Number Of Proper Orthogonal Decomposition Modes Research Articles

Space-time adaptive model order reduction utilizing local low-dimensionality of flow field

The cost of unsteady flow simulations, such as large eddy simulations, has been increasing because of the large number of mesh cells and the use of high-order numerical schemes. In contrast, recent data-driven reduced-order models (ROMs) predict a flow field quickly; however, their application is often limited to relatively simple flow problems. In this study, we investigate space-time adaptive model order reduction for unsteady flow simulation, where full-order Navier-Stokes equations and a proper orthogonal decomposition (POD)-based reduced-order model are adaptively switched in a block-by-block manner on a multi-block Cartesian mesh. The full-order model (FOM) is switched to the ROM when POD modes effectively represent the unsteady flow field in each block. Owing to the local low-dimensionality of a flow field, the degree of freedom of fluid flow in each block can be smaller than that of the entire flow field; hence, the flow field is effectively represented by a small number of POD modes. First, the hybrid FOM/ROM approach is tested with a low-Reynolds-number flow around a circular cylinder, where the reduction in computational time and the accuracy of the simulated flow field are evaluated. We then consider a flow around a circular cylinder with a Reynolds number of 1000, where the flow field is reduced except for the highly unsteady wake. The potential computational advantage of this method is demonstrated by load balancing on a distributed memory computer. In addition, we utilize bred vector dimensions to quantify the degree of freedom of the flow field in each block, which is closely related to whether ROMs effectively reduce the flow field.

Towards Reduced Order Models via Robust Proper Orthogonal Decomposition to capture personalised aortic haemodynamics

Data driven, reduced order modelling has shown promise in tackling the challenges associated with computational and experimental haemodynamic models. In this work, we focus on the use of Reduced Order Models (ROMs) to reconstruct velocity fields in a patient-specific dissected aorta, with the objective being to compare the ROMs obtained from Robust Proper Orthogonal Decomposition (RPOD) to those obtained from the traditional Proper Orthogonal Decomposition (POD). POD and RPOD are applied to in vitro, haemodynamic data acquired by Particle Image Velocimetry and compare the decomposed flows to those derived from Computational Fluid Dynamics (CFD) data for the same geometry and flow conditions. In this work, PIV and CFD results act as surrogates for clinical haemodynamic data e.g. MR, helping to demonstrate the potential use of ROMS in real clinical scenarios. The flow is reconstructed using different numbers of POD modes and the flow features obtained throughout the cardiac cycle are compared to the original Full Order Models (FOMs).Robust Principal Component Analysis (RPCA), the first step of RPOD, has been found to enhance the quality of PIV data, allowing POD to capture most of the kinetic energy of the flow in just two modes similar to the numerical data that are free from measurement noise. The reconstruction errors differ along the cardiac cycle with diastolic flows requiring more modes for accurate reconstruction. In general, modes 1–10 are found sufficient to represent the flow field. The results demonstrate that the coherent structures that characterise this aortic dissection flow are described by the first few POD modes suggesting that it is possible to represent the macroscale behaviour of aortic flow in a low-dimensional space; thus significantly simplifying the problem, and allowing for more computationally efficient flow simulations or machine learning based flow predictions that can pave the way for translation of such models to the clinic.

On the stability of POD basis interpolation on Grassmann manifolds for parametric model order reduction

Proper Orthogonal Decomposition (POD) basis interpolation on Grassmann manifolds has been successfully applied to problems of parametric model order reduction (pMOR). In this work we address the necessary stability conditions for the interpolation, all defined from strong mathematical background. A first condition concerns the domain of definition of the logarithm map. Second, we show how the stability of interpolation can be lost if certain geometrical requirements are not satisfied by making a concrete elucidation of the local character of linearization. To this effect, we draw special attention to the Grassmannian exponential map and the optimal injectivity condition of this map, related to the cut–locus of Grassmann manifolds. From this, an explicit stability condition is established and can be directly used to determine the loss of injectivity in practical pMOR applications. A third stability condition is formulated when increasing the number p of POD modes, deduced from the principal angles of subspaces of different dimensions p. Definition of this condition leads to an understanding of the non-monotonic oscillatory behavior of the Reduced Order Model (ROM) error-norm with respect to the number of POD modes, and on the contrary, the well-behaved monotonic decrease of the error-norm in the two numerical examples presented herein. We have chosen to perform pMOR in hyperelastic structures using a non-intrusive approach for inserting the interpolated spatial POD ROM basis in a commercial FEM code. The accuracy is assessed by a posteriori error norms defined using the ROM FEM solution and its high-fidelity counterpart simulation. Numerical studies successfully ascertained and highlighted the implication of stability conditions which are general and can be applied to a variety of other linear or nonlinear problems involving parametrized ROMs generation based on POD basis interpolation on Grassmann manifolds.

