19.3 Lyapunov time, while a three Lyapunov time prediction is still achieved for a highly chaotic system. A comparative study demonstrates that the POD-NGRC outperforms the other existing methods in terms of either predictability or efficiency. The efforts open a new avenue for the chaotic prediction of high-dimensional nonlinear dynamic systems.

A novel accelerated convergence method for solving adjoint equations based on modal reduction

The efficiency of adjoint-based aerodynamic shape optimization depends critically on the solution efficiency of adjoint equations. In this letter, we employ the Proper Orthogonal Decomposition (POD) method to analyze the adjoint field samples and project them from the physical space into a low-order modal space. Subsequently, the full-order adjoint equations are reduced to low-order equations using the POD modes. Thus, we can efficiently predict the initial values for pseudo-time marching, thereby accelerating the solution of adjoint equations. Results indicate that the high-order POD modes are crucial for constructing the low-dimensional system. Moreover, this method can be seamlessly integrated with our previously established Dynamic Mode Decomposition (DMD) acceleration method to form a POD+DMD acceleration approach. Application of this approach to the flow past a National Advisory Committee for Aeronautics 0012 airfoil demonstrates a noteworthy 80.9% reduction in iteration numbers when solving the adjoint equations. Even for the airfoil located on the upper boundary of sampling space, the number of iterations is still reduced by 72.6%. Therefore, we believe that the proposed method holds significant promise for improving the efficiency of adjoint-based aerodynamic shape optimization in future research.

Coupled Dynamics of Steady Jet Flow Control for Flexible Membrane Wings

We present a steady jet-flow-based flow control of flexible membrane wings for the adaptive and efficient motion of bat-inspired drones in complex flight environments. A body-fitted variational computational aeroelastic framework is adopted for the modeling of fluid–structure interactions. High-momentum jet flows are injected from the leading edge and transported to the wake flows to alter the aerodynamic performance and the membrane vibration. The coupled dynamic effect of active jet flow control on membrane performance is systematically explored. While the results indicate that the current active flow control strategy performs well at low angles of attack, its effectiveness degrades at high angles of attack with large flow separation. To understand the coupling mechanism, the variations of the vortex patterns are examined by the proper orthogonal decomposition modes, and the fluid transport process is studied by the Lagrangian coherent structures. Two scaling relations that quantitatively connect the membrane deformation with the aerodynamic loads presented in our previous work are verified even when active jet flow control is applied. A unifying feedback loop that reveals the fluid–membrane coupling mechanism is proposed. These findings can facilitate the development of next-generation bio-inspired drones that incorporate smart sensing and intelligent control.

Investigation of Unsteady Combustion Regimes in a Kerosene-Fueled Scramjet with Air Throttling

This paper describes an experimental study investigating unsteady combustion regimes in a kerosene-fueled scramjet. The results are obtained under inflow conditions of a 2.9 MPa stagnation pressure, 1900 K stagnation temperature, and a Mach number of 3.0. The air throttling position is 240 mm downstream of the combustor entrance, with an air throttling flow rate (ratio of air throttling mass flux to inflow mass flux) of 38% and a fuel equivalence ratio of 0.37. Combustion is relatively stable when air throttling is applied and is dominated by auto-ignition. When air throttling is turned off, the combustion becomes more unsteady and is dominated by flame propagation. At the same time, the combustion mode changes, and the frequency of the combustion mode transition is 286 Hz. Schlieren images and one-dimension analysis show that the effect of air throttling is the coupling of cold throat (aerodynamic throat) and hot throat (thermal throat). The proper orthogonal decomposition and dynamic mode decomposition analysis present that when air throttling is applied or removed, the frequencies of injector–flame feedback are almost the same, while the frequencies of shock–flame feedback exhibit considerable variation, which is caused by the location of the precombustion shock affected by air throttling.

Data-driven modal decomposition of R134a refrigerant cavitating flow in Venturi tube

This study utilized high-speed camera and large eddy simulation methods to explore the cavitating flow mechanisms and turbulence structures of R134a refrigerant inside a Venturi tube under varying cavitation numbers (CNs). Data-driven modal analysis approaches, proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD), were introduced to identify and extract the energy hierarchy and transient characteristics within the cavitating flow. The analysis of grayscale images indicated that the cavitating flow gradually transitioned from quasi-periodic to unsteady flow as the CN decreased, and the severity of cavitation correlates with lower peak frequencies. The POD analysis facilitated the extraction of coherent structures in the cavity's temporal evolution, and the results indicate that the quasi-ordering shedding and collapse of large-scale cavity clouds predominantly occur under low cavitation intensity conditions. As the CN increases, the influence of small-scale cavity shedding becomes more significant. The first 30 most energetic modes occupied over 75% of the entire energy, and they were used to reconstruct the cavitating flow, achieving good consistency with transient flow snapshots. Additionally, the DMD results of the cavitating flow yield three frequency spans, including several prominent characteristic frequencies. These spans are closely linked to the cavity cloud structures of varying scales, unveiling the structural characteristics of unsteady cavitating flow.