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arxiv: 2508.19940 · v2 · submitted 2025-08-27 · ⚛️ physics.flu-dyn

Convection velocities and velocity coupling of outer-scaled wall-pressure fluctuations in canonical turbulent boundary layers

Rahul Deshpande , Abdelrahman Hassanein , Woutijn J. Baars This is my paper

Pith reviewed 2026-05-18 21:15 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords turbulent boundary layerwall-pressure fluctuationslogarithmic regionouter scalingvelocity-pressure couplingconvection velocityReynolds number effectslarge-scale structures
0
0 comments X

The pith

Velocities in the logarithmic region correlate most strongly with outer-scaled wall-pressure fluctuations in turbulent boundary layers.

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

The paper establishes that in zero-pressure-gradient turbulent boundary layers, the streamwise velocities most tightly linked to large-scale wall-pressure fluctuations that scale with boundary-layer thickness are located in the logarithmic region. Wake-region contributions exist but prove statistically weaker. These conclusions rest on space-time correlations obtained from a custom microphone array spanning five boundary-layer thicknesses that isolates outer-scale pressure signals while measuring velocity at the downstream end. The coupling strength grows with Reynolds number, and the outer pressure field convects at roughly three-quarters of the freestream speed.

Core claim

Synchronized wall-pressure data from the 63-microphone array and hot-wire velocity measurements show that linear coherence between outer-scaled wall pressure and streamwise velocity peaks inside the logarithmic region across the tested Reynolds-number range. Wake-region velocities contribute but remain less dominant. Both the frequency-wavenumber pressure spectrum and the space-time correlations exhibit outer scaling with a convection velocity of 0.75U_infty.

What carries the argument

Microphone array spanning 5δ that spatially filters wall-pressure signals to resolve the large-scale portion of the frequency-wavenumber spectrum without aliasing small-scale energy, allowing direct computation of space-time pressure-velocity correlations.

If this is right

  • Large-scale wall pressure is driven primarily by logarithmic-region velocities rather than wake velocities.
  • Outer-scaled pressure fluctuations convect at a constant 0.75U_infty across the tested range.
  • Linear coherence between large-scale pressure and velocity increases with Reynolds number inside the inner region.
  • Wake contributions to outer pressure remain statistically secondary even as large-scale energy grows.

Where Pith is reading between the lines

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

  • Models that predict surface pressure for drag or noise calculations should weight logarithmic-region turbulence more heavily than wake turbulence.
  • The observed growth of pressure-velocity coupling with Reynolds number suggests that inner-outer interactions strengthen at higher Re_tau and could be tested in larger facilities.
  • These results may help refine low-order representations of wall-pressure spectra used in aeroacoustic predictions.

Load-bearing premise

The microphone array accurately resolves the large-scale pressure spectrum without small-scale aliasing, a property checked only against lower-Reynolds-number simulation data.

What would settle it

Independent measurements at higher Reynolds numbers or with a different spatial-filter design that instead show peak coherence in the wake region rather than the logarithmic region.

Figures

Figures reproduced from arXiv: 2508.19940 by Abdelrahman Hassanein, