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An analysis of the effect of the jet initial conditions on the wavelet separated near-field acoustic pressure 分析射流初始条件对小波分离近场声压的影响
IF 2.2 3区 工程技术 Q2 MECHANICS Pub Date : 2024-11-21 DOI: 10.1007/s00162-024-00727-9
Stefano Meloni, Roberto Camussi, Christophe Bogey

This paper reports a parametric investigation of the effect of the nozzle exhaust initial conditions on the wavelet separated acoustic pressure generated by a single stream compressible jet in its near field from a database obtained by Large-Eddy Simulations of jet flows at M = 0.9 and Re = (10^5). The nozzle–exit boundary–layer conditions consist of different turbulence intensities for fixed thickness and several thicknesses in laminar conditions. Pressure time series are extracted from virtual probes distributed in the near field of the jets and the acoustic components of the near field pressure are extracted using a wavelet-based procedure able to decontaminate the signals from the hydrodynamic contribution. The reconstructed acoustic time series are analyzed in the frequency domain and in terms of Overall Sound Pressure Level (OASPL). The results show that both the boundary-layer thickness and the turbulence level significantly affect the acoustic pressure in terms of both intensity and directivity. In the laminar case, strong sideline components are observed and strongly depend on the boundary layer thickness. These components clearly appearing in the energy spectra are associated with the Kelvin–Helmholtz instability waves. For large nozzle-exit turbulence intensities, the acoustic field is more uniform and less intense in the sideline direction. On the other hand, the streamwise directivity of the acoustic pressure appears to be strictly correlated to the length of the jet potential core which strongly varies with the initial conditions.

本文报告了喷嘴排气初始条件对单流可压缩射流在其近场产生的小波分离声压的影响的参数研究,该参数是通过对 M = 0.9 和 Re =(10^5) 条件下的射流流进行 Large-Eddy 模拟获得的数据库。喷嘴出口边界层条件包括固定厚度下的不同湍流强度和层流条件下的多种厚度。压力时间序列是从分布在射流近场的虚拟探头中提取的,近场压力的声学分量则是通过一种基于小波的程序提取的,该程序能够从流体动力贡献中消除信号污染。对重建的声学时间序列进行了频域分析和整体声压级(OASPL)分析。结果表明,边界层厚度和湍流水平对声压的强度和指向性都有显著影响。在层流情况下,可以观察到很强的边线成分,并且与边界层厚度密切相关。这些明显出现在能谱中的成分与开尔文-赫尔姆霍兹不稳定波有关。在喷嘴出口湍流强度较大的情况下,边线方向的声场更加均匀,强度较低。另一方面,声压的流向指向性似乎与射流势核的长度密切相关,而射流势核的长度随初始条件变化很大。
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引用次数: 0
Analyzing particulate behavior in high-speed, high-altitude conditions through an overlay-based computational approach 通过基于叠加的计算方法分析高速、高空条件下的微粒行为
IF 2.2 3区 工程技术 Q2 MECHANICS Pub Date : 2024-11-18 DOI: 10.1007/s00162-024-00724-y
Akhil V. Marayikkottu, Nathaniel K. Myers, Irmak T. Karpuzcu, Deborah A. Levin, Qiong Liu

This paper presents an overlay-based one-way coupled Eulerian–Lagrangian computational approach designed to investigate the dynamics of particulate phases in extreme high-speed, high-altitude flight conditions characterized by very low particulate mass loading. Utilizing the Direct Simulation Monte Carlo method to generate accurate gas flow fields, this study explores two canonical hypersonic flow systems. First we focus on the hypersonic flow over a sphere-cone, revealing the formation of dust-free zones for small particulate diameters and describing the particulate interaction with gas shocks. As particulate diameter and flight speed increase, the characteristics of the particulate phase evolve, leading to the emergence of distinctive features such as high particulate concentration bands or regions void of particulates. Subsequently, the investigation considers flow over a double-cone, emphasizing the behavior of particulate phases in separated vortex-dominated systems where particulate-inertia-driven interactions with vortices result in unique particulate-free zones in the vicinity of the primary and secondary vortices. Additionally, the paper addresses the importance of using realistic fractal-like particulate shapes and demonstrates that the shape effect tends to decelerate the fractal aggregates and trap them along the boundaries of the primary vortex. This research contributes to a deeper understanding of particulate phase dynamics in extreme flight conditions, offering insights relevant to aerospace and aerodynamic applications.

