Publications

2026

1. Data-driven forecasting of high-dimensional transient and stationary processes via space–time projection

   O. T. Schmidt

   Proceedings of the Royal Society A, 2026, 482, 20250454

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2025

1. Stochastic reduced-order Koopman model for turbulent flows

   T. Chu, and O. T. Schmidt

   Proceedings of the Royal Society A, 2025, 481(2323), 20250270

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   A stochastic data-driven reduced-order model applicable to a wide range of turbulent natural and engineering flows is presented. Combining ideas from Koopman theory and spectral model order reduction, the stochastic low-dimensional inflated convolutional Koopman model accurately forecasts short-time transient dynamics while preserving long-term statistical properties. A discrete Koopman operator is used to evolve convolutional coordinates that govern the temporal dynamics of spectral orthogonal modes, which, in turn, represent the energetically most salient large-scale coherent flow structures. Turbulence closure is achieved in two steps: first, by inflating the convolutional coordinates to incorporate nonlinear interactions between different scales, and second, by modelling the residual error as a stochastic source. An empirical dewhitening filter informed by the data is used to maintain the second-order flow statistics. The model uncertainty is quantified through either Monte–Carlo simulation or by directly propagating the model covariance matrix. The model is demonstrated on the Ginzburg–Landau equations, large-eddy simulation data of a turbulent jet, and particle image velocimetry data of the flow over an open cavity. In all cases, the model is predictive over time horizons indicated by a detailed error analysis and integrates stably over arbitrary time horizons, generating realistic surrogate data.

2. Data Fusion Using Gappy-POD

   C. E. Tinney, Y. Zhao-Dubuc, O. T. Schmidt, and 3 more authors

   AIAA Paper 2025-2203, 2025

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   A framework for fusing numerical and experimental databases using heterogeneous forms of the gappy-POD is presented in order to reconstruct real observations from reduced sensor sets. The problem is demonstrated in the context of the jet noise problem where the observation space comprises wavefronts corresponding to the unsteady pressure field within the hydrodynamic periphery of a Mach 3 jet flow. The data fusion approach leverages a numerical model of the unsteady density field (generated by way of large eddy simulation) for training, followed by entries from experiments (high speed schlieren) for real-time re- construction. The compatibility of these databases is evaluated to ensure that observations are generated using the smallest number of synthesized basis functions. The input to the reconstruction is a sensor set from experimentally captured schlieren images of the same jet flow. A further simplification utilizes heterogeneous forms of the gappy-POD so that only a reduced sensor set is required for the reconstruction. This comprises the XX-topos and YX forms where the linear algebraic system of equations are formed using the eigenvectors and expansion coefficients, respectively while the gappy sensor set is determined using a random number generator. An error analysis reinforces the general requirement that 2��+1 sensors are needed to properly resolve the ��th POD mode. Sample reconstructions of the density field are performed in real time using only 10% of available POD modes and 20% of the sensors and are shown to generate qualitatively satisfactory images of wavefronts evolving across space and time.

3. Parametric reduced-order modelling and mode sensitivity of actuated cylinder flow from a matrix manifold perspective

   S. Sato, and O. T. Schmidt

   Journal of Fluid Mechanics, 2025, 1021, A44

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4. Spectral dynamics of natural and forced supersonic twin-rectangular jet flow

   B. Yeung, and O. T. Schmidt

   Journal of Fluid Mechanics, 2025, 1018, A34

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5. Nonlinear dynamics of vortex pairing in transitional jets

   A. Nekkanti, T. Colonius, and O. T. Schmidt

   Journal of Fluid Mechanics, 2025, 1018, A32

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6. Linear model reduction using spectral proper orthogonal decomposition

   P. Frame, C. Lin, O. T. Schmidt, and 1 more author

   Computer Methods in Applied Mechanics and Engineering, 2025, 447, 118382

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   Most model reduction methods reduce the state dimension and then temporally evolve a set of coefficients that encode the state in the reduced representation. In this paper, we instead employ an efficient representation of the entire trajectory of the state over some time interval of interest and then solve for the static coefficients that encode the trajectory on the interval. We use spectral proper orthogonal decomposition (SPOD) modes, which are provably optimal for representing long trajectories and substantially outperform any representation of the trajectory in a purely spatial basis (e.g., POD). We develop a method to solve for the SPOD coefficients that encode the trajectories for forced linear dynamical systems given the forcing and initial condition, thereby obtaining the accurate prediction of the dynamics afforded by the SPOD representation of the trajectory. The method, which we refer to as spectral solution operator projection (SSOP), is derived by projecting the general time-domain solution for a linear time-invariant system onto the SPOD modes. We demonstrate the new method using two examples: a linearized Ginzburg-Landau equation and an advection-diffusion problem. In both cases, the error of the proposed method is orders of magnitude lower than that of POD-Galerkin projection and balanced truncation. The method is also fast, with CPU time comparable to or lower than both benchmarks in our examples. Finally, we describe a data-free space-time method that is a derivative of the proposed method and show that it is also more accurate than balanced truncation in most cases.

7. Robust spectral proper orthogonal decomposition

   A. Colanera, O. T. Schmidt, and M. Chiatto

   Computer Physics Communications, 2025, 307, 109432

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   Experimental measurements often present corrupted data and outliers that can strongly affect the main coherent structures extracted with the classical modal analysis techniques. This effect is amplified at high frequencies, whose corresponding modes are more susceptible to contamination from measurement noise and uncertainties. Such limitations are overcome by a novel approach proposed here, the robust spectral proper orthogonal decomposition (robust SPOD), which implements the robust principal component analysis within the SPOD technique. The new technique is firstly presented with details on its algorithm, and its effectiveness is tested on two different fluid dynamics problems: the subsonic jet flow field numerically simulated, and the flow within an open cavity experimentally analyzed in [48]. The analysis of the turbulent jet data, corrupted both with salt and pepper and Gaussian noise, shows how the robust SPOD produces more converged and physically interpretable modes than the classical SPOD; moreover, the use of the robust SPOD as a tool for de-noising data, based on the signal reconstruction from de-noised modes, is also presented. Applying robust SPOD to the open cavity flow has revealed that it yields smoother spatial distributions of modes, particularly at high frequencies and when considering higher-order modes, compared to standard SPOD.

8. Spectral Proper Orthogonal Decomposition of Transitional Flow Over an Open Cavity

   F. O. Aguirre, O. T. Schmidt, and M. A. Medeiros

   AIAA Paper 2025-3454, 2025

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   This study investigates boundary layer transition over an open cavity under subsonic flow conditions, motivated by the economic and environmental impact of reducing aerodynamic drag. Using Direct Numerical Simulation (DNS), Linear Stability Theory (LST), and Spectral Proper Orthogonal Decomposition (SPOD), the research examines how cavity-induced instabilities, such as Rossiter (acoustic feedback-driven) and centrifugal modes, interact to drive transition, building on prior work linking surface imperfections to bypass transition mechanisms. Results reveal nonlinear couplings between these modes, with Rossiter modes persisting into turbulent regions and centrifugal instabilities introducing three-dimensional flow distortions, highlighting their combined role in destabilizing the boundary layer.

