Turbulence-Induced Noise (TIN)

• Turbulence-Induced Noise (TIN) is the conversion of turbulent fluctuations into measurable macroscopic signals, manifesting as acoustic, hydrodynamic, or optical noise.
• In aeroacoustics, TIN arises when spanwise-coherent turbulent structures scatter wall-pressure fluctuations at trailing edges, leading to broadband noise.
• TIN research spans applications in wind energy, turbomachinery, and state transitions in fluid dynamics, driving advances in reduced-order modeling and signal analysis.

Searching arXiv for papers on turbulence-induced noise and closely related usages across aeroacoustics, turbulence dynamics, and optical propagation. Turbulence-Induced Noise (TIN) is a cross-disciplinary term whose meaning depends on context, but in its most established usage it denotes sound generated when turbulent flow fluctuations generate and/or scatter acoustic waves. In aeroacoustics, TIN commonly refers to broadband noise produced when turbulent eddies or wall-pressure fluctuations interact with solid boundaries such as trailing edges, leading edges, tips, stators, shrouds, or casings (Demange et al., 2024). In fluid-dynamical studies of two-dimensional turbulence, the same acronym is used differently: turbulent fluctuations act as an effective noise that drives random transitions between metastable coherent structures such as large-scale vortices and jets (Xu et al., 2023). In free-space optical communications, turbulence-induced noise refers to excess phase and intensity fluctuations caused by refractive-index inhomogeneities, quantified through reconstructed photon statistics and the Fano factor (Sadhukhan et al., 24 Oct 2025). The common thread is the conversion of turbulent or turbulence-like fluctuations into measurable macroscopic variability, whether acoustic, hydrodynamic, or statistical.

1. Terminological scope and canonical definitions

The dominant technical usage of TIN is aeroacoustic. In that setting, fluctuating aerodynamic loads associated with turbulent flows scatter into sound, and trailing-edge noise is the most prominent realization for airfoils and blades (Tian et al., 2023). A standard mechanism is the scattering of turbulent boundary-layer wall-pressure fluctuations by a sharp trailing edge, which produces broadband sound and often dominates airfoil self-noise at low-to-moderate Mach number (Yuan et al., 2024). The same general category also includes leading-edge interaction noise from incoming turbulence, rotor–stator broadband interaction noise, gap-turbulence tones, and tip-clearance noise (Wohlbrandt et al., 2017).

For airfoils, trailing-edge noise is generated when wall-pressure fluctuations convect to the trailing edge and are scattered into acoustic waves. The edge behaves as a spanwise-wavenumber filter: only sufficiently low spanwise wavenumbers radiate efficiently, while higher-wavenumber content is evanescent in the far field (Demange et al., 2024). This wavenumber-selection principle links classical TE-noise theory, modal decomposition, and reduced-order modeling.

A different but related usage appears in statistical fluid mechanics. In anisotropic two-dimensional turbulence, turbulent fluctuations produced by forcing and cascade act as effective noise that kicks the system between metastable attractors, specifically large-scale vortices (LSVs) and unidirectional jets (Xu et al., 2023). In that framework, TIN does not denote sound emission; it denotes turbulence-induced stochastic switching of coherent flow states.

A further extension occurs in optical turbulence. There, random refractive-index fluctuations impose time-varying phase and amplitude distortions on an optical field, and the resulting excess fluctuations appear as super-Poissonian photon-number statistics at the receiver (Sadhukhan et al., 24 Oct 2025). This suggests that TIN has evolved into a broader label for turbulence-driven macroscopic noise processes, although the physical observables differ markedly across disciplines.

2. Trailing-edge turbulence-induced noise on airfoils

Trailing-edge noise is the most extensively characterized form of TIN in the supplied literature. In the broadband regime, turbulent boundary-layer wall-pressure fluctuations convect downstream and are scattered at the trailing edge into acoustic waves, producing a broadband spectrum rather than discrete tones (Yuan et al., 2024). For airfoil applications, this mechanism is often the dominant contributor to the far-field spectrum, including in wind turbines and many low-Mach lifting-surface configurations (Demange et al., 2024).