本文提出了一种基于叠加的单向欧拉-拉格朗日耦合计算方法,旨在研究在颗粒质量负荷极低的极端高速、高空飞行条件下颗粒相的动力学。本研究利用直接模拟蒙特卡洛方法生成精确的气体流场,探索了两种典型的高超音速流动系统。首先,我们重点研究了球锥上方的高超音速流动,揭示了小颗粒直径无尘区的形成,并描述了颗粒与气体冲击的相互作用。随着微粒直径和飞行速度的增加,微粒相的特征也会发生变化,从而出现一些明显的特征,如高浓度微粒带或无微粒区域。随后,研究考虑了在双锥体上的流动,强调了微粒相在分离的涡流主导系统中的行为,在这种系统中,微粒惯性驱动与涡流的相互作用导致在主涡流和副涡流附近形成独特的无微粒区。此外,论文还论述了使用逼真的分形颗粒形状的重要性,并证明了形状效应往往会使分形聚集体减速,并将它们困在主涡的边界上。这项研究有助于加深对极端飞行条件下微粒相态动力学的理解,为航空航天和空气动力学应用提供相关见解。
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引用次数: 0
Long wavelength analysis amendment on the cilia beating assisted peristalsis in a tube 管内纤毛跳动辅助蠕动的长波长分析修正案
IF 2.2 3区 工程技术 Q2 MECHANICS Pub Date : 2024-11-07 DOI: 10.1007/s00162-024-00721-1
Mustafa Turkyilmazoglu

This work delves into the peristaltic rheology of two-wave sinusoidal cilia beating within a tubular pipe. Cilia movement drives the dynamic phenomenon of peristaltic fluid flow. Employing the traditional long-wavelength lubrication assumption, the flow equations are transformed into similarity form. The main objective is to take into account the true peristaltic-ciliary motion effects. We then derive analytical solutions for the radial and axial velocities of fluid particles within the tube. Notably, at this leading approximation level, the impacts of cilia beating are negligible, suggesting the motion is solely driven by peristaltic surface waves. However, analyzing the correction to the long-wavelength limit reveals the emergence of ciliated boundary effects through their largely eccentric elliptic paths. This correction enables us to extract expressions for the pressure gradient, stream function, axial and radial velocities, resultant pressure rise, and drag force, all based on the time-averaged mean flow rate across the pipe. Finally, we present a general discussion of fluid rheology due to cilia-assisted peristaltic motion, illustrated with informative graphical displays. It is shown that the drag force on the tube walls owing to the cilia beating waves in biology or biomedical applications necessitates addition of correction terms to the traditional long-wavelength adoption.

这项研究深入探讨了管状管道内双波正弦纤毛跳动的蠕动流变学。纤毛运动推动了蠕动流体流动的动态现象。采用传统的长波长润滑假设,将流动方程转化为相似形式。主要目的是考虑到真正的蠕动-纤毛运动效应。然后,我们得出了管内流体颗粒径向和轴向速度的解析解。值得注意的是,在这一领先近似水平上,纤毛跳动的影响可以忽略不计,这表明运动完全由蠕动表面波驱动。然而,通过分析对长波长极限的修正,我们发现纤毛的边界效应通过其偏心的椭圆路径显现出来。这种修正使我们能够提取压力梯度、流函数、轴向和径向速度、结果压力上升和阻力的表达式,所有这些都基于管道上的时间平均平均流速。最后,我们对纤毛辅助蠕动运动引起的流体流变学进行了一般性讨论,并用翔实的图表进行了说明。研究表明,在生物或生物医学应用中,由于纤毛跳动波对管壁产生的阻力,有必要在传统的长波长采用法中添加修正项。
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引用次数: 0
Wave reflections and resonance in a Mach 0.9 turbulent jet 0.9 马赫湍流喷流中的波反射和共振
IF 2.2 3区 工程技术 Q2 MECHANICS Pub Date : 2024-11-07 DOI: 10.1007/s00162-024-00722-0
Robin Prinja, Eduardo Martini, Peter Jordan, Aaron Towne, André V. G. Cavalieri

