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arxiv: 2508.13575 · v2 · submitted 2025-08-19 · ⚛️ physics.flu-dyn

Wake-induced variations in noise levels and amplitude modulation for two interacting wind turbines

Jules Colas , Ariane Emmanuelli , Didier Dragna , Richard J.A.M. Stevens This is my paper

Pith reviewed 2026-05-18 23:07 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords wind turbine noisewake effectsamplitude modulationsound propagationturbine interactionsaeroacousticslarge-eddy simulation
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The pith

A second wind turbine placed directly downstream boosts sound pressure levels and amplitude modulation by several decibels through wake-induced flow focusing.

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

The paper examines how pairs of wind turbines interact to change how their noise travels. Using simulations that combine airflow modeling with sound source and propagation calculations, it compares three layouts: one turbine directly behind the other, turbines side by side, and a staggered arrangement. The key finding is that the wake from the first turbine focuses sound when the second sits directly downstream, raising both overall noise levels and the up-and-down variation in loudness several decibels farther downwind. Side-by-side and staggered setups produce smaller noise increases and often less variation because sound from the two machines averages out. Rotor speed differences add beating patterns that make the loudness swings intermittent, showing that small changes in how the blades turn matter for what people hear.

Core claim

When a second turbine is positioned directly downstream, wake-induced flow focusing enhances sound pressure levels (SPL) and amplitude modulation (AM) by several decibels downwind. In side-by-side and staggered configurations, SPL increases are limited to less than 2 dBA and AM is generally reduced due to spatial averaging, with distinct AM patterns where acoustic contributions from both turbines are comparable. For identical rotor speeds AM depends strongly on angular offset; slight speed differences produce beating that creates intermittent AM.

What carries the argument

Combined large-eddy simulation of the flow field, an aeroacoustic source model for turbine emission, and parabolic equation methods for far-field sound propagation through the wakes.

If this is right

  • Aligned turbine pairs produce noticeably higher noise and stronger loudness swings downwind than isolated turbines.
  • Side-by-side or staggered placement keeps noise increases small and reduces amplitude modulation through spatial averaging.
  • Angular offset between rotors strongly changes amplitude modulation when the machines turn at the same speed.
  • Small differences in rotor speed create beating that makes amplitude modulation intermittent rather than steady.

Where Pith is reading between the lines

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

  • Wind-farm layout rules could include minimum downstream spacing to limit noise spikes from wake focusing.
  • Active control of rotor speeds might be used to reduce the beating effects that produce noticeable loudness changes.
  • The same simulation approach could be extended to three or more turbines to check whether wake focusing adds up or saturates.

Load-bearing premise

The aeroacoustic source model together with parabolic equation propagation correctly represents real sound emission and travel through turbulent wakes even without direct experimental checks for these two-turbine cases.

What would settle it

Field measurements of sound pressure levels and amplitude modulation at downwind locations in a real two-turbine array aligned with the wind, compared against the same turbines operating in isolation.

read the original abstract

The influence of turbine-turbine interactions on sound propagation is investigated using numerical simulations. Three configurations are examined: turbines aligned downstream of each other, placed side by side, and arranged in a staggered pattern. The simulation framework combines large-eddy simulations for aerodynamic interactions, an aeroacoustic source model to simulate turbine sound emission, and parabolic equation methods for sound propagation. When a second turbine is positioned directly downstream, wake-induced flow focusing enhances sound pressure levels (SPL) and amplitude modulation (AM) by several decibels downwind. In side-by-side and staggered configurations, SPL increases are limited (<2 dBA), and AM is generally reduced due to spatial averaging. Distinct AM patterns emerge in regions where acoustic contributions from both turbines are comparable. For identical rotor speeds, AM is strongly affected by the angular offset between rotors. When rotor speeds differ slightly, beating effects occur, resulting in intermittent AM. These findings highlight the sensitivity of AM to rotor dynamics, a key factor influencing sound perception, with implications for environmental impact and turbine siting.

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

2 major / 2 minor

Summary. The paper examines the effects of interactions between two wind turbines on noise levels and amplitude modulation using numerical simulations. Three configurations are studied: turbines aligned in the downstream direction, placed side by side, and in a staggered arrangement. The approach integrates large-eddy simulations (LES) for capturing aerodynamic wake interactions, an aeroacoustic source model for sound emission, and parabolic equation methods for far-field sound propagation. Key results indicate that direct downstream positioning leads to wake-induced flow focusing that increases sound pressure levels (SPL) and amplitude modulation (AM) by several decibels in the downwind direction. In contrast, side-by-side and staggered setups show limited SPL increases (less than 2 dBA) and generally reduced AM due to spatial averaging. The study also highlights distinct AM patterns when contributions from both turbines are comparable and the influence of rotor speed differences leading to beating effects.