The fundamental radiation constraint is spanwise. The acoustic wavenumber is

$k_a=\frac{\omega}{c_0}=\frac{2\pi f}{c_0},$

the spanwise wavenumber is

$k_z=\frac{2\pi}{\lambda_z},$

and efficient radiation occurs only when

$|k_z|\le k_a.$

In nondimensional form, with $He = k_a c = 2\pi f c / c_0 = 2\pi\,St\,M$,

$$\max(k_z c)=He,\quad \min\left(\frac{\lambda_z}{c}\right)=\frac{2\pi}{He}.$$

This establishes the trailing edge as a spanwise low-pass filter: large spanwise wavelengths radiate, small wavelengths do not (Demange et al., 2024).

The experimental study on a NACA0012 airfoil shows that broadband TE noise is radiated primarily by spanwise-coherent turbulent structures with very large spanwise wavelengths (Demange et al., 2024). At frequencies corresponding to peak TE-noise emission, the turbulent structures responsible for radiation have strikingly large spanwise wavelengths, exceeding $60\%$ of the airfoil chord length. The numerical companion study identifies the corresponding hydrodynamic structures more specifically as streamwise-travelling wavepackets that are energetic near the trailing edge and radiate when their spanwise wavenumber satisfies the cut-on condition (Yuan et al., 2024).

The aerodynamic source field is low rank in the acoustic subspace. In the numerical study, acoustic extended SPOD shows that the leading acoustic mode captures more than $80\%$ of acoustic energy for $3\le He\le 25$ at $n_z=0$, whereas hydrodynamic SPOD is less compact (Yuan et al., 2024). This low-rank structure supports reduced-order acoustic reconstruction and suggests that only a small subset of the turbulent field is acoustically efficient.

3. Role of coherence, inflow turbulence, roughness, and serrations

A central result across the airfoil papers is that acoustically efficient TIN is controlled less by the full turbulence field than by its low-$k_z$, spanwise-coherent component. Pointwise flow–acoustic coherence is weak, but coherence rises sharply when both the surface-pressure field and the radiated acoustics are spanwise averaged, that is, when the $k_z=\frac{2\pi}{\lambda_z},$0 component is isolated (Demange et al., 2024). In the LES, coherence between spanwise-averaged wall pressure and far-field pressure reaches up to $k_z=\frac{2\pi}{\lambda_z},$1 within $k_z=\frac{2\pi}{\lambda_z},$2–6, whereas single-point coherence remains low (Yuan et al., 2024).

High inflow turbulence changes the boundary layer and thereby amplifies TIN. For a NACA 0012 under urban-like turbulence conditions, high free-stream turbulence increases the velocity fluctuations and integral length scale along the entire boundary layer, producing an increment of the surface pressure spectrum more than 6 dB and 10 dB in the entire frequency range for $k_z=\frac{2\pi}{\lambda_z},$3 and $k_z=\frac{2\pi}{\lambda_z},$4 of free-stream turbulence, respectively (Botero-Bolivar et al., 2021). The same study reports that $k_z=\frac{2\pi}{\lambda_z},$5 free-stream turbulence increases the velocity fluctuations just in the low-frequency range, whereas $k_z=\frac{2\pi}{\lambda_z},$6 inflow turbulence influences the velocity spectrum in the entire frequency range, increasing the size of the smallest structures of the turbulence (Botero-Bolivar et al., 2021). Under those conditions, Amiet-based predictions yield corresponding increases in far-field trailing-edge noise.

Surface roughness used for tripping can also alter TIN by changing wall-pressure spectra and spanwise coherence (Santos et al., 2021). Trip heights in the range $k_z=\frac{2\pi}{\lambda_z},$7–$k_z=\frac{2\pi}{\lambda_z},$8 of the undisturbed boundary-layer thickness produce only slight increases in low-frequency TE wall-pressure fluctuations and far-field noise, while preserving similar high-frequency wall-pressure spectra in $k_z=\frac{2\pi}{\lambda_z},$9 (Santos et al., 2021). For $|k_z|\le k_a.$0, high-frequency far-field increases are dominated by trip self-noise rather than TE scattering (Santos et al., 2021). Geometry matters: sharkskin-like roughness behaves like a smaller effective zigzag for high-frequency TE wall-pressure spectra but generates pronounced high-frequency self-noise, including a tone at $|k_z|\le k_a.$1 (Santos et al., 2021).

Serrated trailing edges modify the acoustically efficient coherence. One study reports that serrated trailing edges significantly reduce blunt vortex shedding noise and laminar separation bubble noise across a broader frequency range, particularly in the mid-to-high frequency range, while not significantly altering directivity patterns (Xue et al., 2023). Wake measurements show reduced power spectral density of turbulent velocity fluctuations and suppressed larger vortex structures. However, serration models based on frozen turbulence overpredict attainable reductions. A later study shows that the finite streamwise coherence of real turbulent boundary layers must be accounted for through a non-frozen model with

$|k_z|\le k_a.$2

which spreads the streamwise spectrum around the convective ridge and reduces the predicted interference benefit (Tian et al., 2023). The key control parameter becomes $|k_z|\le k_a.$3: when serration amplitude is not small relative to the streamwise coherence length, decoherence undermines destructive interference (Tian et al., 2023).

4. TIN in turbomachinery, tip-clearance flows, and gap-driven tones

In turbomachinery, TIN includes both broadband and tonal components generated by organized turbulence interacting with rotating or stationary surfaces (Ottersten et al., 2021). A fan-stage example is rotor–stator interaction broadband noise, where turbulent structures in rotor wakes convect into the stator and scatter at stator leading edges (Wohlbrandt et al., 2017). In that environment, the inflow is cyclostationary. The cyclostationary stochastic hybrid method shows that periodic mean flow and periodic turbulent kinetic energy have negligible impact on the radiated broadband sound power, whereas periodic integral turbulence length scale has a substantial effect (Wohlbrandt et al., 2017). When background and wake turbulence are comparable, a stationary representation of the turbulence length scale fails to reproduce the cyclostationary spectral shape.

A distinct tonal TIN mechanism occurs in a voluteless centrifugal HVAC fan. There, turbulence generated in the upstream inlet gap between the stationary inlet duct and the rotating shroud is swept downstream and interacts with the top side of the blade leading edge (Ottersten et al., 2021). At $|k_z|\le k_a.$4 rpm with $|k_z|\le k_a.$5, the paper identifies a tone at approximately $|k_z|\le k_a.$6 Hz, close to $|k_z|\le k_a.$7, and shows numerically that this tone disappears when the gap turbulence is artificially suppressed by coarsening the mesh near the inlet gap and shroud (Ottersten et al., 2021). The source localizes to the shroud and blade contributions, not the backplate, establishing a turbulence–blade interaction mechanism distinct from classic blade-passing tones.

Tip-clearance flows generate another form of TIN. In a stationary airfoil–wall configuration, the radiated sound is produced by turbulence in the leakage flow and by a tip-separation vortex near the trailing edge (Awasthi et al., 2024). Beamforming shows that mid-to-high-frequency noise is dominated by leading-edge and mid-chord leakage-flow regions, while a distinct low-frequency source is located near the trailing edge and is attributed to the tip-separation vortex (Awasthi et al., 2024). The mid-frequency band scales with the sixth power of Mach number and collapses with the Helmholtz number $|k_z|\le k_a.$8; the low-frequency band scales closer to $|k_z|\le k_a.$9 and with $He = k_a c = 2\pi f c / c_0 = 2\pi\,St\,M$0 (Awasthi et al., 2024). Smaller gaps reduce the low-frequency trailing-edge source but increase high-frequency leading-edge noise.

Hydrodynamic precursors of tip-leakage TIN have also been isolated in a linear cascade. A Zonalised LES study identifies self-excited unsteadiness involving tip-gap vortex separation, tip-leakage-jet/mainstream interaction, primary tip-leakage-vortex wandering, and induced endwall separation (Liu et al., 2024). SPOD shows a dominant high-frequency mode before vortex breakdown and multiple lower-frequency modes after breakdown. A micro-offset tip design suppresses the self-excited unsteadiness and reduces associated turbulence generation and pressure fluctuations (Liu et al., 2024). This suggests a hydrodynamic route to TIN control even though that study does not compute radiated sound.

5. Atmospheric and wind-energy manifestations

In atmospheric flows, TIN can refer to intrinsic pressure fluctuations produced by turbulence itself. A recent theory of wind noise pressure spectra distinguishes turbulence–turbulence and turbulence–shear interaction sources, and develops the turbulence–turbulence contribution for homogeneous anisotropic turbulence using Kraichnan’s mirror flow model (Yu et al., 15 Feb 2025). In that framework, the pressure source follows the incompressible pressure–Poisson relation

$He = k_a c = 2\pi f c / c_0 = 2\pi\,St\,M$1

and anisotropy changes the inertial-range pressure spectral slope from the isotropic $He = k_a c = 2\pi f c / c_0 = 2\pi\,St\,M$2 result to approximately $He = k_a c = 2\pi f c / c_0 = 2\pi\,St\,M$3 (Yu et al., 15 Feb 2025). The anisotropic turbulence–turbulence interaction pressure spectrum is reported to be not sensitive to height, while the dominant tensor contributions differ between the source region and inertial region (Yu et al., 15 Feb 2025).

In wind farms, TIN assumes the form of leading-edge interaction noise caused by inflow turbulence impinging on rotating blades (Colas et al., 18 Aug 2025). In the strip-theory framework used there, TIN and trailing-edge noise contribute equally in the first turbine row, with TIN dominating at low frequencies and trailing-edge noise at higher frequencies (Colas et al., 18 Aug 2025). Downstream, trailing-edge noise decreases due to lower wind speeds, whereas TIN mostly persists because turbulence dissipation increases within wakes (Colas et al., 18 Aug 2025). These effects are stronger in aligned farms because wake interactions are stronger, but staggered farms are noisier overall because the turbines operate at higher wind speeds (Colas et al., 18 Aug 2025).

The same study shows that wind-farm flow not only affects emission but also propagation. Wake superposition modifies sound focusing downwind, leading to different amplification areas than for an isolated turbine (Colas et al., 18 Aug 2025). For staggered layouts, enhanced focusing yields higher sound levels and higher amplitude modulation downwind than for aligned layouts (Colas et al., 18 Aug 2025). This indicates that realistic TIN assessment in wind farms requires coupled flow–acoustic modeling rather than isolated-turbine source models.

6. Turbulence as effective noise in nonlinear flow dynamics and in optics

Outside aeroacoustics, TIN denotes turbulence-driven stochasticity in nonlinear systems. In anisotropic two-dimensional turbulence, randomly forced flow in a periodic rectangular domain exhibits LSVs for $He = k_a c = 2\pi f c / c_0 = 2\pi\,St\,M$4, jets for $He = k_a c = 2\pi f c / c_0 = 2\pi\,St\,M$5, and metastable coexistence in the intermediate range (Xu et al., 2023). Turbulent fluctuations act as effective noise that drives random transitions between these metastable condensates. The transitions occur in two stages: an initial fast redistribution of large-scale kinetic energy by nonlinear triadic interactions, followed by slow viscous adjustment to the new equilibrium energy (Xu et al., 2023). Lifetimes of jets and LSVs are exponentially distributed,

$He = k_a c = 2\pi f c / c_0 = 2\pi\,St\,M$6

consistent with a memoryless Poisson process, and mean lifetimes grow approximately exponentially with Reynolds number (Xu et al., 2023). This is a usage of TIN in which “noise” refers to internally generated turbulent fluctuations rather than acoustics.

A more radical interpretation is proposed in a study of the “noise-expansion cascade” in two-dimensional turbulent Kolmogorov flow (Liao et al., 2024). There, micro-level disturbances of amplitude $He = k_a c = 2\pi f c / c_0 = 2\pi\,St\,M$7 and $He = k_a c = 2\pi f c / c_0 = 2\pi\,St\,M$8 in the initial condition are shown to grow separately and sequentially to macro-level amplitudes $He = k_a c = 2\pi f c / c_0 = 2\pi\,St\,M$9, at approximately $$\max(k_z c)=He,\quad \min\left(\frac{\lambda_z}{c}\right)=\frac{2\pi}{He}.$$0 and $$\max(k_z c)=He,\quad \min\left(\frac{\lambda_z}{c}\right)=\frac{2\pi}{He}.$$1, respectively (Liao et al., 2024). Each disturbance, once amplified, alters macroscopic flow symmetry and statistics. This suggests that unavoidable micro-level disturbances can become a source of macroscopic randomness in turbulence, though that study concerns hydrodynamic unpredictability rather than acoustic radiation.