Numerical characterization of turbine blade dynamic properties via proper orthogonal decomposition

Abstract Forced vibration analysis is an essential process during the design of a turbine blade and requires enormous computational expense because of its complicated numerical procedures with large size matrices. This paper focuses on the application of the proper orthogonal decomposition (POD). It is under the spotlight for its usefulness on the reduced order model (ROM) construction. POD applications include nonlinear static, modal analysis, and forced vibration (harmonic response) analysis of the turbine blade. Performance of POD-ROM is examined for various operating conditions, and effect of the number of POD modes used is also investigated. With the sufficient number of POD modes, accurate results of turbine blade response are obtained with drastically reduced computational resources.

A sparse optimal closure for a reduced-order model of wall-bounded turbulence

In the present study, a set of physics-informed and data-driven approaches are examined towards the development of an accurate reduced-order model for a turbulent plane Couette flow. Based on the utilisation of the proper orthogonal decomposition (POD), a particular focus is given to the development of a reduced-order model where the number of POD modes are not large enough to cover the full dynamics of the given turbulent state, the situation directly relevant to the reduced-order modelling for turbulent flows. Starting from the conventional Galerkin projection approach ignoring the truncation error, three approaches enhanced by both physics and data are examined: (1) sparse regression of the POD-Galerkin dynamics; (2) Galerkin projection with an empirical eddy-viscosity model; (3) Galerkin projection with an optimal eddy viscosity obtained from a newly proposed sparse regression – an idea applying the sparse identification of nonlinear dynamics framework to an eddy-viscosity model. The sparse regression of the POD-Galerkin dynamics does not perform well, as the number of POD modes for the given chaotic dynamics appears to be too small. While the unsatisfactory performance of the Galerkin projection model with an empirical eddy viscosity is observed, the newly proposed approach, which combines the concept of an optimal eddy-viscosity closure with a sparse regression, more accurately approximates the chaotic dynamics than the other reduced-order models considered. This is demonstrated with the mean and time scales of the POD mode amplitudes as well as the first- and second-order turbulence statistics.

POD associated with modal projection-based reduced order model for prestress structural vibrations

The study deals with the computation of the linear vibrations of prestress elastic structures. The originality of the proposed approach is based on a Proper Orthogonal Decomposition (POD) associated with a modal projection-based Reduced Order Model (ROM) to evaluate the natural frequencies of an elastic structure in function of a static pressure load parameter. It is shown that a finite number of POD modes combined with linear prestress eigenmodes are able to evaluate efficiently the frequencies function of the evolution parameter. The generated reduced order model can be used in future works on parametric studies, sensitivity analyses, optimization procedure or feedback control loops systems.

Study of Unsteady Thermal and Flow Structure near Reattachment Point behind a Backward Facing Step with POD Analysis

In this study, the mechanism of heat transfer enhancement near the reattachment point behind a backward facing step is experimentally investigated at a Reynolds number of 5400. The unsteady fluctuations of the velocity and temperature were simultaneously measured by using 2 dimensions and 3 components (2D-3C) Particle Image Velocimetry (PIV) at x/H = 4.5 and the high-speed infrared (IR) thermograph on the heated wall. In order to discuss the thermal and flow structure near the reattachment point, 3 components of the velocity and the heat transfer coefficient were calculated. The spatial distribution of the flow and thermal fluctuations was reconstructed by using proper orthogonal decomposition (POD) analysis. As a result, the characteristic structure of the flow and thermal fluctuations appeared for the lower number of POD modes. These downwash and upwash flow in the transverse direction corresponded to the increasing and decreasing of the heat transfer coefficients at x/H of 4.5.

