Fluid-Borne Noise Signals

• Fluid-borne noise signals are pressure or velocity fluctuations generated by turbulence, coherent flow structures, and fluid–structure interactions.
• They are analyzed using high-fidelity modeling, advanced signal processing, and experimental benchmarking to isolate contributions from different noise sources.
• Accurate FBN measurements support practical applications such as leak detection, sonar performance optimization, and noise control in industrial and marine systems.

Fluid-borne noise (FBN) signals are pressure or velocity fluctuations that propagate within a fluid medium due to flow turbulence, coherent flow structures, acoustic generation mechanisms, or mechanical–fluid transmissions. FBN arises in a vast range of engineered and natural systems, from pipeline networks and hydraulic pumps to boundary-layer–induced noise in sonar applications, and is both a critical diagnostic observable and a design constraint in aeroacoustics, hydroacoustics, and fault detection. Modern FBN analysis integrates high-fidelity modeling, advanced signal processing, and experimental benchmarking to disentangle the contributions of turbulence, coherent structures, and fluid–structure interactions across an enormous frequency span.

1. Fundamental FBN Generation Mechanisms

FBN in internal and external flows primarily results from several fluid-dynamic noise sources:

• Turbulent Eddies: Random velocity and pressure fluctuations in turbulent flows radiate broadband noise via quadrupole (volume) sources, as formalized by Lighthill’s acoustic analogy. These dominate in high-Reynolds flows, e.g., fan ducts, jets, and open-channel flows (Schoder, 26 Mar 2024).
• Shear-Layer and Jet-Edge Interactions: Flow separation, jet leakage, and vortex shedding at geometric discontinuities generate pronounced dipole and, less frequently, monopole sources, especially evident in open jet and leak-induced FBN (Giro et al., 2022).
• Flow-Induced Surface Pressure Fluctuations: For bodies submerged in turbulent flows (e.g., sonar windows, foils), wall-pressure fluctuations excite structural vibrations (bending waves), which then couple into the fluid as acoustic signals (Henke, 2016). Low Mach number flows favor dipole dominance.
• Unsteady Flow Features: Coherent structures (large-scale vortices, impinging shear layers) exhibit intermittent, power-law–distributed dwell times, producing 1/f-type noise spectra through renewal-process statistics (Herault et al., 2016).
• Oscillating Body Dynamics: Motions akin to biological or bio-inspired appendages create tonal dipole patterns at actuation and harmonic frequencies (Khalid et al., 2018).

The diversity of mechanisms necessitates detailed multi-physical treatments for FBN prediction, particularly where engineering control or diagnostic sensitivity is critical.

2. Governing Principles and Analytical Frameworks

2.1. Acoustic Analogies

The present consensus places Lighthill’s acoustic analogy as the foundational equation for FBN, expressing density or pressure perturbations via the inhomogeneous wave equation: $$\frac{\partial^2 \rho'}{\partial t^2} - c_0^2 \nabla^2 \rho' = \frac{\partial^2 T_{ij}}{\partial x_i \partial x_j}$$ with the acoustic stress tensor $T_{ij}$ combining Reynolds stress, pressure, and viscous terms (Schoder, 26 Mar 2024).

In complex configurations with moving surfaces, the Ffowcs Williams–Hawkings (FW-H) formulation generalizes the acoustic source decomposition, providing explicit integral representations for monopole, dipole, and quadrupole source strengths: $$p'(x,t) = \frac{\partial}{\partial t}\left[\int Q G dV \right] - \frac{\partial}{\partial x_i} \left[ \int F_i G dS \right] + \frac{\partial^2}{\partial x_i \partial x_j}\left[ \int T_{ij} G dV \right]$$ where $G$ is the appropriate Green's function (Schoder, 26 Mar 2024, Khalid et al., 2018).