2024

1. Mesh-free hydrodynamic stability

   T. Chu, and O. T. Schmidt

   Journal of Computational Physics, 2024, 502, 112822

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   A specialized mesh-free radial basis function-based finite difference (RBF-FD) discretization is used to solve the large eigenvalue problems arising in hydrodynamic stability analyses of flows in complex domains. Polyharmonic spline functions with polynomial augmentation (PHS+poly) are used to construct the discrete linearized incompressible and compressible Navier-Stokes operators on scattered nodes. Rigorous global and local eigenvalue stability studies of these global operators and their constituent RBF stencils provide a set of parameters that guarantee stability without the need for hyperviscosity or other ad hoc regularizations, while balancing accuracy and computational efficiency. Specialized elliptical stencils to compute boundary-normal derivatives are introduced, and the treatment of reflectional and rotational symmetries is discussed. In particular, treating the pole singularity in cylindrical coordinates permits dimensionality reduction from 3D to 2D in rotational flows like jets. The numerical framework is demonstrated and validated on several hydrodynamic stability methods ranging from classical linear theory of laminar flows to state-of-the-art non-modal approaches that are applicable to turbulent mean flows. The examples include linear stability, resolvent, and wavemaker analyses of cylinder flow at Reynolds numbers ranging from 47 to 180, and resolvent and wavemaker analyses of the self-similar flat-plate boundary layer at a Reynolds number as well as the turbulent mean of a high-Reynolds-number transonic jet at Mach number 0.9. All previously-known results are found in close agreement with the literature. Finally, the resolvent-based wavemaker analyses of the Blasius boundary layer and turbulent jet flows offer new physical insight into the modal and non-modal growth in these flows.

2. Modal Decomposition of K- and H-Type Boundary Layer Transition

   C. Lin, and O. T. Schmidt

   AIAA Paper 2024-0495, 2024

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   We perform a data-driven discovery of the physics within transition mechanisms by using a suite of modal decomposition techniques on the DNS of deterministic K-type boundary layer transition. Specifically, we deploy Spectral Proper Orthogonal Decomposition (SPOD) and Space-Time POD (STPOD) along with a D1 Symmetry Decomposition to educe coherent structures in time and frequency domain, with different optimality properties each, and establish their relationships to each other. Our study is in part a data-driven counterpart to a recent harmonic balancing study by Rigas et al. [1]: Therein we verify which pre-turbulence transition mechanisms are reproducible by a varying number of Fourier-type modes at the fundamental frequency and its harmonics. In extension, we identify from data the prototypical transition scenario, extract modes associated with various instability mechanisms and uncover how far these distinct coherent structures persevere into the developed turbulence. We investigate energetic exchanges in the transitional and turbulent regimes with particular emphasis on the emergence of periodic and non-periodic, as well as symmetric and anti-symmetric structures within the flow.

3. Unlocking massively parallel spectral proper orthogonal decompositions in the PySPOD package

   M. Rogowski, B. C. Y. Yeung, O. T. Schmidt, and 4 more authors

   Computer Physics Communications, 2024, 302, 109246

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   We propose a parallel (distributed) version of the spectral proper orthogonal decomposition (SPOD) technique. The parallel SPOD algorithm distributes the spatial dimension of the dataset preserving time. This approach is adopted to preserve the non-distributed fast Fourier transform of the data in time, thereby avoiding the associated bottlenecks. The parallel SPOD algorithm is implemented in the PySPOD library and makes use of the standard message passing interface (MPI) library, implemented in Python via mpi4py. An extensive performance evaluation of the parallel package is provided, including strong and weak scalability analyses. The open-source library allows the analysis of large datasets of interest across the scientific community. Here, we present applications in fluid dynamics and geophysics, that are extremely difficult (if not impossible) to achieve without a parallel algorithm. This work opens the path toward modal analyses of big quasi-stationary data, helping to uncover new unexplored spatio-temporal patterns. Program summary Program Title: PySPOD CPC Library link to program files: https://doi.org/10.17632/jf5bf26jcj.1 Developer’s repository link: https://github.com/MathEXLab/PySPOD Licensing provisions: MIT License Programming language: Python Nature of problem: Large spatio-temporal datasets may contain coherent patterns that can be leveraged to better understand, model, and possibly predict the behavior of complex dynamical systems. To this end, modal decomposition methods, such as the proper orthogonal decomposition (POD) and its spectral counterpart (SPOD), constitute powerful tools. The SPOD algorithm allows the systematic identification of space-time coherent patterns. This can be used to understand better the physics of the process of interest, and provide a path for mathematical modeling, including reduced order modeling. The SPOD algorithm has been successfully applied to fluid dynamics, geophysics and other domains. However, the existing open-source implementations are serial, and they prevent running on the increasingly large datasets that are becoming available, especially in computational physics. The inability to analyze via SPOD large dataset in turn prevents unlocking novel mechanisms and dynamical behaviors in complex systems. Solution method: We provide an open-source parallel (MPI distributed) code, namely PySPOD, that is able to run on large datasets (the ones considered in the present paper reach about 200 Terabytes). The code is built on the previous serial open-source code PySPOD that was published in https://joss.theoj.org/papers/10.21105/joss.02862.pdf. The new parallel implementation is able to scale on several nodes (we show both weak and strong scalability) and solve some of the bottlenecks that are commonly found at the I/O stage. The current parallel code allows running on datasets that was not easy or possible to analyze with serial SPOD algorithms, hence providing a path towards unlocking novel findings in computational physics. Additional comments including restrictions and unusual features: The code comes with a set of built-in postprocessing tools, for visualizing the results. It also comes with extensive continuous integration, documentation, and tutorials, as well as a dedicated website in addition to the associated GiHub repository. Within the package we also provide a parallel implementation of the proper orthogonal decomposition (POD), that leverages the I/O parallel capabilities of the SPOD algorithm.

4. Nonlinear Interactions in Turbulent Jets

   A. Nekkanti, E. Pickering, T. Colonius, and 1 more author

   AIAA Paper 2024-3414, 2024

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   Bispectral mode decomposition is used to investigate triadic interactions within a Mach 0.4 turbulent jet. We explore its potential to identify dominant triadic interactions and their associated spatial structures in an unforced turbulent jet. The bispectral measure is broadband in frequency for each azimuthal wavenumber triad. The [1,1,2] and [0,0,0] azimuthal wavenumber triads are dominant, emphasizing the importance of the self-interactions of the helical and axisymmetric components. Bispectral modes reveal that streaky structures are fed by the interaction of a Kelvin-Helmholtz wavepacket with its conjugate. Streaks are also observed in other frequency interactions, occurring in regions where the structures of these frequencies are spatially active. Furthermore, integral interaction maps and nonlinear transfer terms are computed to determine the direction of energy transfer and to pinpoint the spatial regions where nonlinearity is most active. As the shear layer develops, small scales interact nonlinearly, transferring energy to larger scales. Moving downstream, near the potential core closure, larger scales become more active, resulting in a forward energy cascade.

5. Adaptive spectral proper orthogonal decomposition of broadband-tonal flows

   B. C. Y. Yeung, and O. T. Schmidt

   Theoretical and Computational Fluid Dynamics, 2024, 1–20

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6. Linstab2D: stability and resolvent analysis of compressible viscous flows in MATLAB

   E. Martini, and O. T. Schmidt

   Theoretical and Computational Fluid Dynamics, 2024, 38(5), 665–685

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   We present LinStab2D, an easy-to-use linear stability analysis MATLAB tool capable of handling complex domains, performing temporal and spatial linear stability, and resolvent analysis. We present the theoretical foundations of the code, including the linear stability and resolvent analysis frameworks, finite differences discretization schemes, and the Floquet ansatz. These concepts are explored in five different examples, highlighting and illustrating the different code capabilities, including mesh masking, mapping, imposition of boundary constraints, and the analysis of periodic flows using Cartesian or axisymmetric coordinates. These examples were constructed to be a departure point for studying other flows.