This work aims to provide a more complete understanding of the resonance mechanisms that occur in turbulent jets at high subsonic Mach number, as shown by Towne et al. (J. Fluid Mech., vol. 825, 2017, pp. 1113-1152). Resonance was suggested by that study to exist between upstream- and downstream-travelling guided waves. Five possible resonance mechanisms were postulated, each involving different families of guided waves that reflect in the nozzle exit plane and at a number of downstream turning points. However, that study did not identify which of the five resonance mechanisms underpin the observed spectral peaks. In this work, the waves underpinning resonance are identified via a biorthogonal projection of Large Eddy Simulation data on eigenbases provided by a locally parallel linear stability analysis. Two of the five scenarios postulated by Towne et al. are thus confirmed to exist in the turbulent jet. The reflection-coefficients in the nozzle exit and turning-point planes are, furthermore, identified. Such information is required as input for simplified resonance-modelling strategies such as developed in Jordan et al. (J. Fluid Mech., vol. 853, 2018, pp. 333-358) for jet-edge resonance, and in Mancinelli et al. (Exp. Fluids, vol. 60, 2019, pp. 1-9) for supersonic screech.

这项工作旨在更全面地了解 Towne 等人(《流体力学》,第 825 卷,2017 年,第 1113-1152 页)所述的亚音速高马赫数湍流射流中发生的共振机制。该研究认为上游和下游导波之间存在共振。研究假设了五种可能的共振机制,每种机制都涉及不同系列的导波,这些导波在喷嘴出口平面和若干下游转折点处发生反射。然而,该研究并未确定这五种共振机制中哪一种是观测到的光谱峰的基础。在这项工作中,通过对局部并行线性稳定性分析提供的特征基上的大涡流模拟数据进行双向投影,确定了支撑共振的波。因此,Towne 等人假设的五种情况中有两种被证实存在于湍流射流中。此外,还确定了喷嘴出口和转折点平面的反射系数。这些信息需要作为简化共振建模策略的输入,如 Jordan 等人(《流体力学》,第 853 卷,2018 年,第 333-358 页)针对喷流边缘共振和 Mancinelli 等人(《流体学报》,第 60 卷,2019 年,第 1-9 页)针对超音速尖啸所开发的策略。
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引用次数: 0
Extended cluster-based network modeling for coherent structures in turbulent flows 湍流中相干结构的扩展聚类网络建模
IF 2.2 3区 工程技术 Q2 MECHANICS Pub Date : 2024-10-25 DOI: 10.1007/s00162-024-00723-z
Antonio Colanera, Johann Moritz Reumschüssel, Jan Paul Beuth, Matteo Chiatto, Luigi de Luca, Kilian Oberleithner

This study introduces the Extended Cluster-based Network Modeling (eCNM), a methodology to analyze complex fluid flows. The eCNM focuses on characterizing dynamics within specific subspaces or subsets of variables, providing valuable insights into complex flow phenomena. The effectiveness of the eCNM is demonstrated on a swirl flame in unforced conditions, characterized by a precessing vortex core (PVC), using synchronized data from PIV measurements, UV-images filtered around the OH* chemiluminescence wavelength, featuring the heat release rate distribution, and pressure signals from jet inlet probes. The analysis starts with choosing the distance metric for the coarse-graining process and the number of clusters of the model. This has been pursued by designing a filtered distance metric based on the filtered correlation matrix and minimizing the Bayesian information criterion (BIC) score, balancing the goodness of the fit of a model with its complexity. The standard cluster-based network model on the velocity fluctuations allowed for determining the characteristic frequency of the PVC. The construction of extended cluster centroids of the heat release rate reveals a rotating flame pattern, predominantly localized within regions influenced by PVC’s vortices roll-up. Spatial subdomain analysis is carried out, demonstrating the benefits of focusing on specific regions of interest within the fluid system and providing significant computational savings. Furthermore, eCNM allows for the handling of different sampling frequencies among datasets. Leveraging high-resolution pressure measurements as a reference dataset and velocity components as undersampled data, extended cluster centroids for velocity are successfully estimated, even when the velocity sampling frequency is artificially reduced. This study showcases the adaptability and robustness of eCNM as a valuable tool for comprehending and analyzing coherent structures in complex fluid flows.

