This study evaluates the potential of resolvent analysis to model broadband trailing-edge (TE) noise generated by a turbulent boundary layer over an airfoil. A compressible resolvent formulation is applied to the mean flow obtained from large-eddy simulation (LES) of a NACA0012 airfoil at a chord Reynolds number of [Formula: see text]. The resulting modes are validated against spectral proper orthogonal decomposition of the LES data, enabling direct comparison between a physics-based model and data-driven analysis. We identify regions in the frequency–spanwise-wavenumber spectrum where the flow exhibits low-rank behavior, notably for low Helmholtz numbers and spanwise wavenumbers, coinciding with peak acoustic emissions. In these regions, the leading resolvent mode captures the dominant hydrodynamic and acoustic structures: wave packets on the suction side exploiting the Orr mechanism. The resolvent framework isolates the structures responsible for sound generation from the complete turbulent dynamics and links them to the mean flow, offering a physics-based model suited for noise control. Unlike empirical models requiring full turbulent spectra or high-fidelity simulations with prohibitive cost, the resolvent approach provides a low-order, efficient alternative. These results demonstrate its potential as a foundation for future sensitivity-based design strategies targeting broadband TE noise reduction.

We consider a round turbulent jet grazing a rectangular plate angled at 45^∘. Through sound pressure measurements, the tonal dynamics associated with jet-edge interaction are explored in a parameter space comprising jet Mach number, M_j, and plate radial position, R/D. A variety of spectral signatures are observed and classified. The classification - based on analysis of power-spectral density and bicoherence, and on the resonance model proposed by Jordan et al. (2018) - comprises: broadband spectra; tonal spectra associated with purely linear frequency-selection mechanisms; tonal spectra associated with both linear and non-linear frequency selection. The classification identifies regions in the parameter space (M_j, R/D); and clarifies mechanisms underpinning regime changes. The linear frequency selection (LFS) regime comprises multiple tones, with no evidence of triad interaction. A regime involving non-linear frequency selection emerges from this state, with the strong amplification of one LFS tone, which then generates multiple harmonics. Intermediate regimes are identified involving weaker, non-harmonic triadic interactions where two LFS tones interact to generate a third tone. In addition to these mechanisms a mode-switching mechanism is identified at M_j = 0.84 and shown to result from the cut-on of a new upstream-travelling wave at that Mach number. The mode-switch is found to be remarkably robust, occurring in a repeatable manner over a Mach-number increment of 0.01 regardless of whether the Mach number is increased or decreased (no hysteresis is observed).

Coherent structures in aspect ratio 2, axis-switching elliptical jets are studied using direct numerical simulation (DNS). Three different datasets are studied with varying near-nozzle forcing levels. Increasing the forcing level causes the jet to axis switch at an earlier streamwise location. Spectral proper orthogonal decomposition was applied to the dataset to extract the most-energetic coherent structures in the flow, and modes associated with the main symmetries of the flow were identified. The flapping mode was found to decay faster at the high forcing level, a feature that was linked to the axis-switching behavior. The axis-switching phenomenon causes the flapping mode to become a wagging mode relative to the new axis, lowering the growth rate of the structure. Two different coherent structures were found in the SA (dihedral group D_2) symmetry for the axis-switching cases: the wagging mode which was dominant in the pre-axis-switch region and a new flapping mode which is dominant in the post-axis-switch region. The new flapping mode was dominant in the low-frequency region of the full-field SPOD spectrum which was overtaken by the wagging mode at St≈ 0.2 for the medium-forcing case and at St≈ 0.4 for the high-forcing case. This new flapping mode is likely a flapping mode relative to the axis-switched mean flow, which develops due to the slower growth of the shear layer in the major axis.

