arXiv subjects

Oliver T. Schmidt

Publications and source records attributed to Oliver T. Schmidt.

At least 19 recordsLinked to original sources

arXiv2026

Mollified-sharp decomposition: a probabilistic regularization of parametric POD for shock-bearing flows

This paper introduces the mollified-sharp decomposition, a probabilistic regularization of moving shocks in parametric reduced-order models. Each detected shock location is treated as a random variable with a prescribed probability density. Averaging over this artificial distribution replaces the localized pressure change by a smooth transition whose spatial extent is set by the density width, rather than by direct filtering of the pressure field. Each snapshot is decomposed exactly into a regularized mollified field and a local sharp correction that restores the shock. This probabilistic construction and exact additive split define the general method; the detector, kernel, treatment of multiple shocks, alignment coordinates, and regression are implementation choices. In the present realization, a calibrated indicator detects shocks, a compactly supported Wendland kernel mollifies them, and a peak-normalized and, where necessary, partitioned weight derived from each shock-location probability density defines the centroid, principal axes, and scales of its local alignment domain. Separate POD-GPR models represent the mollified field and aligned corrections, with additional regressions for shock presence and alignment. The method is demonstrated on the transonic airfoil pressure data of Catalani et al. (2023) and compared with a standard POD-GPR model constructed from the same data and POD-energy criterion. The mollified-sharp model reduces the mean test-set relative $L^2$ pressure error by 31.2% and the mean test-set surface-pressure-coefficient error by 33.2%, while also improving the predicted shock locations and pressure changes; the trade-off is a median online evaluation time 2.24 times as long. The construction is applicable in principle to other parameter-dependent fields with moving sharp features, such as moving material interfaces in multiphase flows.

physics.comp-ph↗

arXiv2026

Wake interactions drive synchronized vortex merging in a hovering quadcopter

The most energetic coherent structure of a hovering full-scale quadcopter is associated with a self-organizing process in which the individual rotor vortices synchronize their frequencies while undergoing merging events, yielding a globally correlated structure. We identify and characterize this phenomenon by applying spectral modal and conditional analyses to assimilated three-dimensional velocity data acquired via Shake-The-Box Lagrangian particle tracking. The dataset captures a high-Re, turbulent flow further complicated by time-varying rotor speeds stemming from active flight control, low-frequency vehicle drift, finite spatio-temporal resolution, and measurement uncertainty. Most coherent structures recover established single-rotor features such as tip vortices and their subharmonic pairing. The globally synchronized vortex merging manifests as a spectral peak at an incommensurate frequency below the rotor band, which cannot be explained by single-rotor aerodynamics, subharmonic instabilities, or band-to-band triadic interactions. Instead, conditional averaging provides evidence of the aforementioned intermittent, distinctly non-subharmonic vortex-merging process involving all four rotor wakes. Establishing whether or not this phenomenon is observed across different flight conditions and configurations remains speculative; however, the consistent characterization of the globally synchronized vortex merging using complementary frequency- and time-domain analyses despite experimental complexities, in particular rotor speed variations, demonstrates its robustness.

physics.flu-dyn↗

arXiv2026

Band-Ensemble Spectral Proper Orthogonal Decomposition with Frequency Attribution

This study presents band-ensemble Spectral Proper Orthogonal Decomposition (bSPOD). The approach is inspired by frequency smoothing, a method used to reduce estimator variance in power spectral density estimates, and is here extended to SPOD. The algorithm estimates SPOD modes from consecutive Fourier coefficients obtained from a single Fourier transform of the full time record and thus avoids time segmentation. In this study, bSPOD is applied to artificial test data and to a PIV data set of a broadband-tonal cavity flow. Compared to the more commonly used Welch-based SPOD formulation, bSPOD reduces spectral leakage, permits increased frequency resolution, and retains frequency information of tonal components at comparable computational cost. These features enable reduced estimator variance while maintaining low bias for tonal components, making bSPOD particularly effective for broadband-tonal flows.