7. Analysis of streaks in unstratified and stratified wakes

   S. Nidhan, A. Nekkanti, O. T. Schmidt, and 1 more author

   AIAA Paper 2024-2561, 2024

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   A turbulent circular disk wake \citechongsiripinyo_decay_2020 is investigated through visualizations, conditional averaging, and spectral analysis to analyze the presence of large-scale streaks. The near wake and intermediate wake are dominated by the vortex shedding mode residing at \m=1, \St=0.135 in the unstratified wake (\\Fr = ∞\). Once the influence of the \m=1 mode is filtered, large-scale streaks become apparent in the flow. These streaks predominantly reside at \m=2 \St →0\. The effect of stratification on streaks is investigated through the analysis of two body-based Froude numbers \\Fr = 2 and \10\. Streaks are present and the lift-up mechanism is active in the near wake of the \\Fr = 10 wake. However, as the \\Fr = 10 wake evolves downstream, the signature of these streaks get weaker. The \\Fr = 2 wake is significantly different from the other two cases from the very beginning. Large-scale streaks are significantly attenuated and the energy at \\St →0 is notably lower than the other two cases throughout the course of its evolution. Conditionally averaged streamwise vorticity fields reveal that streaks are generated through the lift-up mechanism. Higher stratification diminishes the strength of the streamwise vortices thereby diminishing the lift-up effect.

8. An Orthogonal Decomposition for Nonlinear Modal Analysis

   T. Chu, B. Yeung, and O. T. Schmidt

   AIAA Paper 2024-4187, 2024

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   An orthogonal modal decomposition for identifying triadic interactions in fluid flows is presented. The decomposition is based on spectral momentum transfer and extracts coherent structures that partake in three-wave interactions and are optimal in terms of the third-order space-time flow statistics. The method distinguishes between two quadratically interacting components, one acting as a catalyst and the other as a donor of momentum, that collectively contribute to a tertiary component, the recipient. The resulting modes maximize the covariance between the donor and recipient for each triad. The method can be understood as an extension of bispectral mode decomposition (BMD) by considering the exact form of the quadratic nonlinearity of the Navier-Stokes equations. Unlike BMD, and more similar to classical proper orthogonal decomposition (POD), it provides ranked bases for the donor and recipient that are jointly optimal and orthonormal in their respective inner products. Two applications are considered: numerical data of a canonical unsteady cylinder wake and experimental data of a turbulent wind turbine wake by Biswas and Buxton (JFM, 2024).

9. Space-Time Proper Orthogonal Decomposition of Actuation Transients of a Plasma-Controlled Twin-Rectangular Jet

   B. Yeung, and O. T. Schmidt

   AIAA Paper 2024-4192, 2024

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   The transient dynamics of a turbulent supersonic twin-rectangular jet flow, forced symmetrically at a Strouhal number of 0.9, are investigated using large-eddy simulations (LES). The forcing is provided by localized arc filament plasma actuators (LAFPA), modeled as source terms in the energy equation. Under plasma-actuated control, the statistically stationary jet evolves towards a cyclostationary state over a transient phase. Forcing-induced perturbations of the natural jet are extracted using synchronized simulations of the natural and forced jets. A database is collected that captures an ensemble of realizations of the perturbations within the initial transient. The spatiotemporal dynamics and statistics of the transient are investigated using space-time proper orthogonal decomposition (space-time POD) for each D2 symmetry component. The eigenvalue spectra unveil low-rank dynamics in the symmetric component. The spatial and temporal structures of the leading modes indicate that the initial pulse of the actuators produces large, impulsive perturbations to the flow field. The symmetric mode reveals the contraction of the shock cells due to the forcing, and shows the evolution of the mean flow deformation transient.

10. Perturbation amplification near the stagnation point of blunt bodies

    E. Martini, C. Caillaud, G. Lehnasch, and 2 more authors

    Theoretical and Computational Fluid Dynamics, 2024, 1–15

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11. Linear stability and spectral modal decomposition of three-dimensional turbulent wake flow of a generic high-speed train

    X.-B. Li, S. Demange, G. Chen, and 4 more authors

    Journal of Fluid Mechanics, 2024, 1000, A64

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12. On the role of eddy viscosity in resolvent analysis of turbulent jets

    J. G. R. Saldern, O. T. Schmidt, P. Jordan, and 1 more author

    Journal of Fluid Mechanics, 2024, 1000, A51

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13. Direct observation of small scale capillary wave turbulence using high speed digital holographic microscopy

    W. Connacher, J. Orosco, O. T. Schmidt, and 1 more author

    Frontiers in Acoustics, 2024

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2023

1. RBF-FD discretization of the Navier-Stokes equations on scattered but staggered nodes

   T. Chu, and O. T. Schmidt

   Journal of Computational Physics, 2023, 474, 111756

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   A semi-implicit fractional-step method that uses a staggered node layout and radial basis function-finite differences (RBF-FD) to solve the incompressible Navier-Stokes equations is developed. Polyharmonic splines (PHS) with polynomial augmentation (PHS+poly) are used to construct the global differentiation matrices. A systematic parameter study identifies a combination of stencil size, PHS exponent, and polynomial degree that minimizes the truncation error for a wave-like test function on scattered nodes. Classical modified wavenumber analysis is extended to RBF-FDs on heterogeneous node distributions and used to confirm that the accuracy of the selected 28-point stencil is comparable to that of spectral-like, 6th-order Padé-type finite differences. The Navier-Stokes solver is demonstrated on two benchmark problems, internal flow in a lid-driven cavity in the Reynolds number regime 102≤Re≤104, and open flow around a cylinder at Re=100 and 200. The combination of grid staggering and careful parameter selection facilitates accurate and stable simulations at significantly lower resolutions than previously reported, using more compact RBF-FD stencils, without special treatment near solid walls, and without the need for hyperviscosity or other means of regularization.

2. Gappy spectral proper orthogonal decomposition

   A. Nekkanti, and O. T. Schmidt

   Journal of Computational Physics, 2023, 478, 111950

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   Experimental spatio-temporal flow data often contain gaps or other types of undesired artifacts. To reconstruct flow data in the compromised or missing regions, a data completion method based on spectral proper orthogonal decomposition (SPOD) is developed. The algorithm leverages the temporal correlation of the SPOD modes with preceding and succeeding snapshots, and their spatial correlation with the surrounding data at the same time instant. For each gap, the algorithm first computes the SPOD of the remaining, unaffected data. In the next step, the compromised data are projected onto the basis of the SPOD modes. This corresponds to a local inversion of the SPOD problem and yields expansion coefficients that permit the reconstruction in the affected regions. This local reconstruction is successively applied to each gap. After all gaps are filled in, the procedure is repeated in an iterative manner until convergence. This method is demonstrated on two examples: direct numerical simulation of laminar flow around a cylinder, and time-resolved PIV data of turbulent cavity flow obtained by Zhang et al. (2019) [47]. Randomly added gaps correspond to 1%, 5%, and 20% of data loss. Even for 20% data corruption, and in the presence of measurement noise in the experimental data, the algorithm recovers 97% and 80% of the original data in the corrupted regions of the simulation and PIV data, respectively. These values are higher than those achieved by established methods like gappy POD and Kriging.

3. RBF-FD-based global resolvent analysis: the Blasius boundary layer

   T. Chu, and O. T. Schmidt

   AIAA Paper 2023-3567, 2023

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   View Video Presentation: https://doi.org/10.2514/6.2023-3567.vidA high-order mesh-free hydrodynamic stability analysis framework is developed based on radial basis function-based finite differences (RBF-FD). The global linearized Navier-Stokes operator is discretized using polyharmonic spline RBFs with polynomial augmentation (PHS+poly). As a validation test case, the non-parallel flat-plate boundary layer within a computational domain corresponding to a local Reynolds number of 0 ≤ Re_x ≤ 6x10^5 is considered. The computational domain is discretized using scattered nodes created by an unstructured mesh generator. The discrete resolvent operator is constructed, and its singular components are analyzed. The resulting optimal response modes are identified as Tollmien-Schlichting (TS) wavepackets. These responses are optimally forced by the upstream tilted structures that leverage the Orr mechanism. Favorable comparisons to previous literature, both qualitatively and quantitatively, validate the novel framework.