Manifold reduction techniques for the comparison of crank angle-resolved particle image velocimetry (PIV) data and Reynolds-averaged Navier-Stokes (RANS) simulations in a spark ignition direct injection (SIDI) engine

In this article, different manifold reduction techniques are implemented for the post-processing of Particle Image Velocimetry (PIV) images from a Spark Ignition Direct Injection (SIDI) engine. The methods are proposed to help make a more objective comparison between Reynolds-averaged Navier-Stokes (RANS) simulations and PIV experiments when Cycle-to-Cycle Variations (CCV) are present in the flow field. The two different methods used here are based on Singular Value Decomposition (SVD) principles where Proper Orthogonal Decomposition (POD) and Kernel Principal Component Analysis (KPCA) are used for representing linear and non-linear manifold reduction techniques. To the authors’ best knowledge, this is the first time a non-linear manifold reduction technique, such as KPCA, has ever been used in the study of in-cylinder flow fields. Both qualitative and quantitative studies are given to show the capability of each method in validating the simulation and incorporating CCV for each engine cycle. Traditional Relevance Index (RI) and two other previously developed novel indexes: the Weighted Relevance Index (WRI) and the Weighted Magnitude Index (WMI), are used for the quantitative study. The results indicate that both POD and KPCA show improvements in capturing the main flow field features compared to ensemble-averaged PIV experimental data and single cycle experimental flow fields while capturing CCV. Both methods present similar quantitative accuracy when using the three indexes. However, challenges were highlighted in the POD method for the selection of the number of POD modes needed for a representative reconstruction. When the flow field region presents a Gaussian distribution, the KPCA method is seen to provide a more objective numerical process as the reconstructed flow field will see convergence with an increasing number of modes due to its usage of Gaussian properties. No additional criterion is needed to determine how to reconstruct the main flow field feature. Using KPCA can, therefore, reduce the amount of analysis needed in the process of extracting the main flow field while incorporating CCV.

A Comprehensive Deep Learning-Based Approach to Reduced Order Modeling of Nonlinear Time-Dependent Parametrized PDEs

Conventional reduced order modeling techniques such as the reduced basis (RB) method (relying, e.g., on proper orthogonal decomposition (POD)) may incur in severe limitations when dealing with nonlinear time-dependent parametrized PDEs, as these are strongly anchored to the assumption of modal linear superimposition they are based on. For problems featuring coherent structures that propagate over time such as transport, wave, or convection-dominated phenomena, the RB method may yield inefficient reduced order models (ROMs) when very high levels of accuracy are required. To overcome this limitation, in this work, we propose a new nonlinear approach to set ROMs by exploiting deep learning (DL) algorithms. In the resulting nonlinear ROM, which we refer to as DL-ROM, both the nonlinear trial manifold (corresponding to the set of basis functions in a linear ROM) as well as the nonlinear reduced dynamics (corresponding to the projection stage in a linear ROM) are learned in a non-intrusive way by relying on DL algorithms; the latter are trained on a set of full order model (FOM) solutions obtained for different parameter values. We show how to construct a DL-ROM for both linear and nonlinear time-dependent parametrized PDEs. Moreover, we assess its accuracy and efficiency on different parametrized PDE problems. Numerical results indicate that DL-ROMs whose dimension is equal to the intrinsic dimensionality of the PDE solutions manifold are able to efficiently approximate the solution of parametrized PDEs, especially in cases for which a huge number of POD modes would have been necessary to achieve the same degree of accuracy.

Toward understanding waked flow fields behind a wind turbine using proper orthogonal decomposition

This study proposes the use of an approach based on proper orthogonal decomposition (POD) to explore reduced-order wake turbulence fields. Waked turbulence fields are first extracted using large eddy simulation (LES) downwind of a wind turbine in a single plane orthogonal to the streamwise flow field. Based on this extracted turbulence field, statistical summaries in the form of covariance matrices and cross power spectral density (CPSD) matrices are estimated. Using proper orthogonal decomposition, important “modes” organized by eigenvalues (dominant energy contributions) are evaluated. Based on a subset of these sorted modes, reduced-order turbulence fields can be generated and these are analyzed and compared directly with the original LES-based target wake turbulence field. Statistical descriptions of the turbulence and their effect on wind turbine loads are investigated. To serve as reference, the free-stream turbulence field upwind of the selected wind turbine is also captured using LES. The same decomposition and simulation procedures are performed on the free-stream field. Compared to POD eigenmodes and eigenvalues of the free-stream field, those for the waked wind fields show distinct patterns that describe a systematic increase in turbulence energy around the top of the rotor. CPSD-based POD (spectral proper transformation) is found to be more efficient in capturing dynamic characteristics and spatial patterns in the waked wind fields using a small number of modes. Reduced-order simulation of waked wind fields using varying numbers of POD modes suggests that the top 10% of these most dominant modes—a greater proportion than what is needed for the free-stream field—is required to yield turbine loads comparable to those based directly on the original LES wind fields.

Chaotic systems learning with hybrid echo state network/proper orthogonal decomposition based model

Abstract We explore the possibility of combining a knowledge-based reduced order model (ROM) with a reservoir computing approach to learn and predict the dynamics of chaotic systems. The ROM is based on proper orthogonal decomposition (POD) with Galerkin projection to capture the essential dynamics of the chaotic system while the reservoir computing approach used is based on echo state networks (ESNs). Two different hybrid approaches are explored: one where the ESN corrects the modal coefficients of the ROM (hybrid-ESN-A) and one where the ESN uses and corrects the ROM prediction in full state space (hybrid-ESN-B). These approaches are applied on two chaotic systems: the Charney–DeVore system and the Kuramoto–Sivashinsky equation and are compared to the ROM obtained using POD/Galerkin projection and to the data-only approach based uniquely on the ESN. The hybrid-ESN-B approach is seen to provide the best prediction accuracy, outperforming the other hybrid approach, the POD/Galerkin projection ROM, and the data-only ESN, especially when using ESNs with a small number of neurons. In addition, the influence of the accuracy of the ROM on the overall prediction accuracy of the hybrid-ESN-B is assessed rigorously by considering ROMs composed of different numbers of POD modes. Further analysis on how hybrid-ESN-B blends the prediction from the ROM and the ESN to predict the evolution of the system is also provided.

On Stochastic Reduced-Order and LES-based Models of Offshore Wind Turbine Wakes

In this paper, the primary objective is to investigate flow structures in the wake of wind turbines based on applying a truncated Proper Orthogonal Decomposition (POD) approach. This scheme decomposes the three-dimensional velocity fields produced by the high-fidelity PArallelized LES Model (PALM) into a number of orthogonal spatial modes and time-dependent weighting coefficients. PALM has been combined with an actuator disk model with rotation to incorporate the effects of a turbine array. The time-dependent deterministic weights from applying the POD scheme are replaced by stochastic weights, estimated from two independent stochastic techniques that aim to account for unresolved small-scale features for a number of POD modes. We then reconstruct the flow field by a small number of stochastic modes to investigate how well the applied stochastic methodologies can reproduce the flow field compared to the original LES results.

Recurrence analysis and time extrapolation of a confined turbulent jet using modal decomposition

We investigated the long-term dynamics of a turbulent, submerged jet at Re = 16 400 to develop a strategy for data-assisted, fast calculations of passive species transport. We obtained our data from high-fidelity large eddy simulations LES, which we validated against in-house particle image velocimetry measurements. The flow was split into coherent and incoherent fields using the method of proper orthogonal decomposition (POD). Depending on the number of POD modes to construct coherent velocity fields, different patterns in the recurrence plot of the system were found. For low mode numbers, line segments parallel to the main diagonal were present, which indicated that close states evolved similarly for a finite duration. Strong turbulent fluctuations in the original velocity fields, on the other hand, hid any large-scale recurrences and caused a structureless recurrence statistics. Using an iterated method of analogs, we time-extrapolated a short time series of coherent, distinctly recurring velocity fields of 50 s to 250 s and performed a study of species transport. We found that coherent dynamics alone could not reproduce LES results due to the lack of turbulent, small-scale fluctuations, but already a small set of incoherent flow fields sufficed to cure this shortcoming considerably. Surprisingly, time extrapolation of the original database without decomposition and without any obvious recurrences led to the best results in very close agreement with LES but with high demands regarding memory. Our data-assisted simulations outperformed LES on the same computational mesh by a speed-up factor of 15.

Uncertainty Quantification of Stochastic Impact Dynamic Oscillator Using a Proper Orthogonal Decomposition-Polynomial Chaos Expansion Technique

Abstract A proper orthogonal decomposition (POD)-based polynomial chaos expansion (PCE) is utilized in this article for the uncertainty quantification (UQ) of an impact dynamic oscillator. The time-dependent nonsmooth behavior and the uncertainties are decoupled using the POD approach. The uncertain response domain is reduced using the POD approach, and the dominant POD modes are utilized for the UQ of the response quantity. Furthermore, the PCE model is utilized for the propagation of the input uncertainties. Two different cases of impact oscillator are considered, namely, single impact and multiple impact. The contact between two bodies is modeled by Hertz’s law. For both the cases, UQ is performed on the projectile displacement, projectile velocity, and contact force. A highly nonsmooth behavior is noticed for the contact force. For that reason, most number of POD modes are required to assess the UQ of contact force. All the results are compared with the Monte Carlo simulation (MCS) and time domain PCE results. Very good accuracies are observed for the PCE and the POD-PCE predicted results using much less number of model evaluations compared to MCS. As the PCE coefficients are dependent on time, the PCE model is computed at each time step. On the contrary, for the POD-PCE model, the PCE coefficients are computed for the number of POD modes only: it is much less than the PCE model.

Proper orthogonal decomposition assisted inverse design optimisation method for the compressor cascade airfoil

Inverse design is by far the most physically explicit method in the turbomachinery field for designing a cascade airfoil shape for a prescribed distribution of aerodynamic parameters on the airfoil surface. However, a vital drawback of the available inverse design methods for cascade airfoils is the lack of effective techniques to specify optimal target aerodynamic parameters, particularly optimal pressure distribution on the airfoil surface. This drawback hinders the wide application of inverse design optimisation methods in the turbomachinery field. To overcome this vital drawback, we proposed a proper orthogonal decomposition (POD) assisted inverse design optimisation method for cascade airfoils, in which an optimal pressure distribution on airfoil surface was automatically obtained by solving a direct design optimisation problem and accurately parameterised via the POD method. The effectiveness of the proposed inverse design optimisation method was demonstrated using the inverse designs of a compressor cascade airfoil with two different optimisation objectives. Results highlighted the proposed inverse design method's capability to significantly improve the aerodynamic performance of the compressor cascade. The POD method can provide an adequate and flexible description of airfoil surface pressure distribution with a small number of POD modes. This work is valuable for the further development of inverse design optimisation methods for advanced compressor blades.

Nonintrusive reduced order modeling framework for quasigeostrophic turbulence.

In this study, we present a nonintrusive reduced order modeling (ROM) framework for large-scale quasistationary systems. The framework proposed herein exploits the time series prediction capability of long short-term memory (LSTM) recurrent neural network architecture such that (1) in the training phase, the LSTM model is trained on the modal coefficients extracted from the high-resolution data snapshots using proper orthogonal decomposition (POD) transform, and (2) in the testing phase, the trained model predicts the modal coefficients for the total time recursively based on the initial time history. Hence, no prior information about the underlying governing equations is required to generate the ROM. To illustrate the predictive performance of the proposed framework, the mean flow fields and time series response of the field values are reconstructed from the predicted modal coefficients by using an inverse POD transform. As a representative benchmark test case, we consider a two-dimensional quasigeostrophic ocean circulation model which, in general, displays an enormous range of fluctuating spatial and temporal scales. We first demonstrate that the conventional Galerkin projection-based reduced order modeling of such systems requires a high number of POD modes to obtain a stable flow physics. In addition, ROM-Galerkin projection (ROM-GP) does not seem to capture the intermittent bursts appearing in the dynamics of the first few most energetic modes. However, the proposed nonintrusive ROM framework based on LSTM (ROM-LSTM) yields a stable solution even for a small number of POD modes. We also observe that the ROM-LSTM model is able to capture quasiperiodic intermittent bursts accurately, and yields a stable and accurate mean flow dynamics using the time history of a few previous time states, denoted as the lookback time window in this paper. We show several features of ROM-LSTM framework such as significantly higher accuracy than ROM-GP, and faster performance using larger time step size. Throughout the paper, we demonstrate our findings in terms of time series evolution of the field values and mean flow patterns, which suggest that the proposed fully nonintrusive ROM framework is robust and capable of predicting chaotic nonlinear fluid flows in an extremely efficient way compared to the conventional projection-based ROM framework.