physics.flu-dyn↗

arXiv2026

Data-Driven Reduced-Complexity Modeling of Fluid Flows: A Community Challenge

We introduce a community challenge designed to facilitate direct comparisons between data-driven methods for compression, forecasting, and sensing of complex aerospace flows. The challenge is organized into three tracks that target these complementary capabilities: compression (compact representations for large datasets), forecasting (predicting future flow states from a finite history), and sensing (inferring unmeasured flow states from limited measurements). Across these tracks, multiple challenges span diverse flow datasets and use cases, each emphasizing different model requirements. The challenge is open to anyone, and we invite broad participation to build a comprehensive and balanced picture of what works and where current methods fall short. To support fair comparisons, we provide standardized success metrics, evaluation tools, and baseline implementations, with one classical and one machine-learning baseline per challenge. Final assessments use blind tests on withheld data. We explicitly encourage negative results and careful analyses of limitations. Outcomes will be disseminated through an AIAA Journal Virtual Collection and invited presentations at AIAA conferences.

cs.LG↗

arXiv2025

Boundary Layer Transition as Succession of Temporal and Spatial Symmetry Breaking

We show that both temporal and spatial symmetry breaking in canonical K-type transition arise as organized hydrodynamic structures rather than stochastic fluctuations. Before the skin-friction maximum, the flow is fully described by a periodic, spanwise symmetric, harmonic response to the Tollmien-Schlichting wave, forming a spatially compact coherent structure that produces hairpin packets. This fundamental harmonic response may visually resemble turbulence, but remains fully periodic and delimits the exact extent of the deterministic regime. A distinct regime change occurs after this point; a hierarchy of new (quasi-)periodic and aperiodic space-time structures emerges, followed shortly by anti-symmetric structures that develop similarly despite no anti-symmetric inputs, marking the onset of aperiodicity and spanwise asymmetry. We identify these structures as symmetry-decomposed spectral and space-time proper orthogonal modes that resolve the full progression from deterministic to broadband dynamics. The key insight is that laminar-turbulent transition can be viewed as a sequence of symmetry breaking events, each driven by energetically dominant, space-time coherent modes that gradually turn an initially harmonic flow into broadband turbulence.

physics.flu-dyn↗

arXiv2025

Stochastic reduced-order Koopman model for turbulent flows

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 (SLICK) 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 modeling the residual error as a stochastic source. An empirical dewhitening filter informed by the data is used to maintain the second-order flow statistics within the long-time limit. 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 (LES) data of a turbulent jet, and particle image velocimetry (PIV) 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.

physics.flu-dyn↗

arXiv2025

Data-Driven Forecasting of High-Dimensional Transient and Stationary Processes via Space-Time Projection

Space-Time Projection (STP) is introduced as a data-driven forecasting approach for high-dimensional and time-resolved data. The method computes extended space-time proper orthogonal modes from training data spanning a prediction horizon comprising both hindcast and forecast intervals. Forecasts are then generated by projecting the hindcast portion of these modes onto new data, simultaneously leveraging their orthogonality and optimal correlation with the forecast extension. Rooted in Proper Orthogonal Decomposition (POD) theory, dimensionality reduction and time-delay embedding are intrinsic to the approach. For a given ensemble and fixed prediction horizon, the only tunable parameter is the truncation rank--no additional hyperparameters are required. The hindcast accuracy serves as a reliable indicator for short-term forecast accuracy and establishes a lower bound on forecast errors. The efficacy of the method is demonstrated using two datasets: transient, highly anisotropic simulations of supernova explosions in a turbulent interstellar medium, and experimental velocity fields of a turbulent high-subsonic engineering flow. In a comparative study with standard Long Short-Term Memory (LSTM) neural networks--acknowledging that alternative architectures or training strategies may yield different outcomes--the method consistently provided more accurate forecasts. Considering its simplicity and robust performance, STP offers an interpretable and competitive benchmark for forecasting high-dimensional transient and chaotic processes, relying purely on spatiotemporal correlation information.