Abstract The actuator line method (ALM) has emerged in recent years as a widely used technique for simulating wind turbines and other rotating blade applications. This method reduces computational costs by avoiding the need for fine mesh resolution near solid boundaries, as it does not resolve the boundary layer directly. Instead, the ALM represents the airfoil as a body force (typically a Gaussian function) integrated into the Navier-Stokes equations. Although its use in engineering has grown, several corrections have been developed to improve its precision. Recent studies have particularly addressed ALM limitations in unsteady aerodynamics. Although ALM can yield consistent results under specific conditions, these often require significantly finer meshes, thereby increasing computational cost. This paper explores a correction for two-dimensional ALM simulations under unsteady conditions. Using the indicial function associated with the ALM (derived from a linear approximation) to determine the quasi-steady lift, and applying Duhamel’s integral with Wagner’s function, we reconstruct the lift coefficient to obtain results consistent with classical unsteady aerodynamics. To validate this approach, simulations were performed at varying reduced frequencies ( k ) and ratios of Gaussian width to chord length ( ε/c ). The results demonstrate the accuracy of the method, even at higher parameter values where previous works showed typically shows significant discrepancies.

Reduced-order models (ROMs) for turbulent flows based on Galerkin projection can achieve reasonable accuracy using equation-based modal bases derived from the linearized Navier-Stokes equations through the controllability and observability Gramians. The use of the modal bases obtained from linearized equations around a mean state has been seen to enhance the first- and second-order statistics in the ROM, but the use of the mean state was not necessarily extended to the equations of motion, as it implies the treatment of the divergence of the Reynolds stresses in the Galerkin projection. In this work, we present a mean-flow-based framework for ROMs in which the projection of the Reynolds stresses is solved through a modified modal basis and the knowledge of the mean flow. This framework achieves turbulence statistics comparable to those of a reference direct numerical simulation (DNS) in a minimal channel at Re_τ ≈ 185. Short-time forecasting with this framework is assessed, where balanced truncation modal bases outperform controllability modes in ROMs, yielding a reconstruction of the velocity field comparable to the Galerkin projection of proper orthogonal decomposition (POD) modes. This framework can extend analysis based on linearisations around the mean turbulent flow, which became widespread in recent years, to include explicitly non-linear interactions between modes, enabling accurate models at higher Reynolds number.

In this work, we develop a state estimation framework for two-dimensional Rayleigh-Bénard (RB) convection that combines a stable Galerkin reduced-order model (ROM) with an extended Kalman filter (EKF). The ROM, constructed from controllability modes of the linearised Boussinesq equations, provides the nonlinear dynamical model for the filter prediction step. Direct numerical simulations (DNS) are used to generate synthetic measurements for data assimilation. We assess filter performance across periodic, quasiperiodic, and chaotic regimes, demonstrating that the filter tracks the most energetic modes with high fidelity and achieves time-averaged reconstruction errors below 14% for velocity and 9% for temperature. We apply the ROM-based EKF to a hybrid simulation scenario where the system state is assimilated from coarse PIV-like velocity measurements. It is shown that velocity observations alone suffice to reconstruct the state, including the temperature field. Finally, we exploit the Kalman gain matrix to develop a greedy sensor placement strategy that progressively removes the least informative sensors. The algorithm reveals a clear hierarchy among sensor types and can be used to derive skeletal observation configurations. It also provides guidance on which measurement variables and spatial locations are most informative for state correction. The present framework is general, and may be applied to other quadratic Galerkin ROMs for state estimation.

A linear theory for unsteady aerodynamic effects of the actuator line method (ALM) is developed. This theory is validated using two-dimensional ALM simulations, where we compute the unsteady lift generated by the plunging and pitching motion of a thin aerofoil in uniform flow, comparing the results with Theodorsen's theory. This comparison elucidates the underlying characteristics and limitations of ALM when applied to unsteady aerodynamics. Numerical simulations were conducted across a range of chord lengths and oscillation frequencies. Comparison of ALM results with theoretical predictions shows consistent accuracy, with all Gaussian parameter choices yielding accurate results at low reduced frequencies. Furthermore, the study indicates that selecting a width parameter ratio of $\varepsilon /c$ (the Gaussian width parameter over the chord length) between 0.33 and 0.4 in ALM yields the closest alignment with analytical results across a broader frequency range. Additionally, a proper definition of angle of attack for a pitching aerofoil is shown to be important for accurate computations. These findings offer valuable guidance for the application of ALM in unsteady aerodynamics and aeroelasticity.