4. Self-consistent closure modeling for linearized mean field methods

   J. G. Saldern, J. M. Reumschüssel, T. L. Kaiser, and 3 more authors

   AIAA Paper 2023-4351, 2023

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   View Video Presentation: https://doi.org/10.2514/6.2023-4351.vidModeling the coherent component of the Reynolds stresses to close the linearized mean field equations has received little attention in recent years, despite the great surge of linearized mean field methods. In this study, we present a modeling approach to account for the coherent component of the Reynolds stresses that is based on a Boussinesq-like model known from steady and unsteady Reynolds-averaged Navier Stokes (RANS) equations. The presented approach is based on two features. Unlike many previous studies, we consider not only a mean eddy viscosity field, but also a fluctuating field derived from linearized algebraic models. Moreover, we introduce the concept of mean field consistency; the mean eddy viscosity field is determined to satisfy the RANS equations along with the other mean field quantities. Practically, this is implemented by assimilating the model constants of the eddy viscosity model from the mean fields, taking into account the RANS equations, which is achieved with a physics-informed neural network. To evaluate the models thus assembled, we propose to perform an a priori analysis. A concept in which the modeled Reynolds stress fluctuations are directly compared to the respective measured quantities. The proposed methods are demonstrated and evaluated on a jet flow at Reynolds number of 50000 and Mach number 0.4.

5. Bispectral mode decomposition of axisymmetrically and non-axisymmetrically forced turbulent jets

   A. Nekkanti, O. T. Schmidt, I. Maia, and 3 more authors

   AIAA Paper 2023-3651, 2023

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   View Video Presentation: https://doi.org/10.2514/6.2023-3651.vidLarge-eddy simulations (LES) of a turbulent unforced jet at \Re = 50,000 and \M_j = 0.4 and jets forced at azimuthal wavenumbers \m=0 \m=\pm1 \m=\pm2 and \m=\pm6 are performed. The objective of this study is to characterize the nonlinear interactions that are initiated by the forcing. To achieve this, we used the bispectral mode decomposition (BMD) technique, which is tailored to extract flow structures associated with triadic interactions. Azimuthal wavenumber triads are investigated using the cross-spectral variant of BMD. Axisymmetric forcing generates peaks at the forcing frequency and its harmonics in the \m=0 component only, whereas non-axisymmetric forcing generates peaks at different azimuthal wavenumbers. The latter aspect is investigated using cross-BMD. Forcing the jet at \m=\pm1 the only odd-\m forcing case considered, creates a cascade of triads that generates peaks at the forcing frequency and its odd harmonics at odd azimuthal wavenumbers and even harmonics at even azimuthal wavenumbers. Forcing the jet at \m = \pm m_f azimuthal wavenumbers produces peaks at the odd harmonics in the odd integer multiples of \m_f and at even harmonic frequencies in the even integer multiples of \m_f\.

6. Investigation of Gas Flow Within a Laser Amplifier Head for Optimal Cooling

   E. Lowell, O. T. Schmidt, F. Batysta, and 1 more author

   AIAA Paper 2023-3479, 2023

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   View Video Presentation: https://doi.org/10.2514/6.2023-3479.vidIn an effort to improve thermal management of the gain medium in high-average power, high-intensity lasers, this study focuses on simulating the gas flow through multiple narrow channels. Actively cooling lasers of this class involves flowing helium gas through an array of closely-spaced vanes, where each vane contains a thin slab of gain medium. Since the role of turbulence is crucial to both the thermal management of the gain material and to the optical quality of the laser, it is imperative that the state of the flow within these channels and over the gain medium is properly understood. In the absence of experimental data, the current work utilizes RANS turbulence models and the Langtry-Menter transition prediction model to obtain flow solutions within a representative helium gas-cooled laser amplifier design. The RANS results reveal three flow features within the amplifier head: separation at the inlet diffuser, potential relaminarization within the channels, and a separation region downstream due to the diverging sections of the channels. While computationally inexpensive and suited for exploring optimal aerodynamic design configurations of the amplifier head, the RANS solutions only provide averaged flow quantities. Since the fluctuating density field is necessary for future aero-optical analyses of the laser propagating through the gas flow, a preliminary LES is also introduced. In addition to aero-optics, it is expected the LES will shed light into the inherent unsteadiness of the aforementioned separation regions, which in turn may highlight any links to structural vibrations of the vanes themselves. A comparison of the mean flows of the RANS and LES solutions indicates good agreement within the channels and near the gain medium, and shows that the LES and RANS capture similar separation and recirculation features.

7. Cyclostationary analysis of forced turbulent jets

   L. Heidt, T. Colonius, A. Nekkanti, and 3 more authors

   AIAA Paper 2023-3652, 2023

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   View Video Presentation: https://doi.org/10.2514/6.2023-3652.vidA variety of actuation methods have been applied to turbulent jets with the aim of reducing far-field sound. However, a detailed understanding of the mechanisms by which actuation alters the turbulence and far-field sound is lacking. We investigate the effect of periodic acoustic forcing by performing a series of large-eddy simulations of turbulent axisymmetric subsonic and supersonic jets subjected to periodic forcing at several frequencies and amplitudes. To analyze data from the forced jets, we employ cyclostationary analysis, which is an extension of the statistically stationary framework to processes that have periodically varying statistics. Both low- St_f=0.3 and high-frequency St_f=1.5 forcing generate an energetic tonal response but have limited effect on the time-averaged mean with a forcing amplitude greater than 1% required to achieve a small change. Similar trends were seen for the turbulent kinetic energy and the energy transfer between the mean and turbulent components. By applying cyclostationary spectral proper orthogonal decomposition (CS-SPOD), we investigate how the dominant coherent structures are modified and modulated by the forcing. For St_f=0.3, a broadband increase in the energy of the dominant coherent structures was found. The low-frequency coherent structures were found to be strongly phase dependent, with substantial energy coupled to the high-velocity and high-shear regions of the mean flow. In contrast, forcing at St_f=1.5 resulted in a broadband decrease in the energy of the dominant coherent structures. No phase-dependent modulation of the low-frequency coherent structures was seen due to a large difference in the wavelength and spatial support between the coherent structures and the mean field. A reduced impact of the St_f=0.3 forcing on the supersonic jet is seen, while the St_f=1.5 forcing results in a similar impact.

8. Plasma Actuation and Bispectral Mode Decomposition of Supersonic Twin-Rectangular Jet Flow

   B. Yeung, and O. T. Schmidt

   AIAA Paper 2023-4177, 2023

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   View Video Presentation: https://doi.org/10.2514/6.2023-4177.vidLarge-eddy simulations (LES) of a Mach 1.5, nominally ideally-expanded, twin-rectangular jet are performed, with and without forcing. The numerical implementation of the periodic forcing is based on companion experiments at Ohio State University that utilize localized arc filament plasma actuators (LAFPA) to control twin-jet coupling and influence jet screech. In the forced jet LES, twelve independently-controlled energy sources, which model LAFPAs, generate bursts of thermal and pressure perturbations in a pattern that is symmetric about the major and minor axes of the jet, or symmetric-symmetric for short. For rigorous statistical analysis, the natural and forced jet data are decomposed into their \D_2\-symmetry components, which are either symmetric or antisymmetric about the major and/or minor axes. To identify large-scale structures involved in triadic interactions, bispectral mode decomposition (BMD) is applied to the forced case, leading to a complex mode bispectrum and three-dimensional BMD modes for each \D_2 symmetry component (auto-BMD) or set of components (cross-BMD). The BMD analyses reveal dominant triadic interactions between symmetric-symmetric modes, associated with the forcing, and between antisymmetric-symmetric modes, associated with the natural screech tone. Both classes of symmetry-self interactions generate superharmonics and mean flow distortions that are symmetric-symmetric. In contrast, symmetry-cross interactions between the symmetric-symmetric forcing and antisymmetric-symmetric screech form superharmonics and mean flow deformations that are antisymmetric-symmetric. Summed mode spectra, obtained from the average along each diagonal of the BMD bispectra, suggest that under the present forcing, consistent symmetry (i.e., either both symmetric, or both antisymmetric) about the minor axis is a prerequisite for two modes to interact quadratically.

