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arxiv: 2605.22546 · v1 · pith:3QB2SHFNnew · submitted 2026-05-21 · ⚛️ physics.flu-dyn

Perpendicular rod-airfoil aeroacoustics: experiments and modelling of interaction noise

Marios I. Spiropoulos , Filipe R. Amaral , Florent Margnat , Vincent Valeau , Peter Jordan This is my paper

Pith reviewed 2026-05-22 02:02 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords aeroacousticscylinder-airfoil interactioninteraction noisevortex soundparticle image velocimetrythree-dimensional wakeNACA-0012 airfoil
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The pith

The acoustic field from a perpendicular cylinder interacting with a downstream airfoil is produced by the three-dimensional cylinder wake.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper studies the noise created when the wake of a cylinder hits a NACA-0012 airfoil placed perpendicular to it, as a simplified model of landing-gear wake and flap interaction on aircraft. Simultaneous acoustic measurements and stereoscopic particle-image velocimetry show that the loudest sound occurs at the cylinder's drag-fluctuation frequency, with strong coherence between the sound and the spanwise velocity fluctuations in the wake. The authors apply Powell-Howe vortex-sound theory together with a compact Green's function for the airfoil and feed it a linearised source term taken directly from the measured velocity field. The resulting sound estimates match the measured sound field to a reasonable degree, and the authors also introduce a semi-empirical source model using Fourier modes along the cylinder span to identify the most important coherent structures.

Core claim

The measured acoustic field is an outcome of the three-dimensional cylinder-wake. Powell-Howe vortex-sound theory combined with an acoustically compact Green function for the NACA-0012 airfoil, supplied with a linearised source-term based on the analysed experimental velocity data, produces sound-field estimates that show reasonable agreement with the measurements. A semi-empirical source-model informed by the experimental data and based on Fourier modes in the cylinder's span direction is proposed to explore the mechanisms of sound generation.

What carries the argument

Linearised source-term derived from experimental velocity data, inserted into Powell-Howe vortex-sound theory with an acoustically compact Green function for the NACA-0012 airfoil.

If this is right

  • Peak noise occurs at frequencies close to the cylinder drag-fluctuation Strouhal number of 0.38.
  • The three-dimensional wake produces the dominant acoustic field rather than two-dimensional mechanisms.
  • The linearised experimental source term can be used to identify acoustically important coherent structures in the flow.
  • A Fourier-mode source model along the cylinder span offers a way to explore sound-generation mechanisms without full flow simulation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same experimental-modelling loop could be applied to other bluff-body and lifting-surface arrangements that produce interaction noise.
  • Accounting for spanwise variation in the wake may be necessary in reduced-order models for aircraft high-lift noise.
  • If the semi-empirical Fourier source model proves robust, it could support rapid parametric studies of geometry changes for noise control.

Load-bearing premise

The linearised source-term derived from the experimental velocity data is sufficient to capture the dominant sound-generation mechanisms when inserted into the compact Green function for the NACA-0012 airfoil.

What would settle it

A clear mismatch between the modelled and measured sound pressure levels at Strouhal number 0.38 for multiple observer locations would indicate that the linearised source term misses essential three-dimensional mechanisms.

Figures

Figures reproduced from arXiv: 2605.22546 by Filipe R. Amaral, Florent Margnat, Marios I. Spiropoulos, Peter Jordan, Vincent Valeau.