cs.LG↗

arXiv2025

Bispectral decomposition and energy transfer in a turbulent jet

We employ bispectral mode decomposition (BMD) to investigate coherent triadic interactions and nonlinear energy transfer in a subsonic turbulent jet. BMD extracts the flow structures corresponding to the dominant triadic interactions. We find a strong triadic correlation among the Kelvin-Helmholtz wavepacket, its conjugate, and the streaks. The most energetic streaks occur at the azimuthal wavenumber $m=2$, with the dominant contributing azimuthal wavenumber triad being $[m_1,m_2,m_3]=[1,1,2]$. The spectral energy budget reveals that nonlinear triadic interactions represent an energy loss to the streaks. Analysis across a wide range of frequencies and azimuthal wavenumbers identifies the direction of nonlinear energy transfer and the spatial regions where these transfers are most active. The turbulent jet exhibits a forward energy cascade in a global sense, though the direction of energy transfer varies locally. In the shear layer near the nozzle exit, triadic interactions between relatively smaller scales are dominant, leading to an inverse energy cascade. Farther downstream, beyond the end of the potential core, triadic interactions between larger scales dominate, resulting in a forward energy cascade.

physics.flu-dyn↗

arXiv2025

Space-time proper orthogonal decomposition of actuation transients: plasma-controlled jet flow

We investigate the forcing-induced transient between statistically stationary and cyclostationary states. The transient dynamics of a turbulent supersonic twin-rectangular jet flow, forced symmetrically at a Strouhal number of 0.9, are studied using synchronized large-eddy simulations (LES) and space-time proper orthogonal decomposition (space-time POD). 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 analyzed using space-time POD for each 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.

physics.flu-dyn↗

arXiv2025

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

We present a framework for parametric proper orthogonal decomposition (POD)-Galerkin reduced-order modeling (ROM) of fluid flows that accommodates variations in flow parameters and control inputs. As an initial step, to explore how the locally optimal POD modes vary with parameter changes, we demonstrate a sensitivity analysis of POD modes and their spanned subspace, respectively rooted in Stiefel and Grassmann manifolds. The sensitivity analysis, by defining distance between POD modes for different parameters, is applied to the flow around a rotating cylinder with varying Reynolds numbers and rotation rates. The sensitivity of the subspace spanned by POD modes to parameter changes is represented by a tangent vector on the Grassmann manifold. For the cylinder case, the inverse of the subspace sensitivity on the Grassmann manifold is proportional to the Roshko number, highlighting the connection between geometric properties and flow physics. Furthermore, the Reynolds number at which the subspace sensitivity approaches infinity corresponds to the lower bound at which the characteristic frequency of the Kármán vortex street exists (Noack & Eckelmann, JFM, 1994). From the Stiefel manifold perspective, sensitivity modes are derived to represent the flow field sensitivity, comprising the sensitivities of the POD modes and expansion coefficients. The temporal evolution of the flow field sensitivity is represented by superposing the sensitivity modes. Lastly, we devise a parametric POD-Galerkin ROM based on subspace interpolation on the Grassmann manifold. The reconstruction error of the ROM is intimately linked to the subspace-estimation error, which is in turn closely related to subspace sensitivity.

physics.flu-dyn↗

arXiv2025

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

We study the stationary, intermittent, and nonlinear dynamics of natural and forced supersonic twin-rectangular turbulent jets using spectral modal decomposition. We decompose large-eddy simulation data into four reflectional symmetry components about the major and minor axes. In the natural jet, spectral proper orthogonal decomposition (SPOD) uncovers two resonant instabilities antisymmetric about the major axis. Known as screech tones, the more energetic of the two is symmetric about the minor axis and steady, while the other is intermittent. We test the hypothesis that flow symmetry can be leveraged for control design. Time-periodic forcing symmetric about the major and minor axes is implemented using a plasma actuation model, and succeeds in removing screech from a different symmetry component. We investigate the spectral peaks of the forced jet using an extension of bispectral mode decomposition (BMD), where the bispectrum is bounded by unity and which conditionally recovers the SPOD. We explain the appearance of harmonic peaks as three sets of triadic interactions between reflectional symmetries, forming an interconnected triad network. BMD modes of active triads distil coherent structures comprising multiple coupled instabilities, including Kelvin-Helmholtz, core, and guided-jet modes (G-JM). Downstream-propagating core modes can be symmetric or antisymmetric about the major axis, whereas upstream-propagating G-JM responsible for screech closure (Edgington-Mitchell et al., 2022, JFM) are antisymmetric only. The dependence of G-JM on symmetry hence translates from the azimuthal symmetry of the round jet to the dihedral group symmetry of the twin-rectangular jet, and explains why the twin jet exhibits antisymmetric but not symmetric screech modes.

physics.flu-dyn↗

arXiv2024

Revealing Structure and Symmetry of Nonlinearity in Natural and Engineering Flows

Energy transfer across scales is fundamental in fluid dynamics, linking large-scale flow motions to small-scale turbulent structures in engineering and natural environments. Triadic interactions among three wave components form complex networks across scales, challenging understanding and model reduction. We introduce Triadic Orthogonal Decomposition (TOD), a method that identifies coherent flow structures optimally capturing spectral momentum transfer, quantifies their coupling and energy exchange in an energy budget bispectrum, and reveals the regions where they interact. TOD distinguishes three components--a momentum recipient, donor, and catalyst--and recovers laws governing pairwise, six-triad, and global triad conservation. Applied to unsteady cylinder wake and wind turbine wake data, TOD reveals networks of triadic interactions with forward and backward energy transfer across frequencies and scales.

physics.flu-dyn↗

arXiv2024

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

This work investigates the spatio-temporal evolution of coherentstructures in the wake of a high-speed train. SPOD is used to extract energy spectra and empirical modes for both symmetric and antisymmetric components of the fluctuating flow field. The spectrum of the symmetric component shows overall higher energy and more pronounced low-rank behavior compared to the antisymmetric one. The most dominant symmetric mode features periodic vortex shedding in the near wake, and wave-like structures in the far wake. The mode bispectrum further reveals the dominant role of self-interaction of the symmetric component, leading to first harmonic and subharmonic triads of the fundamental frequency, with remarkable deformation of the mean field. Then the stability of the three-dimensional wake flow is analyzed based on two-dimensional local linear stability analysis combined with a non-parallelism approximation approach. Temporal stability analysis is first performed, showing a more unstable condition in the near wake. The absolute frequency of the near-wake eigenmode is determined based on spatio-temporal analysis, then tracked along the streamwise direction to find out the global mode growth rate and frequency, which indicate a marginally stable global mode oscillating at a frequency close to the most dominant SPOD mode. The global mode wavemaker is then located, and the structural sensitivity is calculated based on the direct and adjoint modes derived from a local analysis, with the maximum value localized within the recirculation region close to the train tail. Finally, the global mode is computed by tracking the most spatially unstable eigenmode in the far wake, and the alignment with the SPOD mode is computed as a function of streamwise location. By combining data-driven and theoretical approaches, the mechanisms of coherentstructures in complex wake flows are well identified and isolated.

physics.flu-dyn↗

arXiv2024

Unlocking massively parallel spectral proper orthogonal decompositions in the PySPOD package

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 (https://github.com/MathEXLab/PySPOD) library and makes use of the standard message passing interface (MPI) library, implemented in Python via mpi4py (https://mpi4py.readthedocs.io/en/stable/). 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.

physics.comp-ph↗

arXiv2024

Nonlinear dynamics of vortex pairing in transitional jets

This study investigates the onset of linear instabilities and their later nonlinear interactions in the shear layer of an initially-laminar jet using a combination of stability analysis and data from high-fidelity flow simulations. We provide a complete picture of the vortex-pairing process. Hydrodynamic instabilities initiate the transition to turbulence, causing the shear layer to spread rapidly. In this process, the shear layer rolls up to form vortices, accompanied by the exponential growth of the fundamental frequency. As the fundamental frequency grows, it gains energy from the mean flow. Subsequently, as it saturates and begins to decay, the fundamental vortices start to pair. During this vortex pairing process, the subharmonic vortex acquires energy both linearly from the mean flow and nonlinearly through a reverse cascade from the fundamental. The process concludes when the subharmonic vortex eventually saturates. Similarly, two subharmonic vortices merge to form a second subharmonic vortex. Our results confirm Kelly's (1967) hypothesis of a resonance mechanism between the fundamental and subharmonic, which supplies energy to the subharmonic. In this multi-tonal, convective-dominated flow, we clarify the ambiguity surrounding the fundamental frequency by demonstrating that the spatially most amplified frequency should be considered fundamental, rather than the structure associated with the spectral energy peak. For the initially-laminar jet considered here, the fundamental frequency corresponds to the fourth largest spectral peak, highlighting the important distinction between the energetically and dynamical significance of a tone. Despite its low energy, the fundamental frequency is dynamically dominant as it determines all other spectral peaks and supplies energy to the subharmonics through a reverse energy cascade.