In this work, we investigate airfoil tonal noise generation and reduction by the means of streak generators in form of cylindrical roughness elements. Roughness elements attenuate tones in the acoustic field for the case with chord base Reynolds number Re = 80,000 . Further, the coupling between structures generated by surface roughness and instability modes (Kelvin-Helmholtz) of shear layer has been identified through stability analysis, suggesting stabilisation mechanisms of Kelvin-Helmholtz instabilities by which the sound generation by the airfoil is reduced by the roughness elements.

We study the hydrodynamic and acoustic fields of turbulent jets issuing from nozzles modified by the addition of cylindrical tabs on the inner surface, one diameter upstream of the exit. The tabs are designed to promote significant growth of steady streaks in the nozzle turbulent boundary layer. A baseline smooth nozzle is also studied for comparison. Acoustic measurements are made using an azimuthal array for Mach numbers in the range 0.4 $\leqslant M_{\kern-1pt j} \leqslant$ 0.9. The tabs are found to reduce the emitted sound levels by up to 3 dB/St. In terms of overall sound pressure levels, reductions of up to 3 dB are observed at all measured polar angles in the range 20 degrees $\leqslant \theta \leqslant$ 90 degrees. Time-resolved particle image velocimetry experiments are conducted to measure the three components of velocity for a series of cross-stream planes at $M_{\kern-1pt j} =$ 0.7. A Floquet-based Fourier decomposition is applied for the azimuthally periodic flow field, and spectral proper orthogonal decomposition is then employed to extract coherent structures. Comparison of the structures obtained for nozzles with and without tabs shows an enhancement of the streaky structures by the tabs and a damping of Kelvin-Helmholtz wavepackets. A linear model based on the one-way Navier-Stokes equations is employed to explore the underlying amplification mechanisms and how these are impacted by the tabs. The model reproduces the growth-attenuation mechanism observed in the data, showing that the changes in the mean flow induced by the streaks work to reduce the amplification of the noise-generating coherent structures associated with linear spatial growth mechanisms.

In this work, Galerkin projection is used to build reduced-order models (ROM) for two-dimensional Rayleigh-Bénard (RB) convection with no-slip walls. We compare an uncoupled projection approach that uses separate orthonormal bases for velocity and temperature with a coupled formalism where the equations are projected onto a single basis combining velocity and temperature components. Orthonormal bases for modal projection are obtained as the eigenfunctions of the controllability Gramian of the linearized RB equations, eliminating the need for DNS snapshot databases required by traditional POD-based approaches. Various coupled and uncoupled ROMs with different numbers of modes are generated and validated against direct numerical simulations (DNS) over a wide range of Rayleigh numbers. One of the objectives is to determine their domain of validity as a function of the system dimension and the Rayleigh number. DNS and ROM results are compared in terms of mean vertical profiles, heat flux, flow structures, dynamical regimes and energy spectra. Crucially, unlike previous POD-based Galerkin models for thermal convection, these ROMs do not require closure models and remain numerically stable. The coupled approach shows better agreement with DNS in terms of mean vertical profiles and Nusselt number scaling. The capabilities of these models are exploited to conduct a detailed bifurcation analysis at Pr = 10 using Poincaré sections and Lyapunov exponents, precisely identifying the transitions between periodic, quasiperiodic, and chaotic states with significant reductions of computational cost.

The Actuator Line Method (ALM) is a technique that replaces the detailed airfoil geometry with distributed body forces to predict the flow field. ALM has been widely employed for simulating rotating blade wakes due to its flexibility and accuracy in the far field. In this study, the applicability of ALM for unsteady aerodynamics and acoustic field prediction is evaluated. The case study considered is the harmonic transverse oscillation of a thin airfoil in uniform flow. The ALM body forces are distributed over a few grid points following a Gaussian function, with a range of smearing ratio of epsilon/c. (smearing parameter over the chord length) between 0.4 and 1. These forces are computed using thin airfoil theory with the Prandtl-Glauert correction for compressible regime. Based on these computations, the compressible Navier-Stokes equations are numerically solved, yielding the velocity and pressure fields. ALM lift results are validated against unsteady aerodynamic theory in the subsonic regime. Moreover, results demonstrate an acoustic field consistent with a dipole distribution and a spectrum exhibiting a frequency corresponding to the plunging motion. Furthermore, the acoustic results are validated through an acoustic analogy approach, involving the prediction of the acoustic field via Green's function. The prediction of the acoustic far-field using ALM is expected to significantly reduce the computational cost of compressible simulations applied to propeller and wind turbine aeroacoustics.