2.2. Coupled Fluid–Structure and Flow–Acoustics

For applications such as sonar systems, wall-pressure fluctuations from a turbulent boundary layer excite a plate, which in turn radiates into the adjacent fluid. The governing system consists of:

• Turbulent hydrodynamic forcing (Navier–Stokes-derived LES wall pressure)
• Plate bending dynamics (Kirchhoff–Love theory)
• Acoustic wave propagation in the fluid (linear wave equation and interface conditions)

Analytical solutions via spectral-domain decompositions enable exact transfer functions from turbulent input to propagated FBN at sensor locations (Henke, 2016).

2.3. Bubbly and Multiphase Media

In dispersed two-phase media (e.g., bubbly liquids), FBN propagation is described by models such as the Multiple Bagnold Problem (MBP): fluid–bubble chains with polytropic gas dynamics yield discrete eigenmodes and frequency-dependent transmission, including strong attenuation above critical frequencies and complex band-structure effects with polydispersity (Ortega-Roano et al., 10 May 2024).

3. Experimental Observations and Quantitative Trends

Extensive experimental campaigns have delineated the magnitude, frequency-dependence, and directional properties of FBN:

• Turbulence–Acoustic Interaction: Recent experiments reveal that turbulence in water can both absorb and amplify acoustic waves at MHz frequencies, well above turbulence spectral content—without spectral broadening, new frequency generation, or conventional damping effects. Maximum observed attenuation and amplification in pipes/jets reached –77% and +68% of the received amplitude, dependent non-monotonically on frequency, flow regime, and turbulence intensity. This amplifying/absorbing behavior requires introduction of a turbulence–acoustic coupling coefficient $\Gamma(f, I)$ into propagation models, with empirical values up to $|\Gamma| \sim 1~\mathrm{m}^{-1}$ for strong turbulence in narrow pipes (Hu et al., 8 Dec 2025).
• Scaling Laws in Jet/Leak-Induced FBN: Acoustic power generated by turbulent jets through leaks scales with $(\Delta p)^n A_{\rm or}$, where $n \approx 1.5-2$, $\Delta p$ is the pressure drop, and $A_{\rm or}$ the orifice area. FBN signals are found above ~500 Hz up to several kHz, with detection and classification of leaks via pressure/vibration features yielding errors below 15% for moderate-to-large defects (Giro et al., 2022).
• 1/f-Type Spectra in Turbulent FBN: FBN signals exhibit power-law (1/f) behavior in the low-frequency PSD, traceable to the renewal statistics of coherent flow structures (e.g., vorticity filaments, large-scale circulations) with heavy-tailed dwell-time distributions. The spectral exponent $\alpha$ and dwell-time exponent $\beta$ satisfy $\alpha=3-\beta$ or $\alpha=\beta-1$ depending on process symmetry (Herault et al., 2016).

System	PSD Exponent α	Dwell Exponent β	Spectral Law
2D turbulence (Galinstan)	0.7	2.25	$\alpha=3-\beta$
Swirling dynamo (VKS)	0.5	2.5	$\alpha=3-\beta$
von Kármán pressure drops	0.6	1.58	$\alpha=\beta-1$

4. Signal Acquisition, Processing, and Feature Extraction

FBN measurement employs an array of modality-specific methods:

• Hydrophones and High-Bandwidth Sensors: For hydraulic systems, transient pressure sensors with >20 kHz bandwidth capture high-frequency FBN, including fault-induced flow/pressure ripples (Dong et al., 22 Dec 2025).
• Microphone Arrays and Beamforming: Diagonalizing the cross-spectral matrix (CSM), excluding the diagonal (suppressed TBL noise), and performing beam-steering or Source Power Integration (SPI), CLEAN-SC, or Probabilistic Factor Analysis (PFA) enables the reconstruction of spatially distributed FBN from TBL-contaminated measurements up to ~5 kHz (Sijtsma et al., 2019).
• Time–Frequency Analysis: Short-time Fourier transform (STFT) and synchrosqueezed wavelet transforms (SST) dissect the spectral content and temporal evolution of FBN, crucial for leak detection and classification (Giro et al., 2022, Dong et al., 22 Dec 2025).
• Convolutional Neural Networks (CNNs) and Physics-Informed Neural Networks (PINNs): Deep learning models for fault detection in hydraulic pumps employ CNNs on time and frequency representations of FBN signals, while PINNs provide virtual sensing by embedding physical FBN propagation equations (Dong et al., 22 Dec 2025).