Time-Volume Estimation of Velocity Fields From Nonsynchronous Planar Measurements Using Linear Stochastic Estimation

The work presented in this paper combines multiple nonsynchronous planar measurements to reconstruct an estimate of a synchronous, instantaneous flow field of the whole measurement set. Temporal information is retained through the linear stochastic estimation (LSE) technique. The technique is described, applied, and validated with a simplified combustor and fuel swirl nozzles (FSN) geometry flow for which three-component, three-dimensional (3C3D) flow information is available. Using the 3C3D dataset, multiple virtual “planes” may be extracted to emulate single planar particle image velocimetry (PIV) measurements and produce the correlations required for LSE. In this example, multiple parallel planes are synchronized with a single perpendicular plane that intersects each of them. As the underlying dataset is known, it therefore can be directly compared to the estimated velocity field for validation purposes. The work shows that when the input time-resolved planar velocity measurements are first proper orthogonal decomposition (POD) filtered, high correlation between the estimations and the validation velocity volumes are possible. This results in estimated full volume velocity distributions, which are available at the same time instance as the input field—i.e., a time-resolved velocity estimation at the frequency of the single input plane. While 3C3D information is used in the presented work, this is necessary only for validation; in true application, planar technique would be used. The study concludes that provided the number of sensors used for input LSE exceeds the number of POD modes used for prefiltering, it is possible to achieve correlation greater than 99%.

Analysis of Different POD Processing Methods for SPIV-Measurements in Compressor Cascade Tip Leakage Flow

Though the proper orthogonal decomposition (POD) method has been widely adopted in flow analysis, few publications have systematically studied the influence of different POD processing methods on the POD results. This paper investigates the effects of different decomposition regions and decomposition dimensionalities on POD decomposition and reconstruction concerning the tip flow in the compressor cascade. Stereoscopic particle image velocimetry (SPIV) measurements in the blade channel are addressed to obtain the original flow field. Through vortex core identification, development of the tip leakage vortex along the chord is described. Afterwards, each plane is energetically decomposed by POD. Using the identified vortex core center as the geometric center, the effects of different decomposition regions with respect to the vortex core are analyzed. Furthermore, the effects of different single velocity-components as well as their combination are compared. The effect of different decomposition regions on the mode 1 energy fraction mainly impacts the streamwise velocity component. Though the addition of W velocity component in the decomposition does change the spatial structures of high-order modes, it does not change the dynamic results of reconstruction using a finite number of POD modes. UV global analysis is better for capturing the kinetic physics of the tip leakage vortex (TLV) wandering.

Stereoscopic Particle Image Velocimetry Measurements and Proper Orthogonal Decomposition Analysis of the In-Cylinder Flow of Gasoline Direct Injection Engine

Intake generated flows are known to have a fundamental influence on the combustion both in spark ignition (SI) and compression ignition engines. This study experimentally investigated the tumble flow structures inside a cylinder of gasoline direct injection (GDI) engine utilizing a stereoscopic time-resolved particle image velocimetry (PIV). The experiments were conducted in a GDI engine head for a number of fixed valve lifts and 150 mmH2O pressure difference across the intake valves. A tumble flow analysis was carried out considering different vertical tumble planes. In addition, the proper orthogonal decomposition (POD) identification technique was applied on the PIV data in order to spatially analyze the structures embedded in the instantaneous velocity data sets. The results showed that the flow was dominated by a strong tumble motion in the middle of cylinder at high valve lifts (8–10 mm). Moreover, it is worth pointing out that, because of the complexity of the flow at the high valve lifts, the flow energy was distributed over a higher number of POD modes. This was confirmed by the need of a higher number of POD modes needed to reconstruct the original velocity field to the same level of fidelity.

The effects of coherent structures on the global response of floating offshore wind turbines

AbstractThe global dynamic response of floating wind turbines is commonly simulated using aero‐hydro‐servo‐elastic tools that consider numerically generated wind files as input. Based on the guidelines given in existing standards, two methods of generating such wind files are typically used: the Mann uniform shear model and the Kaimal spectral and exponential coherence model. Both models consider the Kaimal spectrum with similar frequency characteristics: The main difference between the approaches is related to the spatial coherence. The present work examines the consequences of using the two different wind file generation methods for estimating the global responses of representative spar, semi‐submersible, and tension leg platform (TLP) 5 MW wind turbines. Predictions of the standard deviation of low‐frequency responses in operational conditions, including motions at the natural frequency in surge and pitch as well as quasi‐static (spar, TLP) and resonant (semi‐submersible) motions in yaw, are seen to differ up to 30% to 40% depending on the wind field model. The differences in motion responses have important consequences for the design of the mooring system components. Proper orthogonal decomposition (POD) techniques are used to qualitatively explain the differing spatial coherence of the wind field. Simulations including a limited number of POD modes in the wind field highlight the importance of the low‐frequency, energy‐rich modes, suggesting that this type of visualization can be a useful tool.