We explore a reduced-order model (ROM) of plane Couette flow with a view to performing near-wall turbulence control. The ROM is derived through Galerkin projections of the incompressible Navier-Stokes system onto a basis of controllability modes. Such ROMs were found to reproduce key aspects of turbulence dynamics in Couette flow with only a few hundred degrees of freedom, and here we use them to devise a control strategy. We consider a ROM with an extra forcing term whose structure is given by a combination of eigenfunctions of a linear viscous diffusion equation, optimised in order to minimise the total fluctuation energy. The optimisation is performed at Reynolds numbers $Re=1000, 2000, 3000$ , and produces a novel control mechanism wherein the optimal forcing leads the flow to laminarisation in all cases. The forcing acts by reducing the shear in a large portion of the channel, hindering the main energy input mechanism. The forced flow possesses a new laminar solution which is linearly stable at $Re=1000$ and unstable at higher $Re$ , but whose transient growth of streaky structures is substantially lower than that of laminar Couette flow, leading the flow to full laminarisation when the forcing is removed. Forcings optimised in the ROM are subsequently applied in direct numerical simulations (DNS). The same control mechanisms are observed in the DNS, where laminarisation is also achieved. We show that the ROMs provide an effective framework to design turbulence control strategies, despite the high degree of truncation, which opens up interesting possibilities for turbulence control.

Reduced-order models (ROMs) of turbulent flows based on Galerkin projection often require many degrees of freedom to resolve the dynamics of the turbulence, or simulation data to obtain an optimal modal basis. However, obtaining simulation data is computationally expensive, and the amount of data required to obtain a converged modal basis can increase this cost. Using the linearized Navier-Stokes equations, one can achieve spatial modes through the controllability and observability Gramians, which can yield a ROM without prior simulation data. In this work, we propose a self-compression of a ROM based on controllability modes, where the time series of the modal coefficients are leveraged to reduce the dimension of the ROM. In the self-compressed ROM (SCROM), we can maintain accurate first- and second-order statistics with respect to the DNS simulation, but in a further reduced dimension. The self-reduced ROM recovers spatial structures equivalent to proper orthogonal decomposition (POD) without relying on any simulation data, recombining spatial modes from linearized equations. This method leads to a novel ROM that can represent turbulence statistics in a data-free approach in a further reduced state space.

This study investigates the two- and three-dimensional convective and absolute instability characteristics of planar viscoelastic jet flows using the Oldroyd-B and Giesekus models. Analyzing instability in different types of flows is fundamental for understanding their behavior in various natural and industrial applications. Convective instability refers to disturbances that propagate and grow downstream, while absolute instability involves disturbances that grow over time regardless of their position in the flow. Understanding these phenomena can help optimize industrial processes and predict complex flow behaviors, for example. Results indicate that concerning convective instability, the Giesekus model exhibits a larger unstable region compared to the Oldroyd-B and Newtonian models. On the other hand, the Oldroyd-B model is more susceptible to absolute instability than the Giesekus model. Notably, in the Giesekus model, the mobility parameter alpha G significantly influences the occurrence of absolute instability, which only occurs for small values of alpha G, for which the fluid tends to the Oldroyd-B behavior. For the tested parameters, only low values of alpha G (close to the Oldroyd-B model, which corresponds to alpha G = 0) led to the emergence of absolute instability, while larger values did not. These observations apply to both two-dimensional and three-dimensional disturbances.