9. Gappy SPOD for TR-PIV data of stationary flows

   O. T. Schmidt, E. Brothers, A. Nekkanti, and 2 more authors

   2023

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10. Large-scale streaks in a turbulent bluff body wake

    A. Nekkanti, S. Nidhan, O. T. Schmidt, and 1 more author

    Journal of Fluid Mechanics, 2023, 974, A47

    DOI PDF

2022

1. Analysis of coherence in turbulent stratified wakes using spectral proper orthogonal decomposition

   S. Nidhan, O. T. Schmidt, and S. Sarkar

   Journal of Fluid Mechanics, 2022, 934, A12

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2. Mesh-free RBF-based discretizations for hydrodynamic stability analysis

   T. Chu, and O. T. Schmidt

   AIAA Paper 2022-4098, 2022

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   View Video Presentation: https://doi.org/10.2514/6.2022-4098.vid Radial basis function-based finite differences (RBF-FD) are used to develop a high-order mesh-free hydrodynamic stability analysis tool for complex geometries. Polyharmonic spline RBFs with polynomial augmentation (PHS+poly) are used to construct the discrete linearized Navier-Stokes and resolvent operators on arbitrarily scattered nodes. The PHS+poly discretization is shown to yield accurate, stable, and computationally efficient discretizations of the large hydrodynamic stability matrix problems arising in two-dimensional classical linear theory and resolvent analysis. The mean-flow stability of the wake behind a cylinder in the vicinity of the critical point is studied using both theories. The predicted flow instabilities, including the vortex shedding frequency and associated coherent structures, closely match those reported in the literature.

3. Spectral proper orthogonal decomposition using multitaper estimates

   O. T. Schmidt

   Theoretical and Computational Fluid Dynamics, 2022, 1–14

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   The use of multitaper estimates for spectral proper orthogonal decomposition (SPOD) is explored. Multitaper and multitaper-Welch estimators that use discrete prolate spheroidal sequences (DPSS) as orthogonal data windows are compared to the standard SPOD algorithm that exclusively relies on weighted overlapped segment averaging, or Welch’s method, to estimate the cross-spectral density matrix. Two sets of turbulent flow data, one experimental and the other numerical, are used to discuss the choice of resolution bandwidth and the bias-variance tradeoff. Multitaper-Welch estimators that combine both approaches by applying orthogonal tapers to overlapping segments allow for flexible control of resolution, variance, and bias. At additional computational cost but for the same data, multitaper-Welch estimators provide lower variance estimates at fixed frequency resolution or higher frequency resolution at similar variance compared to the standard algorithm.

4. Three-Dimensional Spectral POD of Supersonic Twin-Rectangular Jet Flow

   B. C. Y. Yeung, O. T. Schmidt, and G. A. Brès

   AIAA Paper 2022-3345, 2022

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   View Video Presentation: https://doi.org/10.2514/6.2022-3345.vid The statistical analysis of non-axisymmetric turbulent jets using spectral proper orthogonal decomposition (SPOD) is computationally costly; in particular, their non-axisymmetry precludes Fourier decomposition of the three-dimensional flow field into two-dimensional azimuthal modes. Jets in the dihedral group \D_2 including rectangular, elliptic, and twin jets, are invariant under reflection about their major and minor axes. For these jets, we propose an SPOD workflow that exploits their \D_2 geometrical symmetry to obtain a reduction in computational effort, accelerate statistical convergence, and improve the interpretability of results. We decompose the three-dimensional snapshots into four symmetry components. For each symmetry component, we independently perform SPOD on one quadrant of the domain. We demonstrate an application of this \D_2\-symmetric SPOD workflow on a large-eddy simulation of a twin-rectangular supersonic jet. Our analysis indicates that the twin jet exhibits screech at Strouhal number 0.3, and that this screech is dominated by components which are antisymmetric along the minor axis. These observations are consistent with the results from companion experiments at Ohio State University. Furthermore, the same workflow is used to analyze the symmetry-dependence of far-field acoustics at low and high frequencies.

5. Towards Optimal Gas Cooling with Minimal Aero-optical Distortion for a Laser Amplifier Head

   E. Lowell, O. T. Schmidt, F. Batysta, and 2 more authors

   AIAA Paper 2022-3265, 2022

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   View Video Presentation: https://doi.org/10.2514/6.2022-3265.vid Next-generation, high-peak-power, ultrashort-pulse lasers have the potential to efficiently deliver the high-average-power outputs required by many emerging technologies and areas of research. The combination of large size and low-repetition rates of previous-generation lasers make their effective and widespread usage impractical. The critical step in an effort to increase the repetition rate is a proper management of the waste heat generated in the laser gain medium. The current paper presents a computational approach with which to improve upon current gas-cooled amplifier designs; the ultimate goal being to optimize the head geometry for efficient cooling while maintaining minimal aero-optical distortion. This approach consists of several components, the focus of which are low-fidelity RANS simulations, and high-fidelity LES and aero-optical simulations. Preliminary results indicate that these components interface properly in handling the prescribed base case, and lay the groundwork for continued progress towards simulating, modeling, and optimizing the amplifier head for efficient cooling.

6. Triadic nonlinear interactions and acoustics of forced versus unforced turbulent jets

   A. Nekkanti, I. Maia, P. Jordan, and 3 more authors

   12th International Symposium on Turbulence and Shear Flow Phenomena, 2022

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7. Neural-network learning of SPOD latent dynamics

   A. Lario, R. Maulik, O. T. Schmidt, and 2 more authors

   Journal of Computational Physics, 2022, 468, 111475

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   We aim to reconstruct the latent space dynamics of high dimensional, quasi-stationary systems using model order reduction via the spectral proper orthogonal decomposition (SPOD). The proposed method is based on three fundamental steps: in the first, once that the mean flow field has been subtracted from the realizations (also referred to as snapshots), we compress the data from a high-dimensional representation to a lower dimensional one by constructing the SPOD latent space; in the second, we build the time-dependent coefficients by projecting the snapshots containing the fluctuations onto the SPOD basis and we learn their evolution in time with the aid of recurrent neural networks; in the third, we reconstruct the high-dimensional data from the learnt lower-dimensional representation. The proposed method is demonstrated on two different test cases, namely, a compressible jet flow, and a geophysical problem known as the Madden-Julian Oscillation. An extensive comparison between SPOD and the equivalent POD-based counterpart is provided and differences between the two approaches are highlighted. The numerical results suggest that the proposed model is able to provide low rank predictions of complex statistically stationary data and to provide insights into the evolution of phenomena characterized by specific range of frequencies. The comparison between POD and SPOD surrogate strategies highlights the need for further work on the characterization of the interplay of error between data reduction techniques and neural network forecasts.