Figure 1
Figure 1. Figure 1: Coordinate system of the experimental set-up, side (a) and top (b) view. The [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Side (left) and top (right) view of the experimental set-up: The dots in magenda [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Measured sound pressure levels (microphone 16 at [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Phase of the cross-spectral density of the microphones symmetrically placed at a [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Sound pressure levels obtained by the extreme microphones placed [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Normalised root mean square of the velocity-fluctuation field of the three [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Normalised mean vorticity field for the 𝑦1 − 𝑦2 plane (left) and 𝑦1 − 𝑦3 plane (right), non-dimensionalised by the diameter of the cylinder and the flow speed. ω rms 3 d/U∞ y1 -1 0 1 y 2 -1 -0.5 0 0.5 1 0 0.5 1 ω rms 2 d/U∞ y1 -1 0 1 y 3 -0.5 0 0.5 0 0.5 1 [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Normalised root mean square of the vorticity-fluctuation components, [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Coherence plots between 𝑝16 and the three velocity fluctuation components: 𝑢 ′ 1 (top row), 𝑢 ′ 2 (middle row), 𝑢 ′ 3 (bottom row), for the 𝑦1 − 𝑦2 plane (left column) and 𝑦1 − 𝑦3 plane (right column), at St = 0.38. The solid black vertical lines correspond to the leading and trailing edges of the airfoil. The colormap is kept the same in all figures and takes values from 0 (blue) to 0.6 (yellow). 𝜔2-vorti… view at source ↗
Figure 10
Figure 10. Figure 10: Coherence of the upwash velocity and the microphone located 6 [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Experimentally fitted support of the airfoil-span-aligned vorticity fluctuations [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Real part of the linearised source term ℜ[𝑢¯1𝜔 2D 3 (𝑦1, 𝑦2, St = 0.38)] vs real part of the windowed linearised source term W (𝑦1, 𝑦2)ℜ[𝑢¯1𝜔 2D 3 (𝑦1, 𝑦2, St = 0.38)] for 𝑦1,𝑐 = 1, 𝑦2,𝑐 = 0, 𝐿1 = 2.45, 𝐿2 = 0.90, 𝑛 = 10 . The estimation of the acoustic field (shown in figure 13), based on eq. (3.21), gives an acceptable agreement when compared to experiments for St = 0.19; 0.30; 0.38; 0.45. Particularly … view at source ↗
Figure 13
Figure 13. Figure 13: Data-based estimation of radiated sound pressure level for different [PITH_FULL_IMAGE:figures/full_fig_p020_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Wavenumber spectrum [PITH_FULL_IMAGE:figures/full_fig_p021_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Streamwise-averaged 𝑘2−spectrum (black) and dominant wavenumbers (blue) [PITH_FULL_IMAGE:figures/full_fig_p022_15.png] view at source ↗
Figure 17
Figure 17. Figure 17: Semi-empirical source term (left) and acoustic field (right), computed by ( [PITH_FULL_IMAGE:figures/full_fig_p024_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Experimental set-up of the s-PIV campaign for the measurements taken on the [PITH_FULL_IMAGE:figures/full_fig_p027_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Experimental set-up of the s-PIV campaign for the measurements taken on the [PITH_FULL_IMAGE:figures/full_fig_p027_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Calibration of cameras by using the calibration plates for the [PITH_FULL_IMAGE:figures/full_fig_p028_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Raw sTR-PIV-images as obtained from one of the two cameras for the [PITH_FULL_IMAGE:figures/full_fig_p028_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: Mean velocity field components, as obtained from the TR-PIV measurements [PITH_FULL_IMAGE:figures/full_fig_p030_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: Estimation of the non-dimensional, unsteady Lamb-vector component ( ˆ𝑢 [PITH_FULL_IMAGE:figures/full_fig_p032_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: Comparison of the source-term components of Equation ( [PITH_FULL_IMAGE:figures/full_fig_p033_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: Computed Kirchhoff vector components using 900 panels (left) compared with [PITH_FULL_IMAGE:figures/full_fig_p034_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: Computed derivatives of the Kirchhoff vector component [PITH_FULL_IMAGE:figures/full_fig_p034_26.png] view at source ↗
Figure 27
Figure 27. Figure 27: Computed derivatives of the Kirchhoff vector component [PITH_FULL_IMAGE:figures/full_fig_p035_27.png] view at source ↗
Figure 28
Figure 28. Figure 28: Influence of the window function of eq ( [PITH_FULL_IMAGE:figures/full_fig_p035_28.png] view at source ↗
Figure 29
Figure 29. Figure 29: Amplitude of the wavenumber-transformed source term in [PITH_FULL_IMAGE:figures/full_fig_p036_29.png] view at source ↗
read the original abstract

