arXiv subjects

André V. G. Cavalieri

Publications and source records attributed to André V. G. Cavalieri.

At least 19 recordsLinked to original sources

arXiv2026

Mean-flow-based reduced-order models of turbulent channel flow

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 $Re_τ \approx 185$. 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.

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arXiv2026

Galerkin reduced order model for two-dimensional Rayleigh-Bénard convection

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.

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arXiv2026

State estimation of Rayleigh-Bénard convection with reduced-order models

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.

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arXiv2026

Coherent structures in axis-switching elliptical jets

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 $St\approx 0.2$ for the medium-forcing case and at $St\approx 0.4$ 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.

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arXiv2026

Jet-edge interaction: linear and non-linear frequency-selection mechanisms

We consider a round turbulent jet grazing a rectangular plate angled at $45^\circ$. 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).

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arXiv2025

On the applicability of the actuator line method for unsteady aerodynamics

A linear theory for unsteady aerodynamic effects of the actuator line method (ALM) was 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 airfoil 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 airfoil is shown to be important for accurate computations. These findings offer valuable guidance for the application of ALM in unsteady aerodynamics and aeroelasticity.

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arXiv2025

Jet-noise reduction via streak generation in the nozzle boundary layer

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 $\leq M_j \leq$ 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 (OASPL), reductions of up to 3 dB are observed at all measured polar angles in the range 20 deg $\leq θ\leq$ 90 deg. Time-resolved particle image velocimetry (TR-PIV) experiments are conducted to measure the three components of velocity for a series of cross-stream planes at $M_j =$ 0.7. A Floquet-based Fourier decomposition is applied for the azimuthally periodic flow field, and spectral proper orthogonal decomposition (SPOD) 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 (K-H) wavepackets. A linear model based on the one-way Navier-Stokes equations (OWNS) 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.

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arXiv2024

Identification of structures driving trailing-edge noise. Part I -- Experimental investigation

Trailing-edge (TE) noise is the main contributor to the acoustic signature of flows over airfoils. It originates from the interaction of turbulent structures in the airfoil boundary layer with the TE. This study experimentally identifies the flow structures responsible for TE noise by decomposing the data into spanwise modes and examining the impact of spanwise coherent structures on sound emission. We analyse a NACA0012 airfoil at moderate Reynolds numbers, ensuring broadband TE noise, and use synchronous measurements of surface and far-field acoustic pressure fluctuations with custom spanwise microphone arrays. Our results demonstrate the key role of coherent structures with large spanwise wavelengths in generating broadband TE noise. Spanwise modal decomposition of the acoustic field shows that only waves with spanwise wavenumbers below the acoustic wavenumber contribute to the radiated acoustic spectrum, consistent with theoretical scattering conditions. Moreover, a strong correlation is found between spanwise-coherent (zero wavenumber) flow structures and radiated acoustics. At frequencies corresponding to peak TE noise emission, the turbulent structures responsible for radiation exhibit strikingly large spanwise wavelengths, exceeding $60\%$ of the airfoil chord length. These findings have implications for numerical and experimental TE noise analysis and flow control. The correlation between spectrally decomposed turbulent fluctuations and TE noise paves the way for future aeroacoustic modelling through linearized mean field analysis. A companion paper further explores the nature of the spanwise-coherent structures using high-resolution numerical simulations of the same setup.

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arXiv2024

Identification of structures driving trailing-edge noise. Part II -- Numerical investigation