8. Non-Modal Mechanisms in the Flow over the Leading Edge of Blunt Bodies

   E. Martini, C. Caillaud, O. T. Schmidt, and 2 more authors

   12th International Symposium on Turbulence and Shear Flow Phenomena, 2022
9. Interaction between wavepackets and streaks in turbulent jets

   P. A. S. Nogueira, A. V. G. Cavalieri, V. Jaunet, and 3 more authors

   12th International Symposium on Turbulence and Shear Flow Phenomena, 2022
10. Gappy spectral proper orthogonal decomposition for reconstruction of turbulent flow data

    O. T. Schmidt, and A. Nekkanti

    12th International Symposium on Turbulence and Shear Flow Phenomena, 2022

2021

1. Waves in screeching jets

   D. Edgington-Mitchell, T. Wang, P. Nogueira, and 5 more authors

   Journal of Fluid Mechanics, 2021, 913, A7

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2. Optimal eddy viscosity for resolvent-based models of coherent structures in turbulent jets

   E. Pickering, G. Rigas, O. T. Schmidt, and 2 more authors

   Journal of Fluid Mechanics, 2021, 917, A29

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3. An RBF-based finite difference discretization of the Navier-Stokes equations: error analysis and application to lid-driven cavity flow

   T. Chu, and O. T. Schmidt

   AIAA Paper 2021-2743, 2021

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   View Video Presentation: https://doi.org/10.2514/6.2021-2743.vidRadial basis function-finite differences (RBF-FD) are used to solve the incompressible Navier-Stokes equations on scattered nodes. We present a semi-implicit fractional-step method that uses a staggered grid arrangement. The RBF-QR method devised by Fornberg and Piret[1] is used to obtain the RBF-FD weights for the spatial derivatives. We propose a rigorous error analysis strategy to identify optimal combinations of the shape parameter, ε, and the stencil size,n. A modified wavenumber analysis shows that the accuracy of the RBF differentiation matrices based on the optimal parameters is comparable to 4th-order Padé-type finite differences, for both first and second derivatives. The internal flow in a lid-driven cavity is studied as an example. We demonstrate that stable solutions are obtained without the need for hyperviscosity.

4. Analysis of forced subsonic jets using spectral proper orthogonal decomposition and resolvent analysis

   L. Heidt, T. Colonius, A. Nekkanti, and 3 more authors

   AIAA Paper 2021-2108, 2021

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   View Video Presentation: https://doi.org/10.2514/6.2021-2108.vidVarious passive and active control strategies have been applied to turbulent jets and have achieved up to about a 5dB reduction in overall sound pressure level. However, the mechanisms by which forcing alters the turbulence and far-field sound are poorly understood. We investigate the effect of forcing by performing large-eddy simulations of turbulent axisymmetric jets subjected to periodic forcing at multiple frequencies and amplitudes. Spectral proper orthogonal decomposition is used to study the effect of the forcing on the linear spectrum. Low-frequency periodic forcing, with \St_f = 0.3 while producing highly energetic tonal structures and noise, has a limited effect upon the underlying turbulent spectrum of the jet and the most energetic modes. High levels of forcing, 1\% of the jet velocity, are required to achieve a small change to the turbulent mean flow and a minor shift in the turbulent spectrum. The changes in the overall spectrum and the shift in the modes are predicted well via the resolvent analysis performed on the new turbulent mean flow. This shows that the turbulent spectrum stems from the turbulent mean flow and not via interactions between phase-locked structures and the natural turbulence. High-frequency periodic forcing, with \St_f = 1.5 is less effective at altering the mean flow field compared to the low-frequency forcing at the same amplitude, but results in a nonlinear interaction, potentially associated with vortex pairing, amplifying the turbulence spectrum at \St ≈0.75\.

5. Towards large-eddy simulations of supersonic jets from twin rectangular nozzle with plasma actuation

   G. A. Brès, B. Yeung, O. T. Schmidt, and 4 more authors

   AIAA Paper 2021-2154, 2021

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   View Video Presentation: https://doi.org/10.2514/6.2021-2154.vidLarge-eddy simulation of a jet issuing from rectangular nozzles of aspect ratio 2 is performed. The nozzles are operating at their nominal design Mach number of 1.5. This operating condition and the geometry match those of the companion experiment conducted at Ohio State University. The preliminary results show good agreement with near-field and far-field noise measurements in terms of broadband levels and predictions of screech tone frequencies and amplitudes. In particular, the main noise radiation towards the aft angles and the overall sound pressure level directivity are within 1dB for most relevant frequencies and angles. For future simulations of active control, a numerical model of a localized arc filament plasma actuator is implemented and tested in a small test domain inside one of the nozzles. A grid resolution study is conducted to investigate the minimum grid resolution required for correct energy transport within the boundary layer.

6. Nonlinear dynamics of forced wavepackets in turbulent jets

   I. Maia, P. Jordan, L. Heidt, and 3 more authors

   AIAA Paper 2021-2277, 2021

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   View Video Presentation: https://doi.org/10.2514/6.2021-2277.vidWe study the dynamics of harmonically-forced jets under different forcing amplitudes covering linear and nonlinear response regimes. Using a combination of Particle Image Velocimetry (PIV) measurements, Spectral Proper Orthogonal Decomposition (SPOD) and Bispectral Mode Decomposition (BMD), we educe coherent structures on the different forcing regimes and analyse how strong nonlinear interactions affect their dynamics. The forced jets provide a simplified scenario where energy exchange between frequencies can be traced back to a few prominent triadic interactions. These are identified through the mode bispectrum and the associated BMD modes are found to be in good agreement with the most energetic structures computed through SPOD. The mode bispectrum also provides insight into the relative importance of linear and nonlinear mechanisms, with respect to the mean of the forced jet, in determining the amplitudes of velocity fluctuations at the forcing frequency and its harmonics. Unforced jets have a broad signature in the bispectrum, reflecting the broadband nature of nonlinear energy exchange in the unforced jets.

7. A stochastic SPOD-Galerkin model for broadband turbulent flows

   T. Chu, and O. T. Schmidt

   Theoretical and Computational Fluid Dynamics, 2021

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   The use of spectral proper orthogonal decomposition (SPOD) to construct low-order models for broadband turbulent flows is explored. The choice of SPOD modes as basis vectors is motivated by their optimality and space-time coherence properties for statistically stationary flows. This work follows the modeling paradigm that complex nonlinear fluid dynamics can be approximated as stochastically forced linear systems. The proposed stochastic two-level SPOD-Galerkin model governs a compound state consisting of the modal expansion coefficients and forcing coefficients. In the first level, the modal expansion coefficients are advanced by the forced linearized Navier-Stokes operator under the linear time-invariant assumption. The second level governs the forcing coefficients, which compensate for the offset between the linear approximation and the true state. At this level, least squares regression is used to achieve closure by modeling nonlinear interactions between modes. The statistics of the remaining residue are used to construct a dewhitening filter that facilitates the use of white noise to drive the model. If the data residue is used as the sole input, the model accurately recovers the original flow trajectory for all times. If the residue is modeled as stochastic input, then the model generates surrogate data that accurately reproduces the second-order statistics and dynamics of the original data. The stochastic model uncertainty, predictability, and stability are quantified analytically and through Monte Carlo simulations. The model is demonstrated on large eddy simulation data of a turbulent jet at Mach number $M=0.9and Reynolds number \mathrm Re_D≈10^6$.