In a combined experimental and numerical effort, we investigate the generation and reduction of airfoil tonal noise. The means of noise control are streak generators in the form of cylindrical roughness elements. These elements are placed periodically along the span of the airfoil at the mid-chord streamwise position. Experiments are performed for a wide range of Reynolds numbers and angles of attack in a companion work (Alva et al. , AIAA Aviation Forum , 2023). In the present work, we concentrate on numerical investigations for a further investigation of selected cases. We have performed wall-resolved large-eddy simulations for a NACA 0012 airfoil at zero angle of attack and Mach 0.3. Two Reynolds numbers ( ${0.8\times 10^{5}}$ and ${1.0 \times 10^{5}}$ ) have been investigated, showing acoustic results consistent with experiments at the same Reynolds but lower Mach numbers. Roughness elements attenuate tones in the acoustic field and, for the higher Reynolds number, suppress them. Through Fourier decomposition and spectral proper orthogonal decomposition analysis of streamwise velocity data, dominating structures have been identified. Further, the coupling between the structures generated by the surface roughness and the instability modes (Kelvin–Helmholtz) of the shear layer has been identified through stability analysis, suggesting stabilisation mechanisms by which the sound generation by the airfoil is reduced by the roughness elements.

We present the results from a physics-based model of the trailing-edge (TE) noise radiated by an airfoil, obtained from resolvent analysis of the turbulent mean flow. In our approach, the acoustic model input is reduced to the optimal coherent structures identified by the resolvent. This method has the advantage of isolating the main mechanisms generating noise in the turbulent flow and, unlike empirical models, is applicable to a wide variety of cases. We investigate a NACA0012 airfoil at 3 deg angle of attack, equipped with a zigzag trip to trigger a turbulent boundary layer, which results in broadband TE noise. The analysis is based on a large eddy simulation (LES) for a chord-based Reynolds number Re = 2.10(5). The time-averaged flow is used to construct the linear operator underlying resolvent analysis, and a spectral proper orthogonal decomposition (SPOD) of the snapshots is used to extract the main hydrodynamic and acoustic features of the flow, used as a reference for the resolvent model. The results demonstrate that the resolvent-based model can accurately reproduce both the coherent structures associated with TE noise and the directivity of the radiated sound field when low-rank dynamics are identified with SPOD. Although the region of low-rank dynamics corresponds to the peak of acoustic power, a significant portion of the spectrum is associated with high-rank dynamics, which we do not attempt to model here. Nevertheless, the resolvent model identifies a wavepacket on the suction side of the trailing edge as the main driver of TE noise, and allows us to investigate spanwise wavenumbers which are not resolved in the LES.

We study the stability of a zero-pressure gradient boundary layer subjected to free-stream disturbances by means of local stability analysis. The dataset under study corresponds to a direct numerical simulation (DNS) of a flat plate with a sharp leading edge in realistic wind tunnel conditions, with a turbulence level of 3.45 % at the leading edge. We present a method to track the convective evolution of the secondary instabilities of streaks by performing sequential stability calculations following the wave packet, connecting successive unstable eigenfunctions. A scattered nature, in time and space, of secondary instabilities is seen in the stability calculations. These instabilities can be detected before they reach finite amplitude in the DNS, preceding the nucleation of turbulent spots, and whose appearance is well correlated to the transition onset. This represents further evidence regarding the relevance of secondary instabilities of streaks in the bypass transition in realistic flow conditions. Consistent with the spatio-temporal nature of this problem, our approach allows us to integrate directly the local growth rates to obtain the spatial amplification ratio of the individual instabilities, where it is shown that instabilities reaching an N-factor in the range [2.5,4] can be directly correlated to more than 65 % of the nucleation events. Interestingly, it is found that high amplification is not only attained by modes with high growth rates, but also by instabilities with sustained low growth rates for a long time.

The present paper is a follow up of a previous study on the effect of streaky-generating cylindrical tabs located on the inner surface of a round nozzle on jet aeroacoustics (Amaral et al., AIAA AVIATION 2023 Forum, p. 4516, 2023). The aim is to identify coherent structures through stereoscopic particle image velocimetry (stereo PIV) measurements obtained in cross-stream planes parallel to the jet nozzle exit. As the tabbed nozzle has L-fold symmetry, Floquet exponents are used to perform Fourier decomposition in the azimuthal direction. Spectral proper orthogonal decomposition (SPOD) is employed to extract coherent structures. Comparison of the structures obtained for nozzles with and without tabs show the strong enhancement of streaks produced by the tabbed nozzle.