本研究介绍了基于簇的扩展网络建模(eCNM),这是一种分析复杂流体流动的方法。eCNM 专注于描述特定子空间或变量子集内的动力学特征,为复杂的流动现象提供有价值的见解。我们利用 PIV 测量数据、围绕 OH* 化学发光波长滤波的 UV 图像(以热释放率分布为特征)以及喷射入口探头的压力信号等同步数据,演示了 eCNM 在非强制条件下漩涡火焰中的有效性,该火焰的特征是一个前冲漩涡核心 (PVC)。分析工作从选择粗粒化过程的距离度量和模型的簇数开始。为此,我们设计了一种基于滤波相关矩阵的滤波距离度量,并使贝叶斯信息准则(BIC)得分最小化,从而在模型的拟合度和复杂度之间取得平衡。基于速度波动的标准聚类网络模型可以确定聚氯乙烯的特征频率。热释放率扩展聚类中心点的构建揭示了一种旋转火焰模式,主要集中在受聚氯乙烯涡卷影响的区域。通过进行空间子域分析,展示了在流体系统中关注特定区域的好处,并显著节省了计算量。此外,eCNM 还可以处理不同数据集的不同采样频率。利用作为参考数据集的高分辨率压力测量值和作为采样不足数据的速度分量,即使人为降低速度采样频率,也能成功估算出速度的扩展聚类中心点。这项研究展示了 eCNM 的适应性和稳健性,它是理解和分析复杂流体流动中相干结构的重要工具。
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引用次数: 0
Proper orthogonal decomposition reduced-order model of the global oceans 全球海洋的适当正交分解降阶模型
IF 2.2 3区 工程技术 Q2 MECHANICS Pub Date : 2024-09-19 DOI: 10.1007/s00162-024-00719-9
Vassili Kitsios, Laurent Cordier, Terence  J. O’Kane

A reduced-order model (ROM) of the global oceans is developed by projecting the hydrostatic Boussinesq equations of motion onto a proper orthogonal decomposition (POD) basis. Three-dimensional POD modes are calculated from the ocean fields of an ensemble climate reanalysis dataset. The coefficients in the POD ROM are calculated using a regression approach. The performance of various POD ROM configurations are assessed. Each configuration is derived from an alternate sea-water equation of state, linking the density and temperature fields. POD ROM variants incorporating an equation of state in which density is a quadratic function of temperature, are able to reproduce the statistics of the large-scale structures at a fraction of the computational cost required to numerically simulate this flow. Due to the speed and efficiency of calculation, such reduced-order models of the global geophysical system will enable researchers and policy makers to assess the physical risk for a broader range of potential future climate scenarios.

通过将流体静力学布辛斯克运动方程投影到适当的正交分解(POD)基础上,建立了全球海洋的降阶模式(ROM)。三维 POD 模式是根据集合气候再分析数据集的海洋场计算得出的。POD ROM 中的系数采用回归方法计算。评估了各种 POD ROM 配置的性能。每种配置都来自于一个将密度场和温度场联系起来的备用海水状态方程。POD ROM 变体包含密度是温度二次函数的状态方程,能够以数值模拟这种流动所需的计算成本的一小部分再现大规模结构的统计数据。由于计算速度快、效率高,这种全球地球物理系统的降阶模型将使研究人员和决策者能够评估未来更多潜在气候情景下的物理风险。
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引用次数: 0
A hybrid method for aeroacoustic computation of moving rigid bodies in low Mach number flows 低马赫数流动中运动刚体的气动声学计算混合方法
IF 2.2 3区 工程技术 Q2 MECHANICS Pub Date : 2024-09-17 DOI: 10.1007/s00162-024-00710-4
Kai Wang, Tiangui Ye, Xueren Wang, Guoyong Jin, Yukun Chen

To analyze the noise induced by moving rigid structures in low Mach number flows, acoustic governing equations based on the viscous/acoustic splitting method and the arbitrary Lagrangian–Eulerian method are rigorously derived. In order to resolve the numerical instability generated in a non-uniform mean flow, the modified viscous/acoustic method, based on the filtering method, is developed. The acoustic equations are transformed into the same form as the incompressible flow equations by introducing the acoustic co-velocity and solved based on a collocated grid finite volume method. An approach for solving acoustic equation based on the PIMPLE algorithm is presented and computed in open-source computational fluid dynamics software OpenFOAM, which brings down communication costs and speeds up computing efficiency. Furthermore, the source term decomposition is extended to study the noise generated by each source term in a motion grid. Several examples including stationary and moving meshes have been designed to prove the accuracy of this approach. Finally, the aerodynamic and acoustic properties for the flow past a transversely oscillating cylinder at Re = 200, Ma = 0.2 in lock-in and non-lock-in regions is present.