8. Frequency–time analysis, low-rank reconstruction and denoising of turbulent flows using SPOD

   A. Nekkanti, and O. T. Schmidt

   Journal of Fluid Mechanics, 2021, 926, A26

   DOI PDF

2020

1. Lift-up, Kelvin–Helmholtz and Orr mechanisms in turbulent jets

   E. Pickering, G. Rigas, P. A. S. Nogueira, and 3 more authors

   Journal of Fluid Mechanics, 2020, 896, A2

   DOI
2. Role of Coherent Structures in Turbulent Premixed Flame Acoustics

   D. Brouzet, A. Haghiri, M. Talei, and 4 more authors

   AIAA Journal, 2020, 58(6), 2635-2642

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3. Guide to spectral proper orthogonal decomposition

   O. T. Schmidt, and T. Colonius

   AIAA Journal, 2020, 58(3), 1023–1033

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4. Modal Analysis of Acoustic Directivity in Turbulent Jets

   A. Nekkanti, and O. T. Schmidt

   AIAA Journal, 2020, 0(0), 1-12

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   The directivity of noise from three large-eddy simulations of turbulent jets at Mach 0.7, 0.9, and 1.5 is investigated using spectral proper orthogonal decomposition (SPOD). The most energetic patterns of acoustic radiation are extracted using the far-field pressure 2-norm. Specialization of the norm to the far field is accomplished through localized spatial weighting. Radiation patterns to specific jet inlet angles are isolated by further restricting the spatial weighting to small rectangular regions in the far field. The most energetic radiation pattern for all cases and relevant frequencies is a single superdirective acoustic beam in the downstream direction. The source region of these beams is traced back to the end of the potential core for low frequencies and the shear-layer region for higher frequencies. In the sideline direction, to low angles, the acoustic patterns consist of beams that propagate upstream or perpendicular to the jet axis. The sideline radiation patterns are found to originate from the same source locations as the dominant superdirective beams. Inspection of the SPOD modes reveals that sideline radiation is directly linked to directive downstream radiation. Within the restricted radial extent of the computational domain, these results indicate that the sources of sideline and downstream radiation are intimately linked.

5. Extreme events in wall turbulence

   M. J. P. Hack, and O. T. Schmidt

   Journal of Fluid Mechanics, 2020, 907, A9

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6. Bispectral mode decomposition of nonlinear flows

   O. T. Schmidt

   Nonlinear Dynamics, 2020, (102(4)), 2479-2501

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   Triadic interactions are the fundamental mechanism of energy transfer in fluid flows. This work introduces bispectral mode decomposition as a direct means of educing flow structures that are associated with triadic interactions from experimental or numerical data. Triadic interactions are characterized by quadratic phase coupling which can be detected by the bispectrum. The proposed method maximizes an integral measure of this third-order statistic to compute modes associated with frequency triads, as well as a mode bispectrum that identifies resonant three-wave interactions. Unlike the classical bispectrum, the decomposition establishes a causal relationship between the three frequency components of a triad. This permits the distinction of sum- and difference-interactions, and the computation of interaction maps that indicate regions of nonlinear coupling. Three examples highlight different aspects of the method. Cascading triads and their regions of interaction are educed from direct numerical simulation data of laminar cylinder flow. It is further demonstrated that linear instability mechanisms that attain an appreciable amplitude are revealed indirectly by their difference-self-interactions. Applicability to turbulent flows and noise-rejection is demonstrated on particle image velocimetry data of a massively separated wake. The generation of sub- and ultra-harmonics in large eddy simulation data of a transitional jet is explained by extending the method to cross-bispectral information.

7. Amplitude Scaling of Wave Packets in Turbulent Jets

   L. A. Antonialli, A. V. G. Cavalieri, O. T. Schmidt, and 4 more authors

   AIAA Journal, 2020, 0(0), 1-10

   Abs DOI

   This paper studies the amplitude of large-scale coherent wave-packet structures in jets, modeled by the parabolized stability equations (PSEs). Linear PSEs can retrieve the shape of the wave packets, but linearity leads to solutions with a free amplitude, which has traditionally been obtained in an ad hoc manner using limited data. We systematically determine the free amplitude as a function of frequency and azimuthal wave number by comparing the fluctuation fields retrieved from PSEs with coherent structures educed from large-eddy simulation data using spectral proper orthogonal decomposition. The wave-packet amplitude is shown to decay exponentially with the Strouhal number for axisymmetric and helical modes at both Mach numbers considered in the study: 0.4 and 0.9. Analytical fit functions are proposed, and the scaled wave packets provide reasonable reconstructions of pressure and velocity spectra on the jet centerline and lip line over a range of streamwise positions.

8. Spectral proper orthogonal decomposition analysis of the turbulent wake of a disk at Re=50000

   S. Nidhan, K. Chongsiripinyo, O. T. Schmidt, and 1 more author

   Physical Review Fluids, 2020, 5(12), 124606

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9. Modal analysis of the directivity of acoustic emissions from wavepackets in turbulent jets

   A. Nekkanti, and O. T. Schmidt

   AIAA Paper 2020-0745, 2020

   Abs DOI

   The directivity of noise from three large-eddy simulations of turbulent jets at Mach 0.7, 0.9 and 1.5 and the first three azimuthal wavenumbers is investigated using spectral proper orthogonal decomposition (SPOD). First, a weighting function for the pressure 2-norm that is localized to the far-field is employed to educe the overall most energetic radiation patterns. Second, we isolate radiation patterns to specific jet inlet angles by restricting the spatial weighting to small rectangular regions in the far-field. The most energetic radiation pattern for all cases and relevant frequencies is a single superdirective acoustic beam in the downstream direction. The source region of these beams is traced back to the end of the potential core for low frequencies and the shear-layer region for higher frequencies. In the sideline direction to low angles, the acoustic patterns consist of waves that propagate upstream or perpendicular to the jet axis. The sideline radiation patterns are found to originate from the same source locations as the dominant superdirective beams. Inspection of the SPOD modes reveals that sideline radiation is directly slaved to directive downstream radiation. These results indicate that large-scale coherent structures are the dominant source of acoustic radiation to all the angles.

2019

1. Turbulent Inflow Generation by Resolvent Mode Forcing

   B. Selent, C. Wenzel, U. Rist, and 1 more author

   New Results in Numerical and Experimental Fluid Mechanics XII, 2019, 110–119

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2. Spectral Empirical Orthogonal Function Analysis of Weather and Climate Data

   O. T. Schmidt, G. Mengaldo, G. Balsamo, and 1 more author

   Monthly Weather Review, 2019, 147(8), 2979-2995

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   We apply spectral empirical orthogonal function (SEOF) analysis to educe climate patterns as dominant spatiotemporal modes of variability from reanalysis data. SEOF is a frequency-domain variant of standard empirical orthogonal function (EOF) analysis, and computes modes that represent the statistically most relevant and persistent patterns from an eigendecomposition of the estimated cross-spectral density matrix (CSD). The spectral estimation step distinguishes the approach from other frequency-domain EOF methods based on a single realization of the Fourier transform, and results in a number of desirable mathematical properties: at each frequency, SEOF yields a set of orthogonal modes that are optimally ranked in terms of variance in the L2 sense, and that are coherent in both space and time by construction. We discuss the differences between SEOF and other competing approaches, as well as its relation to dynamical modes of stochastically forced, nonnormal linear dynamical systems. The method is applied to ERA-Interim and ERA-20C reanalysis data, demonstrating its ability to identify a number of well-known spatiotemporal coherent meteorological patterns and teleconnections, including the Madden–Julian oscillation (MJO), the quasi-biennial oscillation (QBO), and the El Niño–Southern Oscillation (ENSO) (i.e., a range of phenomena reoccurring with average periods ranging from months to many years). In addition to two-dimensional univariate analyses of surface data, we give examples of multivariate and three-dimensional meteorological patterns that illustrate how this technique can systematically identify coherent structures from different sets of data. The MATLAB code used to compute the results presented in this study, including the download scripts for the reanalysis data, is freely available online.