During the phase of landing, an important aircraft-noise source emanates from the interaction of the landing-gear wake with the deployed flap. In the present work we cast this problem in an academic framework, by studying a simplified configuration that consists of a cylinder placed upstream and perpendicularly to a symmetrical NACA-0012 airfoil. An experimental campaign is conducted, followed by modelling approaches to explore the flow phenomena associated with the acoustic field. Simultaneous acoustic and stereoscopic Time-Resolved Particle Image Velocimetry measurements are taken, to study the sound and flow-fields generated by the interaction of the cylinder-wake with the downstream airfoil, when the spans of the two objects are orthogonally aligned. The experimental data highlight the three-dimensional nature of the problem. The maximum sound pressure levels are obtained at frequencies close to $St \equiv f d/U = 0.38$ (cylinder's drag fluctuation frequency), where also the maximum linear coherence between the acoustic and cylinder-span-oriented fluctuation velocity is observed, demonstrating that the measured acoustic-field is an outcome of the three-dimensional cylinder-wake. Powell-Howe vortex-sound theory combined with an acoustically compact Green function for the NACA-0012 are employed for the aeroacoustic modelling. A linearised source-term based on the analysed experimental data is used as input to estimate the acoustic field and identify the acoustically important coherent structures of the flow-field. A reasonable agreement is obtained between the sound field estimations and the measurements. To further explore the mechanisms of sound generation, a semi-empirical source-model, informed by the experimental data, is proposed, based on Fourier modes in the cylinder's span direction.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper investigates aeroacoustic noise generated by the interaction of a cylinder wake with a downstream perpendicular NACA-0012 airfoil, as a simplified model for landing-gear/flap noise. Simultaneous acoustic measurements and stereoscopic time-resolved PIV are performed to characterize the three-dimensional flow and sound fields. Powell-Howe vortex-sound theory is combined with an acoustically compact Green function for the airfoil; a linearised source term is extracted directly from the measured velocity fluctuations and a semi-empirical spanwise-Fourier-mode model informed by the same data is proposed. The authors report that maximum sound levels and coherence occur near St = 0.38 and that the modeled sound field shows reasonable agreement with measurements, thereby attributing the observed acoustics to the three-dimensional cylinder wake.

Significance. If the modeling assumptions can be placed on a firmer quantitative footing, the work supplies a useful experimental dataset and a practical route to predicting interaction noise in orthogonal rod-airfoil configurations. The simultaneous acoustic-PIV campaign and the identification of acoustically active coherent structures via the source term are clear strengths; the semi-empirical Fourier-mode model offers a compact way to explore parametric dependence once its predictive range is established.

major comments (3)
  1. [Abstract / Modelling section] Abstract and Modelling section: the statement that 'a reasonable agreement is obtained' is not supported by any quantitative error metric (RMS difference, dB deviation, or frequency-by-frequency correlation). Without these, it is impossible to judge whether residuals lie inside experimental uncertainty or indicate missing physics such as nonlinear wake-airfoil straining.
  2. [Modelling section] Modelling section: the linearised source term is constructed from the measured velocity fluctuations and inserted into the compact Green function. The manuscript does not demonstrate that nonlinear contributions (local straining at the airfoil leading edge or additional airfoil vortex shedding) remain negligible at St = 0.38; a direct comparison with a nonlinear formulation or a sensitivity test would be required to confirm that the linearised term captures the dominant mechanism.
  3. [Experimental / Modelling sections] Experimental and Modelling sections: the source term is derived from the identical PIV dataset that informs the semi-empirical Fourier-mode amplitudes. While the underlying Powell-Howe theory is external, the validation would be strengthened by an independent test case or cross-validation to reduce the circular dependence on the specific experimental realization.
minor comments (2)
  1. [Abstract] The Strouhal-number definition St ≡ f d/U should be accompanied by the numerical values of cylinder diameter d and free-stream velocity U employed throughout the campaign.
  2. [Throughout] Notation for spanwise Fourier modes and coherence functions should be introduced once and used consistently; a compact table of operating parameters (Re, Mach, cylinder-airfoil spacing) would aid readability.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thorough and constructive review of our manuscript. We address each major comment point by point below, indicating where revisions will be made to strengthen the paper.

read point-by-point responses

  1. Referee: [Abstract / Modelling section] Abstract and Modelling section: the statement that 'a reasonable agreement is obtained' is not supported by any quantitative error metric (RMS difference, dB deviation, or frequency-by-frequency correlation). Without these, it is impossible to judge whether residuals lie inside experimental uncertainty or indicate missing physics such as nonlinear wake-airfoil straining.

    Authors: We agree that quantitative error metrics would allow a more rigorous evaluation of the agreement. In the revised manuscript we will report the RMS difference between modeled and measured sound pressure levels, along with frequency-by-frequency correlation coefficients, and compare these values against estimated experimental uncertainties. revision: yes

  2. Referee: [Modelling section] Modelling section: the linearised source term is constructed from the measured velocity fluctuations and inserted into the compact Green function. The manuscript does not demonstrate that nonlinear contributions (local straining at the airfoil leading edge or additional airfoil vortex shedding) remain negligible at St = 0.38; a direct comparison with a nonlinear formulation or a sensitivity test would be required to confirm that the linearised term captures the dominant mechanism.