为了分析低马赫数流动中移动刚性结构引起的噪声,基于粘性/声学分裂方法和任意拉格朗日-欧勒方法严格推导了声学控制方程。为了解决在非均匀平均流中产生的数值不稳定性,开发了基于滤波法的改进粘滞/声学方法。通过引入声学共速,将声学方程转换为与不可压缩流动方程相同的形式,并基于同网格有限体积法进行求解。提出了一种基于 PIMPLE 算法的声学方程求解方法,并在开源计算流体力学软件 OpenFOAM 中进行计算,从而降低了通信成本,提高了计算效率。此外,还扩展了源项分解,以研究运动网格中每个源项产生的噪声。为了证明这种方法的准确性,我们设计了几个包括静止和运动网格在内的示例。最后,介绍了在 Re = 200、Ma = 0.2 的锁定和非锁定区域内,流过横向摆动圆柱体的气动和声学特性。
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引用次数: 0
Perturbation amplification near the stagnation point of blunt bodies 钝体停滞点附近的扰动放大
IF 2.2 3区 工程技术 Q2 MECHANICS Pub Date : 2024-09-16 DOI: 10.1007/s00162-024-00715-z
Eduardo Martini, Clement Caillaud, Guillaume Lehnasch, Peter Jordan, Oliver Schmidt

Different transition to turbulence routes for the flow around blunt bodies are possible. Non-modal amplification of perturbations via the lift-up effect has recently been explored to explain transition near the stagnation point in axisymmetric bodies. However, only perturbations already present in the boundary layer can be amplified, and the mechanisms by which free-stream perturbations enter the boundary layer have not yet been fully explored. In this study, we present an investigation of how disturbances enter the boundary layer via the stagnation point. This linear mechanism is expected to dominate over non-linear mechanisms previously identified on the formation of boundary layer perturbations at low turbulence intensity levels. A parametric investigation is presented, revealing trends with Reynolds and Mach numbers.

钝体周围的流体可能有不同的湍流过渡路径。最近有人探讨了通过抬升效应对扰动进行非模式放大,以解释轴对称体停滞点附近的过渡。然而,只有已经存在于边界层中的扰动才能被放大,而自由流扰动进入边界层的机制尚未得到充分探索。在本研究中,我们对扰动如何通过停滞点进入边界层进行了研究。在低湍流强度水平下边界层扰动的形成过程中,这种线性机制预计会比之前确定的非线性机制占主导地位。本文介绍了一项参数研究,揭示了雷诺数和马赫数的变化趋势。
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引用次数: 0
Some effects of limited wall-sensor availability on flow estimation with 3D-GANs 墙壁传感器可用性有限对 3D-GAN 流量估算的一些影响
IF 2.2 3区 工程技术 Q2 MECHANICS Pub Date : 2024-09-09 DOI: 10.1007/s00162-024-00718-w
Antonio Cuéllar, Andrea Ianiro, Stefano Discetti

In this work we assess the impact of the limited availability of wall-embedded sensors on the full 3D estimation of the flow field in a turbulent channel with (Re_{tau }=200). The estimation technique is based on a 3D generative adversarial network (3D-GAN). We recently demonstrated that 3D-GANs are capable of estimating fields with good accuracy by employing fully-resolved wall quantities (pressure and streamwise/spanwise wall shear stress on a grid with DNS resolution). However, the practical implementation in an experimental setting is challenging due to the large number of sensors required. In this work, we aim to estimate the flow fields with substantially fewer sensors. The impact of the reduction of the number of sensors on the quality of the flow reconstruction is assessed in terms of accuracy degradation and spectral length-scales involved. It is found that the accuracy degradation is mainly due to the spatial undersampling of scales, rather than the reduction of the number of sensors per se. We explore the performance of the estimator in case only one wall quantity is available. When a large number of sensors is available, pressure measurements provide more accurate flow field estimations. Conversely, the elongated patterns of the streamwise wall shear stress make this quantity the most suitable when only few sensors are available. As a further step towards a real application, the effect of sensor noise is also quantified. It is shown that configurations with fewer sensors are less sensitive to measurement noise.

