Aeroacoustic Noise Calculator (Turbulence)
Estimate flow-generated noise with Lighthill and Proudman theory: acoustic power, sound power level, peak frequency and Kolmogorov turbulence scales. Free tool.
Aeroacoustic Turbulence Noise Calculator
Estimates aerodynamic noise from turbulent flow using Lighthill’s acoustic analogy and the Von Kármán energy spectrum. Computes quadrupole radiation, Reynolds stress, and viscous dissipation for the chosen flow and observer position.
Uses Decimal.js arbitrary-precision arithmetic to minimise rounding error when solving Lighthill’s compressible Reynolds momentum equations.
⚡ 3D Aerodynamic Viewports // Computational Fluid Core
Deep derived wave propagation, Reynolds scaling, and isotropic flow characteristics
Regime: COMPACT_QUADRUPOLE
λ_peak = 3.4300 m
Taylor scale λ_g: 3.861e-3 m
A clear path from inputs to results.
Estimate the aerodynamic (flow-generated) noise radiated by a patch of turbulence, together with the underlying turbulence scales that drive it. Given a flow speed, turbulence intensity, and eddy length scale, the tool applies Lighthill's acoustic analogy and Proudman's isotropic-turbulence result to predict acoustic power and sound levels, and reports the Kolmogorov and Taylor microscales. It is aimed at acoustics and CFD engineers doing early-stage, order-of-magnitude noise screening.
How to use
- Enter the mean flow speed U in m/s and the turbulence intensity as a percentage; the RMS turbulent velocity is u_rms = U x intensity/100.
- Enter the integral (eddy) length scale L in metres — the characteristic size of the energy-containing turbulent structures.
- Choose the fluid medium (air by default: density 1.225 kg/m^3, sound speed 343 m/s, kinematic viscosity 1.5e-5 m^2/s) and set ambient temperature and relative humidity for the atmospheric-absorption estimate.
- Set the observer position: distance R in metres and the angles theta and phi, which drive the convective (Doppler) amplification and the spreading loss.
- Read the turbulence diagnostics (TKE, dissipation rate, Kolmogorov and Taylor microscales, Reynolds numbers) and the acoustic outputs (acoustic power W, sound power level LW, peak frequency, and the overall sound pressure level OASPL at the observer).
- Use the flow presets (universal, free jet, aerofoil, hypersonic) to load representative speed/intensity/length-scale combinations.
The formula
Reference: Proudman, "The generation of noise by isotropic turbulence," Proc. R. Soc. A 214 (1952); Lighthill, Proc. R. Soc. A 211 (1952); Pope, Turbulent Flows (2000), ch. 6 (Kolmogorov scales); ISO 9613-2:1996 (atmospheric attenuation).
Worked example
Low-speed turbulent flow, 10% intensity (universal preset)
- U = 50 m/s; turbulence intensity 10%; length scale L = 0.1 m; air (rho0 = 1.225 kg/m^3, c0 = 343 m/s, nu = 1.5e-5 m^2/s); observer R = 100 m at theta = 90 deg; 20 C, 70% RH.
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The RMS turbulent velocity is u_rms = 50 x 0.10 = 5.0 m/s, so the turbulent Mach number is M_turb = 5/343 = 0.0146 and the turbulent kinetic energy is k = 1.5 x 5^2 = 37.5 m^2/s^2. The dissipation rate is epsilon = 0.09^(3/4) x 37.5^(3/2) / 0.1 = 377.3 m^2/s^3, which fixes the Kolmogorov length eta = (nu^3/epsilon)^(1/4) = 5.47e-5 m, time tau_eta = (nu/epsilon)^(1/2) = 1.99e-4 s, and velocity v_eta = (nu x epsilon)^(1/4) = 0.274 m/s, plus a Taylor microscale of 3.86e-3 m and a Taylor-microscale Reynolds number Re_lambda = sqrt((20/3) x 33333) = 471. Proudman's relation gives the radiated acoustic power W = 38 x 1.225 x 5^8 / 343^5 x 0.1^2 = 3.83e-8 W, i.e. a sound power level LW = 10 log10(W/1e-12) = 45.83 dB. The Strouhal peak is f = 0.2 x 50 / 0.1 = 100 Hz. Spreading this power to an observer 100 m away (and referencing 20 uPa) yields an overall sound pressure level OASPL of -4.95 dB.