    Authors: The linearised Powell-Howe source term is adopted under the low-Mach-number approximation standard for this class of problems. The strong coherence observed between the acoustic pressure and the spanwise velocity fluctuations at St = 0.38 provides supporting evidence that the cylinder-wake structures dominate. In the revision we will add a quantitative estimate of the relative size of nonlinear straining terms using the measured velocity gradients to justify the linearisation. revision: partial

  3. Referee: [Experimental / Modelling sections] Experimental and Modelling sections: the source term is derived from the identical PIV dataset that informs the semi-empirical Fourier-mode amplitudes. While the underlying Powell-Howe theory is external, the validation would be strengthened by an independent test case or cross-validation to reduce the circular dependence on the specific experimental realization.

    Authors: While the source-term extraction and Fourier-mode amplitudes are derived from the same PIV fields, the acoustic validation is performed against microphone measurements acquired independently of the PIV system. This separation supplies an external check on the modeling. We will clarify this distinction in the revised text and acknowledge that additional independent datasets would further strengthen future work. revision: partial

Circularity Check

0 steps flagged

No circularity: modeling applies external theory to independent velocity data for validation against separate acoustic measurements

full rationale

The derivation applies Powell-Howe vortex-sound theory together with an acoustically compact Green function for the NACA-0012 to a linearised source term constructed from measured velocity fields; the resulting acoustic-field estimate is then compared with independently acquired acoustic measurements, producing only reasonable agreement. This is a standard validation exercise rather than a reduction by construction. Direct coherence between acoustic pressure and cylinder-span velocity fluctuations at St=0.38 is computed from the raw experimental time series and does not rely on the modeling step. The semi-empirical source model is proposed after the primary comparison and is not used to close the central claim. No self-citation chains, fitted parameters renamed as predictions, or ansatzes smuggled via prior work appear in the reported chain. The paper therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The modelling rests on standard aeroacoustic theory (Powell-Howe) and an acoustically compact Green function assumption for the airfoil; the linearised source term and semi-empirical Fourier modes are derived from the present experiment rather than independent first principles.

free parameters (1)
  • spanwise Fourier mode amplitudes
    Chosen to fit the measured coherence and acoustic spectra in the semi-empirical source model.
axioms (2)
  • domain assumption Powell-Howe vortex-sound theory applies to the three-dimensional wake-airfoil interaction
    Invoked to convert measured velocity fluctuations into acoustic source terms.
  • domain assumption NACA-0012 airfoil can be treated as acoustically compact
    Used to simplify the Green function in the acoustic prediction.

pith-pipeline@v0.9.0 · 5852 in / 1380 out tokens · 59880 ms · 2026-05-22T02:02:02.855398+00:00 · methodology

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Reference graph

Works this paper leans on

125 extracted references · 125 canonical work pages

  1. [1]

    10th AIAA/CEAS Aeroacoustics Conference , pages=

    An experimental study of gear wake/flap interaction noise , author=. 10th AIAA/CEAS Aeroacoustics Conference , pages=

    work page

  2. [2]

    and Westerweel, J

    Koschatzky, V. and Westerweel, J. and Boersma, B. J. , journal=. A study on the application of two different acoustic analogies to experimental. 2011 , publisher=

    work page 2011

  3. [3]

    21st AIAA/CEAS Aeroacoustics Conference , pages=

    A comparative study of simulated and measured gear-flap flow interaction , author=. 21st AIAA/CEAS Aeroacoustics Conference , pages=

    work page

  4. [4]

    Proceedings of the Royal Society of London

    The influence of solid boundaries upon aerodynamic sound , author=. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences , volume=. 1955 , publisher=

    work page 1955

  5. [5]

    Philosophical Transactions for the Royal Society of London

    Sound generation by turbulence and surfaces in arbitrary motion , author=. Philosophical Transactions for the Royal Society of London. Series A, Mathematical and Physical Sciences , pages=. 1969 , publisher=

    work page 1969

  6. [6]

    Journal of Fluid Mechanics , volume=

    Contributions to the theory of aerodynamic sound, with application to excess jet noise and the theory of the flute , author=. Journal of Fluid Mechanics , volume=. 1975 , publisher=

    work page 1975

  7. [7]