In free-space optical communications, turbulence-induced noise refers to optical-field randomness induced by refractive-index fluctuations (Sadhukhan et al., 24 Oct 2025). Intensity sequences are processed through a nonlinear reconstruction to recover the complex field, and Wigner-function tomography is used to infer photon-number distributions and the Fano factor

$$\max(k_z c)=He,\quad \min\left(\frac{\lambda_z}{c}\right)=\frac{2\pi}{He}.$$2

Uncorrected turbulence produces super-Poissonian statistics with $$\max(k_z c)=He,\quad \min\left(\frac{\lambda_z}{c}\right)=\frac{2\pi}{He}.$$3–$$\max(k_z c)=He,\quad \min\left(\frac{\lambda_z}{c}\right)=\frac{2\pi}{He}.$$4, a single PMMA slab reduces the factor to about $$\max(k_z c)=He,\quad \min\left(\frac{\lambda_z}{c}\right)=\frac{2\pi}{He}.$$5–$$\max(k_z c)=He,\quad \min\left(\frac{\lambda_z}{c}\right)=\frac{2\pi}{He}.$$6, and dual PMMA slabs bring it near Poissonian values $$\max(k_z c)=He,\quad \min\left(\frac{\lambda_z}{c}\right)=\frac{2\pi}{He}.$$7–$$\max(k_z c)=He,\quad \min\left(\frac{\lambda_z}{c}\right)=\frac{2\pi}{He}.$$8, with occasional near-sub-Poissonian excursions (Sadhukhan et al., 24 Oct 2025). This use preserves the idea of turbulence-induced excess fluctuations while moving the observable from sound or flow structure to photon statistics.

7. Open issues, misconceptions, and research directions

A common misconception is that all turbulent fluctuations contribute equally to TIN. The airfoil studies show the opposite: only a restricted subset of the turbulence field is acoustically efficient, namely the low-spanwise-wavenumber, sufficiently coherent part that satisfies the radiation criterion $$\max(k_z c)=He,\quad \min\left(\frac{\lambda_z}{c}\right)=\frac{2\pi}{He}.$$9 (Demange et al., 2024). Small integral coherence lengths measured in wall-pressure statistics do not contradict large acoustic radiation wavelengths, because the radiating subset is selected by the trailing-edge scattering condition (Demange et al., 2024).

Another misconception is that frozen-turbulence models are adequate whenever wall-pressure spectra are known. For serrated trailing edges, finite streamwise decoherence is a first-order correction, and ignoring it systematically overpredicts achievable noise reduction (Tian et al., 2023). Likewise, high-inflow-turbulence cases fall outside the range of conventional low-TI wall-pressure models, which fail to capture the measured increases in wall-pressure spectra and TE noise under $60\%$0–$60\%$1 turbulence intensity (Botero-Bolivar et al., 2021).

Across turbomachinery and wind energy, a recurring issue is the need to couple source modeling to realistic unsteady or spatially varying flow statistics. Cyclostationary rotor–stator TIN depends primarily on the periodic integral turbulence length scale rather than on periodic mean flow or TKE alone (Wohlbrandt et al., 2017). Wind-farm TIN depends jointly on wake-modified turbulence dissipation, turbine operating state, and wake-induced propagation effects (Colas et al., 18 Aug 2025). These findings argue against single-scale or isolated-source approximations when wake interaction is strong.

In nonlinear fluid dynamics, the term TIN itself is not fully standardized. In anisotropic two-dimensional turbulence it denotes effective stochastic forcing by turbulent fluctuations (Xu et al., 2023); in the noise-expansion literature it denotes macro-level randomness produced by amplification of micro-disturbances (Liao et al., 2024). A plausible implication is that the acronym now spans at least three technical families: aeroacoustic radiation, turbulence-driven state switching, and turbulence-driven excess statistical fluctuations in non-acoustic systems.

Prominent future directions are already indicated in the cited work. For aeroacoustics, these include SPOD- or resolvent-informed low-$60\%$2 source models for trailing-edge noise (Yuan et al., 2024), non-frozen serration theories with realistic coherence lengths (Tian et al., 2023), and integrated LES–acoustic frameworks for wind farms (Colas et al., 18 Aug 2025). For turbulence dynamics, theoretical large-deviation or instanton approaches to metastable switching remain open (Xu et al., 2023). For atmospheric wind noise, the extension of anisotropic pressure-spectrum theory beyond the present mirror-flow assumptions is an explicit next step (Yu et al., 15 Feb 2025). For optical TIN, the quantitative linkage between turbulence-induced phase distortion and photon statistics offers a route to turbulence-aware receiver diagnostics and compensation (Sadhukhan et al., 24 Oct 2025).