Acoustic power W = 3.83e-8 W (sound power level 45.83 dB), peak near 100 Hz; at 100 m the overall sound pressure level is -4.95 dB (far below the 20 uPa reference, i.e. essentially inaudible at that distance). Kolmogorov length 54.7 micrometres, Re_lambda = 471.
Interpreting the result
The headline figure is the acoustic power W and its sound power level LW = 45.83 dB, which depend only on the turbulence and are independent of where you stand. The OASPL instead depends on observer distance: here, 100 m away, the pressure sits below the 20 uPa reference and the level is negative, meaning the sound is effectively inaudible — a direct consequence of the eighth-power velocity scaling, which makes low-speed turbulence an extremely weak noise source. The Kolmogorov microscales tell you the smallest eddies you would need to resolve in a CFD mesh, and Re_lambda characterizes how turbulent the flow is.
Assumptions & limitations
- Proudman's formula assumes homogeneous, isotropic turbulence and quadrupole (free-space) radiation; real jets, aerofoils, and wall-bounded flows have strong anisotropy and surface (dipole) sources that this model does not capture.
- The acoustic-power constant alpha is taken as the isotropic value near 38; published estimates of the Proudman constant vary by a factor of several, so W and LW are order-of-magnitude screening estimates, not certified predictions.
- The dissipation rate uses the standard k-epsilon closure epsilon = C_mu^(3/4) k^(3/2)/L with C_mu = 0.09, which is a modelling choice rather than a measured quantity.
- The turbulence is assumed fully developed and high-Reynolds-number so the Kolmogorov cascade and the isotropic relations (for example Re_lambda^2 = (20/3)Re_L) apply; they lose meaning at low Reynolds number.
- The eighth-power velocity law makes the result extremely sensitive to u_rms: a 10% error in turbulent velocity shifts acoustic power by about 80%, so input accuracy dominates output accuracy.
- Atmospheric attenuation follows ISO 9613-2 for the entered temperature and humidity and applies to outdoor air paths only; near-field, reflecting, or enclosed environments are not modeled.
Frequently asked questions
Why does the sound level come out negative?
Sound pressure level is referenced to 20 micropascals (the threshold of human hearing). When the predicted pressure at the observer is smaller than that reference, the decibel value is negative — it simply means the sound is below the audibility threshold at that distance. In the worked example a weak 50 m/s turbulent patch heard from 100 m produces about -5 dB, i.e. effectively silent. The observer-independent sound power level (45.83 dB) is the more meaningful figure for comparing sources.
What are the Kolmogorov microscales the tool reports?
They are the smallest length, time, and velocity scales in turbulence, where viscosity dissipates kinetic energy into heat: eta = (nu^3/epsilon)^(1/4), tau_eta = (nu/epsilon)^(1/2), and v_eta = (nu x epsilon)^(1/4). In the example eta is about 55 micrometres. For a CFD simulation to resolve all turbulent scales (a direct numerical simulation) the mesh must be comparable to eta, which is why DNS of high-Reynolds flows is so expensive.
What is the peak frequency based on?
It uses a Strouhal relation f = St x U/L with St = 0.2, a value characteristic of many bluff-body and shear-layer flows. With U = 50 m/s and L = 0.1 m this gives 100 Hz. The real spectrum is broadband and the single peak frequency is only an indicative center of the energy-containing range, not a pure tone.
What is the eighth-power law and why does it matter so much?
Lighthill showed that free turbulence radiates as a quadrupole with acoustic power scaling as the eighth power of velocity (W proportional to u^8). This is the single most important fact in jet aeroacoustics: doubling the turbulent velocity multiplies the radiated power by 2^8 = 256, about 24 dB. It is also why the result is so sensitive to the turbulence intensity you enter, and why high-speed jets are so much louder than low-speed flows.
Is this a substitute for a real CFD aeroacoustics simulation?
No. It is a first-order screening tool based on isotropic-turbulence theory. It gives a quick order-of-magnitude estimate of acoustic power and the governing turbulence scales from a handful of inputs. Detailed noise prediction needs a scale-resolving CFD run (LES/DES) coupled with an acoustic analogy such as Ffowcs Williams-Hawkings, which accounts for geometry, surface sources, and directivity that this model only approximates.
How do temperature and humidity affect the result?
They enter the atmospheric-absorption calculation (ISO 9613-2), which adds frequency-dependent loss along the air path to the observer. Higher frequencies and certain temperature/humidity combinations absorb more strongly over distance. They do not change the source acoustic power itself, only how much of it survives the propagation to the listener.
Methodology last reviewed 2026-10-06. Results are informational and not financial or engineering advice — see our disclaimer.