    Journal of Sound and Vibration , volume=

    Noise due to turbulent flow past a trailing edge , author=. Journal of Sound and Vibration , volume=. 1976 , publisher=

    work page 1976

  8. [8]

    Theoretical and Computational Fluid Dynamics , volume=

    A new calculus for two-dimensional vortex dynamics , author=. Theoretical and Computational Fluid Dynamics , volume=. 2010 , publisher=

    work page 2010

  9. [9]

    2016 , issn=

    Numerical evaluation of the compact acoustic Green’s function for scattering problems , journal=. 2016 , issn=. doi:https://doi.org/10.1016/j.apm.2015.10.039 , url=

    work page doi:10.1016/j.apm.2015.10.039 2016

  10. [10]

    2014 , publisher=

    Table of integrals, series, and products , author=. 2014 , publisher=

    work page 2014

  11. [11]

    1998 , publisher=

    Acoustics of fluid-structure interactions , author=. 1998 , publisher=

    work page 1998

  12. [12]

    Journal of Fluid Mechanics , author=

    The generation of sound by aerodynamic sources in an inhomogeneous steady flow , volume=. Journal of Fluid Mechanics , author=. 1975 , pages=. doi:10.1017/S0022112075000493 , number=

    work page doi:10.1017/s0022112075000493 1975

  13. [13]

    Fletcher, C. A. J. , year=. Computational techniques for fluid dynamics:

    work page

  14. [14]

    2011 , publisher=

    Fundamentals of Aerodynamics , author=. 2011 , publisher=

    work page 2011

  15. [15]

    8th Aeroacoustics Conference , pages=

    Rotor-vortex interaction noise , author=. 8th Aeroacoustics Conference , pages=

    work page

  16. [16]

    Journal of Aircraft , volume=

    An experimental investigation of blade-vortex interaction at normal incidence , author=. Journal of Aircraft , volume=

    work page

  17. [17]

    and Jacob, M

    Casalino, D. and Jacob, M. and Roger, M. , journal=. Prediction of rod-airfoil interaction noise using the

    work page

  18. [18]

    Journal of Fluid Mechanics , volume=

    Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis , author=. Journal of Fluid Mechanics , volume=. 2018 , publisher=

    work page 2018

  19. [19]

    Abreu, L. I. and Tanarro, A. and Cavalieri, A. V. G. and Schlatter, P. and Vinuesa, R. and Hanifi, A. and Henningson, D. S. , year=. Spanwise-coherent hydrodynamic waves around flat plates and airfoils , volume=. doi:10.1017/jfm.2021.718 , journal=

    work page doi:10.1017/jfm.2021.718 2021

  20. [20]

    and Schmidt, O

    Nekkanti, A. and Schmidt, O. T. , year=. Frequency–time analysis, low-rank reconstruction and denoising of turbulent flows using. doi:10.1017/jfm.2021.681 , journal=

    work page doi:10.1017/jfm.2021.681 2021

  21. [21]

    Acta Acustica , volume=

    Cylinder aeroacoustics: experimental study of the influence of cross-section shape on spanwise coherence length , author=. Acta Acustica , volume=. 2023 , publisher=

    work page 2023

  22. [22]

    and Henderson, R

    Barkley, D. and Henderson, R. D. , journal=. Three-dimensional. 1996 , publisher=

    work page 1996

  23. [23]

    Physics of Fluids , volume=

    The existence of two stages in the transition to three-dimensionality of a cylinder wake , author=. Physics of Fluids , volume=

    work page

  24. [24]

    Williamson, C. H. K. , journal=. Mode. 1996 , publisher=

    work page 1996

  25. [25]

    Physics of Fluids , volume=

    On secondary vortices in the cylinder wake , author=. Physics of Fluids , volume=. 1996 , publisher=

    work page 1996

  26. [26]

    and Gloerfelt, X

    Margnat, F. and Gloerfelt, X. , journal=. On compressibility assumptions in aeroacoustic integrals:. 2014 , publisher=

    work page 2014

  27. [27]

    Baddoo, P. J. and Ayton, L. J. , booktitle=. The compact

    work page

  28. [28]

    and Grosjean, N

    Boudet, J. and Grosjean, N. and Jacob, M. C. , journal=. Wake-airfoil interaction as broadband noise source:. 2005 , publisher=

    work page 2005

  29. [29]