3. Eddy viscosity for resolvent-based jet noise models

   E. M. Pickering, G. Rigas, D. Sipp, and 2 more authors

   2019, 2454
4. Resolvent-based analysis of streaks in turbulent jets

   P. A Nogueira, A. V. G. Cavalieri, O. T. Schmidt, and 5 more authors

   AIAA Paper 2019-2569, 2019, 2569
5. Streaks and coherent structures in jets from round and serrated nozzles

   G. Rigas, E. M. Pickering, O. T. Schmidt, and 4 more authors

   AIAA Paper 2019-2597, 2019, 2597
6. An investigation of the Mach number dependence of trapped acoustic waves in turbulent jets

   A. Towne, O. T. Schmidt, and G. A. Brès

   2019, 2546
7. Modulation of downstream-propagating waves in aeroacoustic resonance

   D. M. Edgington-Mitchell, D. Duke, T. Wang, and 4 more authors

   AIAA Paper 2019-2689, 2019, 2689

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8. Real-Time Estimation in a Turbulent Jet Using Multiple-Input-Multiple-Output Transfer Functions

   I. Maia, P. Jordan, E. Martini, and 4 more authors

   AIAA Paper 2019-2535, 2019, 2535
9. A conditional space–time POD formalism for intermittent and rare events: example of acoustic bursts in turbulent jets

   O. T. Schmidt, and P. J. Schmid

   Journal of Fluid Mechanics, 2019, 867, R2

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2018

1. Jet–flap interaction tones

   P. Jordan, V. Jaunet, A. Towne, and 4 more authors

   Journal of Fluid Mechanics, 2018, 853, 333–358

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2. Importance of the nozzle-exit boundary-layer state in subsonic turbulent jets

   G. Brès, P. Jordan, M. Le Rallic, and 6 more authors

   Journal of Fluid Mechanics, 2018, 851, 83–124

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3. Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis

   A. Towne, O. T. Schmidt, and T. Colonius

   Journal of Fluid Mechanics, 2018, 847, 821–867

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4. Spectral analysis of jet turbulence

   O. T. Schmidt, A. Towne, G. Rigas, and 2 more authors

   Journal of Fluid Mechanics, 2018, 855, 953–982

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5. An efficient streaming algorithm for spectral proper orthogonal decomposition

   O. T. Schmidt, and A. Towne

   Computer Physics Communications, 2018

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   A streaming algorithm to compute the spectral proper orthogonal decomposition (SPOD) of stationary random processes is presented. As new data becomes available, an incremental update of the truncated eigenbasis of the estimated cross-spectral density (CSD) matrix is performed. The algorithm requires access to only one temporal snapshot of the data at a time and converges orthogonal sets of SPOD modes at discrete frequencies that are optimally ranked in terms of energy. We define measures of error and convergence, and demonstrate the algorithm’s performance on two datasets. The first example considers a high-fidelity numerical simulation of a turbulent jet, and the second example uses optical flow data obtained from high-speed camera recordings of a stepped spillway experiment. For both cases, the most energetic SPOD modes are reliably converged. The algorithm’s low memory requirement enables real-time deployment and allows for the convergence of second-order statistics from arbitrarily long streams of data. A MATLAB implementation of the algorithm along with a test database for the jet example, can be found in the Supplementary material.

6. Amplitude scaling of turbulent-jet wavepackets

   L. A. Antonialli, A. V. G. Cavalieri, O. T. Schmidt, and 4 more authors

   AIAA Paper 2018-2978, 2018

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7. Large-eddy simulations of co-annular turbulent jet using a Voronoi-based mesh generation framework

   G. A. Brès, S. T. Bose, M. Emory, and 4 more authors

   AIAA Paper 2018-3302, 2018

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2017

1. High-frequency wavepackets in turbulent jets

   K. Sasaki, A. V. G. Cavalieri, P. Jordan, and 3 more authors

   Journal of Fluid Mechanics, 2017, 830, R2

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2. Wavepackets and trapped acoustic modes in a turbulent jet: coherent structure eduction and global stability

   O. T. Schmidt, A. Towne, T. Colonius, and 3 more authors

   Journal of Fluid Mechanics, 2017, 825, 1153-1181

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3. Modal analysis of fluid flows: An overview

   K. Taira, S. L. Brunton, S. Dawson, and 7 more authors

   AIAA Journal, 2017

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4. Acoustic resonance in the potential core of subsonic jets

   A. Towne, A. V. G. Cavalieri, P. Jordan, and 4 more authors

   Journal of Fluid Mechanics, 2017, 825, 1113-1152

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5. Wavepacket intermittency and its role in turbulent jet noise

   O. T. Schmidt, T. Colonius, and G. A. Brès

   AIAA Paper 2016-3050, 2017

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6. Linear dynamics of large-scale structures in turbulent jets

   O. T. Schmidt, T. Colonius, and G. A. Brès

   10th International Symposium on Turbulence and Shear Flow Phenomena, 2017

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7. One-Way Navier-Stokes and resolvent analysis for modeling coherent structures in a supersonic turbulent jet

   G. Rigas, O. T. Schmidt, T. Colonius, and 1 more author

   AIAA Paper 2017-4046, 2017, 4046

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2016

1. On the influence of Sommerfeld’s radiation boundary condition on the propagation direction of oblique modes in streamwise corner flow

   J. Staudenmeyer, O. T. Schmidt, and U. Rist

   Journal of Fluid Mechanics, 2016, 807, R3

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2. Large eddy simulation for jet noise: azimuthal decomposition and intermittency of the radiated sound

   G. A. Brès, V. J., M. Le Rallic, and 6 more authors

   AIAA Paper 2016-3050, 2016

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3. High-frequency wavepackets in turbulent jets

   A. V. G. Cavalieri, K. Sasaki, P. Jordan, and 3 more authors

   AIAA Paper 2016-3056, 2016

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4. Tonal dynamics and sound in subsonic turbulent jets

   V. Jaunet, P. Jordan, A. V. G. Cavalieri, and 4 more authors

   AIAA Paper 2016-3016, 2016

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5. Super- and multi-directive acoustic radiation by linear global modes of a turbulent jet

   O. T. Schmidt, A. Towne, T. Colonius, and 4 more authors

   AIAA Paper 2016-2808, 2016

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6. Trapped acoustic waves in the potential core of subsonic jets

   A. Towne, A. V. G. Cavalieri, P. Jordan, and 4 more authors

   AIAA Paper 2016-2809, 2016

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2015

1. Optimal wavepackets in streamwise corner flow

   O. T. Schmidt, S. M. Hosseini, Ulrich Rist, and 2 more authors

   Journal of Fluid Mechanics, 2015, 766, 405–435

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2. Numerical investigation of classical and bypass transition in streamwise corner-flow

   O. T. Schmidt, and U. Rist

   Procedia IUTAM, 2015, 14, 218-226

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2014

1. Viscid–inviscid pseudo-resonance in streamwise corner flow

   O. T. Schmidt, and U. Rist

   Journal of Fluid Mechanics, 2014, 743, 327–357

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2013

1. Direct numerical simulation of boundary layer transition in streamwise corner-flow

   O. T. Schmidt, B. Selent, and U. Rist

   High Performance Computing in Science and Engineering, 2013, 337-348

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2011

1. Linear stability of compressible flow in a streamwise corner

   O. T. Schmidt, and U. Rist

   Journal of Fluid Mechanics, 2011, 688, 569-590

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2. Viscous and inviscid instabilities of supersonic flow in a streamwise corner

   O. T. Schmidt, and U. Rist

   AIAA Paper 2011-3755, 2011

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2004

1. Prediction of attachment line transition for a high-lift wing based on two-dimensional flow calculations with RANS-solver

   J. Wild, and O. T. Schmidt

   New Results in Numerical and Experimental Fluid Mechanics, 2004, 5, 200-207

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