Significance. This work contributes to the understanding of aeroacoustic interactions in wind turbine arrays, which is relevant for optimizing wind farm layouts to minimize noise impact. The finding that wake focusing can enhance noise by several dB in aligned configurations, if confirmed, has practical implications for turbine siting and environmental assessments. The observation of beating effects with slight rotor speed differences underscores the importance of rotor dynamics in sound perception. The combined simulation framework offers a method to study such complex interactions numerically.

major comments (2)
  1. [Simulation framework] The combination of LES aerodynamics, aeroacoustic source model, and parabolic equation propagation underpins the central quantitative claim of several dB SPL/AM enhancement due to wake-induced flow focusing in the aligned configuration, yet the manuscript provides no direct experimental validation or benchmark comparisons for the two-turbine interacting cases (as described in the simulation framework section).
  2. [Results (aligned configuration)] Results for the downstream-aligned case report SPL and AM increases of several decibels without error bars, grid-convergence checks, or sensitivity to turbulence closure/source modeling approximations, which are load-bearing for assessing whether the focusing effect is physical or an artifact of the unvalidated chain.
minor comments (2)
  1. [Abstract] The abstract states SPL increases are limited to <2 dBA in side-by-side and staggered cases; clarify whether this is A-weighted and the exact reference baseline used for all comparisons.
  2. [Introduction] Notation for amplitude modulation (AM) and sound pressure level (SPL) should be defined consistently at first use in the main text to aid readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed review of our manuscript on wake-induced noise variations between interacting wind turbines. We appreciate the recognition of the work's relevance to wind farm layout optimization. Below we respond point by point to the major comments, indicating planned revisions to strengthen the presentation of the simulation framework and results.

read point-by-point responses

  1. Referee: [Simulation framework] The combination of LES aerodynamics, aeroacoustic source model, and parabolic equation propagation underpins the central quantitative claim of several dB SPL/AM enhancement due to wake-induced flow focusing in the aligned configuration, yet the manuscript provides no direct experimental validation or benchmark comparisons for the two-turbine interacting cases (as described in the simulation framework section).

    Authors: We acknowledge that direct experimental validation or benchmark data specifically for the coupled two-turbine aeroacoustic interaction cases is not presented, as comprehensive field or laboratory datasets combining detailed wake aerodynamics with far-field noise for multiple turbines remain scarce. Each component of the framework, however, rests on prior validations: the LES approach for turbine wakes has been compared against field measurements and other high-fidelity simulations in the literature; the aeroacoustic source model has been benchmarked against single-turbine noise measurements; and the parabolic equation method is a standard, validated technique for atmospheric sound propagation. In the revised manuscript we will add a dedicated subsection to the simulation framework section that summarizes these component-level validations with appropriate citations, explicitly states the assumptions involved in coupling the modules, and discusses the resulting limitations for the quantitative claims. This addition will allow readers to better evaluate the reliability of the reported SPL and AM changes. revision: yes

  2. Referee: [Results (aligned configuration)] Results for the downstream-aligned case report SPL and AM increases of several decibels without error bars, grid-convergence checks, or sensitivity to turbulence closure/source modeling approximations, which are load-bearing for assessing whether the focusing effect is physical or an artifact of the unvalidated chain.

    Authors: We agree that reporting numerical uncertainties is important for substantiating the central quantitative findings. In the revised manuscript we will include grid-convergence results for the aligned configuration, demonstrating that the SPL and AM enhancements of several decibels remain consistent under successive grid refinements. We will also add a sensitivity comparison using an alternative sub-grid-scale turbulence model for at least the key aligned case. Error bars derived from temporal statistics over multiple rotor revolutions will be added to the relevant SPL and AM figures. A complete sensitivity analysis covering every modeling approximation would require additional large-scale simulations beyond the scope of the present study; we will therefore note this as a limitation in the discussion while emphasizing the checks that have been performed. These revisions will help confirm that the wake-focusing effect is physical rather than numerical. revision: partial

Circularity Check

0 steps flagged

Forward numerical simulation chain exhibits no circularity

full rationale

The paper computes SPL and AM via a forward simulation pipeline (LES aerodynamics + aeroacoustic source model + parabolic propagation) for three fixed turbine layouts. No parameters are fitted to the downstream noise quantities under study, and no equation or self-citation reduces the reported enhancements to a tautological input. The central quantitative claims are direct outputs of the described numerical framework rather than re-expressions of fitted data or prior self-citations.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The study relies on standard turbulence modeling assumptions and propagation approximations without introducing new free parameters or postulated entities in the reported work.

axioms (1)
  • domain assumption Parabolic equation methods remain valid for sound propagation through turbine wakes at the distances considered.
    Invoked when applying the propagation solver to the LES flow fields.

pith-pipeline@v0.9.0 · 5724 in / 1182 out tokens · 30017 ms · 2026-05-18T23:07:26.951096+00:00 · methodology

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