    Journal of Sound and Vibration , volume=

    Airfoil gust response and the sound produced by airfoil-vortex interaction , author=. Journal of Sound and Vibration , volume=. 1986 , publisher=

    work page 1986

  30. [30]

    and Falissard, F

    Zehner, P. and Falissard, F. and Gloerfelt, X. , journal=. Aeroacoustic study of the interaction of a rotating blade with a. 2018 , publisher=

    work page 2018

  31. [31]

    Proceedings of the Royal Society of London

    Contributions to the theory of sound production by vortex-airfoil interaction, with application to vortices with finite axial velocity defect , author=. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences , volume=. 1988 , publisher=

    work page 1988

  32. [32]

    2017 , issn=

    A model problem for sound radiation by an installed jet , journal=. 2017 , issn=. doi:https://doi.org/10.1016/j.jsv.2016.12.015 , url=

    work page doi:10.1016/j.jsv.2016.12.015 2017

  33. [33]

    Applied Mechanics Reviews , volume=

    Wave-packet models for jet dynamics and sound radiation , author=. Applied Mechanics Reviews , volume=. 2019 , publisher=

    work page 2019

  34. [34]

    Journal of Fluid Mechanics , volume=

    Spanwise-coherent hydrodynamic waves around flat plates and airfoils , author=. Journal of Fluid Mechanics , volume=. 2021 , publisher=

    work page 2021

  35. [35]

    Physical Review Fluids , volume=

    Coherent pressure structures in turbulent channel flow , author=. Physical Review Fluids , volume=. 2024 , publisher=

    work page 2024

  36. [36]

    and Jordan, P

    Kaplan, O. and Jordan, P. and Cavalieri, A. V.G. and Brès, G. A. , year=. Nozzle dynamics and wavepackets in turbulent jets , volume=. doi:10.1017/jfm.2021.566 , journal=

    work page doi:10.1017/jfm.2021.566 2021

  37. [37]

    and Rodr

    Padilla-Montero, I. and Rodr. Eduction of coherent structures from schlieren images of twin jets using. Theoretical and Computational Fluid Dynamics , pages=. 2024 , publisher=

    work page 2024

  38. [38]

    and Yuan, Z

    Demange, S. and Yuan, Z. and Jekosch, S. and Hanifi, A. and Cavalieri, A. V. G. and Sarradj, E. and Kaiser, T. L. and Oberleithner, K. , month = apr, year =. Resolvent model for aeroacoustics of trailing edge noise , volume =. doi:10.1007/s00162-024-00688-z , journal =

    work page doi:10.1007/s00162-024-00688-z

  39. [39]

    Journal of Sound and Vibration , volume=

    On vortex--airfoil interaction noise including span-end effects, with application to open-rotor aeroacoustics , author=. Journal of Sound and Vibration , volume=. 2014 , publisher=

    work page 2014

  40. [40]

    Quaglia, M. E. and Léonard, T. and Moreau, S. and Roger, M. , journal=. A 3. 2017 , publisher=

    work page 2017

  41. [41]

    Journal of Fluid Mechanics , volume=

    On unsteady surface forces, and sound produced by the normal chopping of a rectilinear vortex , author=. Journal of Fluid Mechanics , volume=. 1989 , publisher=

    work page 1989

  42. [42]

    Computers & Fluids , volume=

    Prediction of sound generated by a rod–airfoil configuration using. Computers & Fluids , volume=. 2008 , note=. doi:https://doi.org/10.1016/j.compfluid.2007.02.013 , url=

    work page doi:10.1016/j.compfluid.2007.02.013 2008

  43. [43]

    16th AIAA/CEAS Aeroacoustics Conference , pages=

    Numerical insight into sound sources of a rod-airfoil flow configuration using direct noise calculation , author=. 16th AIAA/CEAS Aeroacoustics Conference , pages=

    work page

  44. [44]

    17th AIAA/CEAS aeroacoustics conference (32nd AIAA aeroacoustics conference) , pages=

    Numerical simulation of broadband noise from airfoil-wake interaction , author=. 17th AIAA/CEAS aeroacoustics conference (32nd AIAA aeroacoustics conference) , pages=

    work page

  45. [45]

    and Sengissen, A

    Giret, J.C. and Sengissen, A. and Moreau, S. and Sanjosé, M. and Jouhaud, J. C. , title=. AIAA Journal , volume=. 2015 , doi=

    work page 2015

  46. [46]

    and Mao, M

    Jiang, Y. and Mao, M. L. and Deng, X. G. and Liu, H. Y. , year=. Numerical investigation on body-wake flow interaction over rod–airfoil configuration , volume=. doi:10.1017/jfm.2015.419 , journal=

    work page doi:10.1017/jfm.2015.419 2015

  47. [47]