在这项工作中,我们评估了墙壁嵌入式传感器的有限可用性对具有 (Re_{tau }=200) 湍流通道中流场的全三维估计的影响。估计技术基于三维生成式对抗网络(3D-GAN)。我们最近证明,三维生成式对抗网络能够通过采用完全解析的壁面量(具有 DNS 分辨率的网格上的压力和流向/跨向壁面切应力)来准确估计流场。然而,由于需要大量传感器,在实验环境中实际应用具有挑战性。在这项工作中,我们的目标是用更少的传感器来估算流场。我们从精度下降和涉及的频谱长度尺度两个方面评估了减少传感器数量对流场重建质量的影响。结果发现,精度下降的主要原因是空间尺度采样不足,而不是传感器数量减少本身。我们探讨了估计器在只有一个壁面量的情况下的性能。在有大量传感器的情况下,压力测量能提供更精确的流场估算。相反,流向壁面剪应力的细长模式使其在仅有少量传感器的情况下成为最合适的参数。在实际应用中,我们还对传感器噪声的影响进行了量化。结果表明,传感器数量较少的配置对测量噪声的敏感度较低。
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引用次数: 0
An invitation to resolvent analysis 解析邀请函
IF 2.2 3区 工程技术 Q2 MECHANICS Pub Date : 2024-08-19 DOI: 10.1007/s00162-024-00717-x
Laura Victoria Rolandi, Jean Hélder Marques Ribeiro, Chi-An Yeh, Kunihiko Taira

Resolvent analysis is a powerful tool that can reveal the linear amplification mechanisms between the forcing inputs and the response outputs about a base flow. These mechanisms can be revealed in terms of a pair of forcing and response modes and the associated energy gains (amplification magnitude) at a given frequency. The linear relationship that ties the forcing and the response is represented through the resolvent operator (transfer function), which is constructed through spatially discretizing the linearized Navier–Stokes operator. One of the unique strengths of resolvent analysis is its ability to analyze statistically stationary turbulent flows. In light of the increasing interest in using resolvent analysis to study a variety of flows, we offer this guide in hopes of removing the hurdle for students and researchers to initiate the development of a resolvent analysis code and its applications to their problems of interest. To achieve this goal, we discuss various aspects of resolvent analysis and its role in identifying dominant flow structures about the base flow. The discussion in this paper revolves around the compressible Navier–Stokes equations in the most general manner. We cover essential considerations ranging from selecting the base flow and appropriate energy norms to the intricacies of constructing the linear operator and performing eigenvalue and singular value decompositions. Throughout the paper, we offer details and know-how that may not be available to readers in a collective manner elsewhere. Towards the end of this paper, examples are offered to demonstrate the practical applicability of resolvent analysis, aiming to guide readers through its implementation and inspire further extensions. We invite readers to consider resolvent analysis as a companion for their research endeavors.

残差分析是一种功能强大的工具,可以揭示基流的强迫输入和响应输出之间的线性放大机制。这些机制可以通过一对作用力和响应模式以及给定频率下的相关能量增益(放大倍数)来揭示。通过对线性化的纳维-斯托克斯算子进行空间离散化处理,可以用解析算子(传递函数)来表示约束和响应之间的线性关系。解析分析的独特优势之一是能够分析统计静止湍流。鉴于越来越多的人对使用旋转分析来研究各种流动感兴趣,我们提供了这本指南,希望能为学生和研究人员消除障碍,帮助他们开始开发旋转分析代码并将其应用于他们感兴趣的问题。为了实现这一目标,我们讨论了解析量分析的各个方面及其在识别基流主导流结构中的作用。本文的讨论以最一般的方式围绕可压缩 Navier-Stokes 方程展开。我们涵盖了从选择基流和适当的能量规范到构建线性算子和执行特征值和奇异值分解的复杂性等基本考虑因素。在整篇论文中,我们提供了读者可能无法在其他地方以集体方式获得的细节和诀窍。在本文末尾,我们还提供了一些实例来演示分解分析的实际应用性,旨在引导读者了解其实现方法,并启发读者进一步扩展。我们邀请读者考虑将 resolvent 分析作为其研究工作的辅助工具。
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引用次数: 0
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Theoretical and Computational Fluid Dynamics
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