The aim of the present work is to investigate the mechanisms of broadband trailing-edge noise generation to improve prediction tools and control strategies. We focus on a NACA 0012 airfoil at 3 degrees angle of attack and chord Reynolds number Re = 200,000. A high-fidelity wall-resolved compressible implicit large eddy simulation (LES) is performed to collect data for our analysis. The simulation is designed in close alignment with the experiment described in detail in the companion paper (Demange et al. 2024b). Zig-zag geometrical tripping elements, added to generate a turbulent boundary layer, are meshed to closely follow the experimental setup. A large spanwise domain is used in the simulation to include propagative acoustic waves with low wavenumbers. An in-depth comparison with experiments is conducted showing good agreement in terms of mean flow statistics, acoustic and hydrodynamic spectra, and coherence lengths. Furthermore, a strong correlation is found between the radiated acoustics and spanwise-coherent structures. To investigate the correlation for higher wavenumbers, spectral proper orthogonal decomposition (SPOD) is applied to the spanwise Fourier-transformed LES dataset. The analysis of all SPOD modes for the leading spanwise wavenumbers reveals streamwise-travelling wavepackets as the source of the radiated acoustics. This finding, confirming observations from experiments in the companion paper, leads to a new understanding of the turbulent structures driving the trailing-edge noise. By performing extended SPOD based on the acoustic region, we confirm the low rank nature of the acoustics, and a reduced-order model based on acoustic extended SPOD is proposed for the far-field acoustic reconstruction.

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arXiv2024

Modal-based generalised quasilinear approximations for turbulent plane Couette flow

We study generalised quasilinear (GQL) approximations applied to turbulent plane Couette flow. The GQL framework is explored in conjunction with a Galerkin reduced-order model (ROM) recently developed by Cavalieri & Nogueira (Phys. Rev. Fluids 7, L102601, 2022), which considers controllability modes of the linearised Navier-Stokes system as basis functions, representing coherent structures in the flow. The velocity field is decomposed into two groups: one composed by high-controllability modes and the other by lowcontrollability modes. The former group is solved with the full nonlinear equations, whereas the equations for the latter are linearised.We also consider a new GQL framework wherein the linearised equations for the lowcontrollability modes are driven by nonlinear interactions of modes in the first group, which are characterised by large-scale coherent structures. It is shown that GQL-ROMs successfully recover the statistics of the full model with relatively high controllability thresholds and sparser nonlinear operators. Driven GQL-ROMs were found to converge more rapidly than standard GQL approximations, providing accurate description of the statistics with a larger number of linearised modes. This indicates that the forcing of linearised flow structures by large-scale coherent structures is an important feature of turbulence dynamics that should be considered in GQL models. The results presented here reveal that further model reductions are attainable with GQL-ROMs, which can be valuable to extend these models to larger Reynolds numbers.

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arXiv2024

Airfoil tonal noise reduction by roughness elements Part I -- Experimental investigation

Laminar separation bubbles around airfoils lead to the growth of instability waves, which enhances to acoustic scattering at the trailing-edge, forming a feedback loop that produces to tonal noise. To reduce the trailing-edge tonal noise, an array of roughness elements was used over a NACA0012 airfoil, at low angles of attack and moderate Reynolds number. Aeroacoustics and flow visualization experiments were performed for four configurations: a baseline smooth airfoil, two configurations with roughness elements on either airfoil surface (pressure side or suction side), and a fourth configuration with roughness elements at both airfoil surfaces. The roughness elements are made up of a row of spanwise periodically spaced cylinders, which were placed close to the mid-chord position. It is expected the proposed array of roughness elements stabilizes the Kelvin-Helmholtz instability mechanism that is present on the separated shear layer through the induction of streak structures. The separation bubble is assessed using oil flow visualizations, and the cases with roughness elements show the generation of streaks downstream of the array cylinders, disrupting the separation bubble. Acoustic measurements results show a decrease, and in some cases the total suppression, of the tonal noise at Reynolds numbers ranging from 0.6$\times$10$^5$ to 2.5$\times$10$^5$, and angles of attack ranging from 0 to 4 degrees.

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arXiv2024

Airfoil Tonal Noise Reduction by Roughness Elements. Part II -- Direct Simulations

In a combined experimental and numerical effort we investigate airfoil tonal noise generation and reduction. The means of noise control are streak generators in form of cylindrical roughness elements. These elements are placed periodically along the span of airfoil at the mid chord streamwise position. Experiments are performed for a wide range of Reynolds number and angle of attack in a companion work (Alva et al. 2024). 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 (80,000 and 100,000) 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 POD analysis of streamwise velocity data, dominating structures have been identified. 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 by which the sound generation by the airfoil is reduced by the roughness elements.