    2014 , issn=

    Scattering of wavepackets by a flat plate in the vicinity of a turbulent jet , journal=. 2014 , issn=. doi:https://doi.org/10.1016/j.jsv.2014.07.029 , url=

    work page doi:10.1016/j.jsv.2014.07.029 2014

  48. [48]

    Theoretical and Computational Fluid Dynamics , volume=

    Experimentally informed, linear mean-field modelling of circular cylinder aeroacoustics , author=. Theoretical and Computational Fluid Dynamics , volume=. 2025 , publisher=

    work page 2025

  49. [49]

    Physical Review Fluids , volume=

    Trailing-edge noise from the scattering of spanwise-coherent structures , author=. Physical Review Fluids , volume=. 2019 , publisher=

    work page 2019

  50. [50]

    Annual Review of Fluid Mechanics , volume=

    Wave packets and turbulent jet noise , author=. Annual Review of Fluid Mechanics , volume=. 2013 , publisher=

    work page 2013

  51. [51]

    Picard and J

    C. Picard and J. Delville , keywords=. Pressure velocity coupling in a subsonic round jet , journal=. 2000 , issn=. doi:10.1016/S0142-727X(00)00021-7 , url=

    work page doi:10.1016/s0142-727x(00)00021-7 2000

  52. [52]

    Coherent structures driving broadband trailing-edge noise:. Phys. Rev. Fluids , author =. 2026 , pages =. doi:10.1103/kxbq-ynzd , number =

    work page doi:10.1103/kxbq-ynzd 2026

  53. [53]

    Aiaa journal , volume=

    Guide to spectral proper orthogonal decomposition , author=. Aiaa journal , volume=. 2020 , publisher=

    work page 2020

  54. [54]

    , journal=

    Welch, P. , journal=. The use of fast. 1967 , publisher=

    work page 1967

  55. [55]

    Journal of Sound and Vibration , volume=

    Acoustic radiation from an airfoil in a turbulent stream , author=. Journal of Sound and Vibration , volume=. 1975 , publisher=

    work page 1975

  56. [56]

    AIAA Journal , volume=

    Airfoil response to an incompressible skewed gust of small spanwise wave-number , author=. AIAA Journal , volume=

    work page

  57. [57]

    and Moreau, S

    Roger, M. and Moreau, S. , journal=. Back-scattering correction and further extensions of Amiet's trailing-edge noise model. 2005 , publisher=

    work page 2005

  58. [58]

    The Journal of the Acoustical Society of America , volume=

    Theory of vortex sound , author=. The Journal of the Acoustical Society of America , volume=. 1964 , publisher=

    work page 1964

  59. [59]

    Journal of Fluid Mechanics , author=

    On vortex sound at low Mach number , volume=. Journal of Fluid Mechanics , author=. 1978 , pages=. doi:10.1017/S0022112078000865 , number=

    work page doi:10.1017/s0022112078000865 1978

  60. [60]

    Howe, M. S. , title=. The Quarterly Journal of Mechanics and Applied Mathematics , volume=. 2001 , month=. doi:10.1093/qjmam/54.1.139 , url=

    work page doi:10.1093/qjmam/54.1.139 2001

  61. [61]

    Liu , keywords=

    W.Y. Liu , keywords=. A review on wind turbine noise mechanism and de-noising techniques , journal=. 2017 , issn=. doi:https://doi.org/10.1016/j.renene.2017.02.034 , url=

    work page doi:10.1016/j.renene.2017.02.034 2017

  62. [62]

    and Wang, K

    Wang, J. and Wang, K. and Wang, M. , year=. Computational prediction and analysis of rotor noise generation in a turbulent wake , volume=. doi:10.1017/jfm.2020.783 , journal=

    work page doi:10.1017/jfm.2020.783 2020

  63. [63]

    and Azarpeyvand, M

    Raposo, H. and Azarpeyvand, M. , year=. Turbulence ingestion noise generation in rotating blades , volume=. doi:10.1017/jfm.2024.7 , journal=

    work page doi:10.1017/jfm.2024.7 2024

  64. [64]

    and Ayton, L.J

    Hales, Alistair D.G. and Ayton, L.J. and Jiang, C. and Mahgoub, A. and Kisler, R. and Dixon, R. and de Silva, C. and Moreau, D. and Doolan, C. , year=. A mathematical model for the interaction of anisotropic turbulence with a rigid leading edge , volume=. doi:10.1017/jfm.2023.630 , journal=

    work page doi:10.1017/jfm.2023.630 2023

  65. [65]