physics.flu-dyn↗

arXiv2024

Adaptive spectral proper orthogonal decomposition of tonal flows

An adaptive algorithm for spectral proper orthogonal decomposition (SPOD) of mixed broadband-tonal turbulent flows is developed. Sharp peak resolution at tonal frequencies is achieved by locally minimizing the bias of the spectrum. Smooth spectrum estimates of broadband regions are achieved by locally reducing the variance of the spectrum. The method utilizes multitaper estimation with sine tapers. An iterative criterion based on modal convergence is introduced to enable the SPOD to adapt to spectral features. For tonal flows, the adaptivity is controlled by a single user input; for broadband flows, a constant number of sine tapers is recommended without adaptivity. The discrete version of Parseval's theorem for SPOD is stated. Proper normalization of the tapers ensures that Parseval's theorem is satisfied in expectation. Drastic savings in computational complexity and memory usage are facilitated by two aspects: (i) sine tapers, which permit post hoc windowing of a single Fourier transform; and (ii) time-domain lossless compression using a QR or eigenvalue decomposition. Sine-taper SPOD is demonstrated on time-resolved particle image velocimetry (TR-PIV) data from an open cavity flow and high-fidelity large-eddy simulation (LES) data from a round jet, with and without adaptivity. For the tonal cavity flow, the adaptive algorithm outperforms Slepian-based multitaper SPOD in terms of variance and local bias of the spectrum, mode convergence, and memory usage.

physics.flu-dyn↗

arXiv2023

Large-scale streaks in a turbulent bluff body wake

A turbulent circular disk wake database (Chongsiripinyo \& Sarkar, \textit{J. Fluid Mech.}, vol. 885, 2020) at Reynolds number $\textit{Re} = U_\infty D/ν= 5 \times 10^{4}$ is interrogated to identify the presence of large-scale streaks - coherent elongated regions of streamwise velocity. The unprecedented streamwise length - until $x/D \approx 120$ - of the simulation enables investigation of the near and far wake. The near wake is dominated by the vortex shedding (VS) mode residing at azimuthal wavenumber $m=1$ and Strouhal number $\textit{St} = 0.135$. After filtering out the VS structure, conclusive evidence of large-scale streaks with frequency $\textit{St} \rightarrow 0$, equivalently streamwise wavenumber $k_x \rightarrow 0$ in the wake, becomes apparent in visualizations and spectra. These streaky structures are found throughout the simulation domain beyond $x/D \approx 10$. Conditionally averaged streamwise vorticity fields reveal that the lift-up mechanism is active in the near as well as the far wake, and that ejections contribute more than sweep to events of intense $-u'_xu'_r$. Spectral proper orthogonal decomposition (SPOD) is employed to extract the energy and the spatiotemporal features of the large-scale streaks. The streak energy is concentrated in the $m=2$ azimuthal mode over the entire domain. Finally, bispectral mode decomposition (BMD) is conducted to reveal strong interaction between $m=1$ and $\textit{St} = \pm 0.135$ modes to give the $m=2, \textit{St} = 0$ streak mode. Our results indicate that the self-interaction of the VS mode generates the $m=2, \textit{St} = 0$ streamwise vortices, which leads to streak formation through the lift-up process. To the authors' knowledge, this is the first study that reports and characterizes large-scale low-frequency streaks and the associated lift-up mechanism in a turbulent wake.

physics.flu-dyn↗

arXiv2023

Mesh-Free Hydrodynamic Stability

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 while balancing accuracy and computational efficiency. Specialized elliptical stencils to compute boundary-normal derivatives are introduced and the treatment of the pole singularity in cylindrical coordinates is discussed. The numerical framework is demonstrated and validated on a number of 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.

physics.flu-dyn↗