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arXiv2024

Turbulence suppression in plane Couette flow using reduced-order models

We explore a reduced-order model (ROM) of plane Couette flow with a view to performing turbulence control. The ROM is derived through Galerkin projections of the incompressible Navier-Stokes (NS) system onto a basis composed of controllability modes, truncated to a few streamwise and spanwise wavenumbers. Such ROMs were found to reproduce key aspects of nonlinear turbulence dynamics in Couette flow with only a few hundreds degrees of freedom. Here we use the ROM to devise a control strategy. For that, we consider a ROM with an extra forcing term, consisting in a steady body force. The spatial structure of the forcing is given by a linear combination of Stokes modes, optimised using a gradient-descent algorithm in order to minimise the total fluctuation energy. The optimisation is performed at different Reynolds numbers, with the optimal forcing leading to laminarisation of the flow in all cases. The forcing mechanism acts by strongly reducing the shear in a large central portion of the channel. This disrupts the dynamics of large-scale streaks and rolls and hinders the main energy input to the system. When the forcing is active, the flow reaches a new laminar state which is linearly stable and whose linear transient growth is substantially reduced with respect to that of laminar Couette flow. These features prompt the flow to return to the laminar Couette state when the forcing is switched off. Body forces optimised in the ROM are subsequently applied to the full NS system in direct numerical simulations (DNS) for the same flow configurations. The same control mechanisms are observed in the DNS, where laminarisation is also achieved. The present work opens up interesting possibilities for turbulence control. We show that the ROMs provide an effective framework to design turbulence control strategies, despite the high degree of truncation with respect to the full system.

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arXiv2024

Modal decomposition of nonlinear interactions in wall turbulence

Coherent structures are found in many different turbulent flows and are known to drive self-sustaining processes in wall turbulence. Identifying the triadic interactions which generate coherent structures can provide insights beyond what is possible with linearized models. There are infinite possible interactions that may generate a given structure. Thus, a method to systematically study those, ranking them in terms of their contribution to the structure of interest, is essential. We here use the resolvent-based extended spectral proper orthogonal decomposition (RESPOD) approach (Karban, U. et al. 2022 Self-similar mechanisms in wall turbulence studied using resolvent analysis. Journal of Fluid Mechanics 969, A36) to rank the triadic interactions which give rise to the dominant coherent structures in minimal Couette flows at Reynolds number 400 and 1000. Our analysis identifies that six triadic interactions dominate the most energetic coherent structure, revealing the capability of the methodology to identify and rank nonlinear interactions. The approach can be used to analyse the energy exchange in turbulent flows and may guide the construction of reduced-order models based on the interplay between different flow modes. Based on this framework, we introduce a modelling strategy where the interactions increasing or reducing the energy of a given mode are grouped as sources and sinks, respectively. The effect of the sinks is embedded in the resolvent operator by using an eddy viscosity model. The sources are used for driving this modified resolvent operator and are shown to yield accurate flow predictions at zero frequency. We discuss that this strategy can be useful when analysing nonlinear interactions or modelling forcing at high-Reynolds-number flows.

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arXiv2024

Improved convergence of the spectral proper orthogonal decomposition through time shifting

Spectral proper orthogonal decomposition (SPOD) is an increasingly popular modal analysis method in the field of fluid dynamics due to its specific properties: a linear system forced with white noise should have SPOD modes identical to response modes from resolvent analysis. The SPOD, coupled with the Welch method for spectral estimation, may require long time-resolved data sets. In this work, a linearised Ginzburg-Landau model is considered in order to study the method's convergence. SPOD modes of the white-noise forced equation are computed and compared with corresponding response resolvent modes. The quantified error is shown to be related to the time length of Welch blocks (spectral window size) normalised by a convective time. Subsequently, an algorithm based on a temporal data shift is devised to further improve SPOD convergence and is applied to the Ginzburg-Landau system. Next, its efficacy is demonstrated in a numerical database of a boundary layer subject to bypass transition. The proposed approach achieves substantial improvement in mode convergence with smaller spectral window sizes with respect to the standard method. Furthermore, SPOD modes display growing wall-normal and span-wise velocity components along the stream-wise direction, a feature which had not yet been observed and is also predicted by a global resolvent calculation. The shifting algorithm for the SPOD opens the possibility for using the method on datasets with time series of moderate duration, often produced by large simulations.