    Theoretical and Computational Fluid Dynamics , volume=

    A rod-airfoil experiment as a benchmark for broadband noise modeling , author=. Theoretical and Computational Fluid Dynamics , volume=. 2005 , publisher=

    work page 2005

  66. [66]

    23rd AIAA/CEAS Aeroacoustics Conference , pages=

    A Study on Landing Gear Wake-Flap Interaction Noise , author=. 23rd AIAA/CEAS Aeroacoustics Conference , pages=

    work page

  67. [67]

    and Moreau, S

    Roger, M. and Moreau, S. , year=. Extensions and limitations of analytical airfoil broadband noise models , volume=. International Journal of Aeroacoustics , doi=

    work page

  68. [68]

    Journal of Aircraft , volume=

    Vortex noise of isolated airfoils , author=. Journal of Aircraft , volume=

    work page

  69. [69]

    Journal of Fluid Mechanics , volume=

    Sound generation by a two-dimensional circular cylinder in a uniform flow , author=. Journal of Fluid Mechanics , volume=. 2002 , publisher=

    work page 2002

  70. [70]

    2024 , issn =

    Revisiting the frozen gust assumption through the aeroacoustic scattering of wavepackets by a semi-infinite plate , journal =. 2024 , issn =. doi:https://doi.org/10.1016/j.jsv.2023.117989 , url =

    work page doi:10.1016/j.jsv.2023.117989 2024

  71. [71]

    2003 , publisher=

    Theory of vortex sound , author=. 2003 , publisher=

    work page 2003

  72. [72]

    Exp Fluids , author =

    Perpendicular rod wake/aerofoil interaction: microphone array and. Exp Fluids , author =. 2025 , pages =. doi:10.1007/s00348-025-04149-z , number =

    work page doi:10.1007/s00348-025-04149-z 2025

  73. [73]

    Journal of Fluid Mechanics , volume=

    Acoustic wave emitted by a vortex ring passing near the edge of a half-plane , author=. Journal of Fluid Mechanics , volume=. 1985 , publisher=

    work page 1985

  74. [74]

    Aeroacoustics of vortex–wedge interaction , volume =. J. Fluid Mech. , author =. 2025 , pages =. doi:10.1017/jfm.2025.10580 , urldate =

    work page doi:10.1017/jfm.2025.10580 2025

  75. [75]

    Abreu, L. I. , Tanarro, A. , Cavalieri, A. V. G. , Schlatter, P. , Vinuesa, R. , Hanifi, A. & Henningson, D. S. 2021 Spanwise-coherent hydrodynamic waves around flat plates and airfoils . Journal of Fluid Mechanics 927 , A1

    work page 2021

  76. [76]

    Ahmadi, A. R. 1986 An experimental investigation of blade-vortex interaction at normal incidence . Journal of Aircraft 23 (1), 47--55

    work page 1986

  77. [77]

    Amaral, F. R. , Spiropoulos, M. I. , Margnat, F. , Marx, D. , Valeau, V. & Jordan, P. 2025 Perpendicular rod wake/aerofoil interaction: microphone array and TR - PIV insights via SPOD and beamforming analysis . Exp Fluids 66 (12), 217

    work page 2025

  78. [78]

    1986 Airfoil gust response and the sound produced by airfoil-vortex interaction

    Amiet, R.K. 1986 Airfoil gust response and the sound produced by airfoil-vortex interaction . Journal of Sound and Vibration 107 (3), 487--506

    work page 1986

  79. [79]

    Amiet, R. K. 1975 Acoustic radiation from an airfoil in a turbulent stream . Journal of Sound and Vibration 41 (4), 407--420

    work page 1975

  80. [80]

    2011 Fundamentals of Aerodynamics\/

    Anderson, J. 2011 Fundamentals of Aerodynamics\/ . McGraw Hill

    work page 2011

Showing first 80 references.