Preprocessing choices—such as mean removal without normalization, log-scaling of spectral axes, and selection of kernel size to match physical feature scales—have clear impacts on both classifier interpretability and transfer learning success.

5. FBN in Fluid–Structure–Acoustic Systems

Applications coupling hydrodynamic FBN sources to compliant structures and adjacent fluid volumes require biorthogonal modal decomposition of the full coupled system:

• Wall-pressure fluctuations (from LES or experimental data) drive structural modes (e.g., plate bending) which then excite acoustic field modes in the adjacent fluid (Henke, 2016).
• The resulting FBN at sensor positions (e.g., inside sonar windows) is predicted by analytical transfer functions and compared to experimental wavenumber–frequency plots.
• Modal damping (orthotropic or isotropic) is necessary to replicate observed $\omega^{-4}$ spectral roll-off and the propagation/broadening of energy along dispersion curves.
• Frequency-dependent impedance boundary conditions at solid/fluid interfaces further tune FBN spectral features (Henke, 2016).

6. Engineering Implications and Inverse Problems

FBN signals, when appropriately modeled and measured, underpin a wide variety of engineering analyses:

• Noise Characterization and Control: Quantitative propagation models embedding turbulence–acoustic coupling (e.g., via $\Gamma(f, I)$) are essential for predicting noise transmission in pipeline, underwater, and fan/ventilation settings, permitting targeted mitigation strategies (attenuation or amplification bands) (Hu et al., 8 Dec 2025, Schoder, 26 Mar 2024).
• Leak and Fault Detection: In hydraulic and process-pipe systems, FBN signatures are directly linked to leak size, pressure regime, and turbulence intensity. Feature-based and deep learning classifiers can localize and size leaks using FBN time–frequency data, even achieving zero-shot diagnosis when synthetic, physics-based signal databases are accurately calibrated (Giro et al., 2022, Dong et al., 22 Dec 2025).
• Inverse Turbulence Characterization: By measuring FBN modulations across frequency sweeps, local turbulence intensities can be inferred, providing non-intrusive turbulence diagnostics (Hu et al., 8 Dec 2025).
• Fluid–Structure Acoustics and Sonar Performance: Accurate modeling of FBN transmission through structures enables robust sonar array design and noise-shielding assessment (Henke, 2016).

7. Outstanding Challenges and Current Research Trajectories

Recent discoveries of turbulence-induced acoustic amplification at high frequencies, incompatible with classical mechanisms (bubble resonance, viscous dissipation, spectral broadening), highlight the existence of previously unrecognized turbulence–acoustic interactions (Hu et al., 8 Dec 2025). Practical FBN modeling thus increasingly relies on empirical or semi-empirical coupling coefficients tailored to specific flow configurations and turbulence levels.

Similarly, in multiphase systems, proper determination of dispersion, attenuation, and resonance bands in bubbly or polydisperse domains requires precise measurement of in situ bubble distributions, volume fractions, and boundary conditions (Ortega-Roano et al., 10 May 2024).

Signal processing developments, especially in TBL-affected environments, integrate advanced beamforming and denoising techniques to isolate coherent FBN from spatially incoherent hydrodynamic noise, using high-density arrays and sophisticated optimization-based diagonal subtraction (Sijtsma et al., 2019).

In summary, FBN signals constitute a rich, multifaceted field at the intersection of turbulence, acoustics, and signal processing. Continued research advances the fundamental understanding of new interaction mechanisms, enhances the precision of diagnostic and control tools, and expands the scope of applications in industrial, marine, and energy sectors.