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arXiv2024

Reactive experimental control of turbulent jets

We present an experimental study of reactive control of turbulent jets. We target axisymmetric disturbances associated with coherent structures, which are known to underpin the peak sound radiation of turbulent jets. We first consider a forced jet flow case, such that the coherent structures can be amplified above background levels, which makes it easier to detect them by the sensors. We then consider the more challenging case of a natural jet, i.e., without artificial forcing. The control strategy explores linear convective mechanisms in the initial jet region, which justifies application of linear control theory. The control law is constructed in the frequency domain, based on empirically determined transfer functions. The Wiener-Hopf formalism is used to enforce causality, providing an optimal causal solution, thus, preventing the drop in performance that may be observed in flow control applications that use simpler wave-cancellation methods. With this approach, we could improve the control performance of forced turbulent jets compared to results obtained in previous studies, attaining order-of-magnitude attenuation of power spectra of velocity fluctuations. Furthermore, we could obtain substantial levels of attenuation of natural turbulent jets, of about 60% in power spectra for the most amplified frequencies. These results open new directions for the control of turbulent flows.

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arXiv2024

Experimental control of Tollmien-Schlichting waves using the Wiener-Hopf formalism

Reactive flow control has been shown as a promising tool to improve, among other aspects, the aerodynamic characteristics of an aircraft. This paper focuses on the use of reactive flow control to attenuate Tollmien-Schlichting (TS) waves over a wing profile. TS waves are an instability mechanism that is one of the first stages of boundary layer transition to turbulence. The Wiener-Hopf technique was used in this work for the experimental boundary layer control. The approach improves previous wave-cancellation techniques that, by constructing control kernels in the frequency domain, lead to control kernels with a non-causal part, i.e., actuation would need future sensor information to be constructed. In practical applications, it is unfeasible to access this type of information. Ignoring the non-causal part of the kernel leads to suboptimal solutions that might significantly degrade the performance of the controller. The Wiener-Hopf formalism allows us to take into account causality constraints in the formulation of the control problem, leading to an optimal realistic solution and a control kernel that is causal by construction. Moreover, it is possible to construct the control strategy based only on the power and cross-spectra obtained experimentally, in a data-driven approach. The present work shows how to apply experimentally the Wiener-Hopf resolvent-based formalism using signals from a wind tunnel experiment, demonstrating that the Tollmien-Schlichting waves can be effectively attenuated via a Wiener-Hopf based controller, which yielded better results than a typical wave-cancellation approach.

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arXiv2024

Linear and nonlinear receptivity mechanisms in boundary layers subject to free-stream turbulence

Large-eddy simulations of a flat-plate boundary layer, without a leading edge, subject to multiple levels of incoming free stream turbulence are considered in the present work. Within an input-output model where non-linear terms of the incompressible Navier-Stokes equations are treated as an external forcing, we manage to separate inputs related to perturbations coming through the intake of the numerical domain, whose evolution represents a linear mechanism, and the volumetric non-linear forcing due to triadic interactions. With these, we perform the full reconstruction of the statistics of the flow, as measured in the simulations, to quantify pairs of wavenumbers and frequencies more affected by either linear or non-linear receptivity mechanisms. Inside the boundary layer, different wavenumbers at near-zero frequency reveal streaky structures. Those that are amplified predominantly via linear interactions with the incoming vorticity occur upstream and display transient growth, while those generated by the non-linear forcing are the most energetic and appear in more downstream positions. The latter feature vortices growing proportionally to the laminar boundary layer thickness, along with a velocity profile that agrees with the optimal amplification obtained by linear transient growth theory. The numerical approach presented is general and could potentially be extended to any simulation for which receptivity to incoming perturbations needs to be assessed.

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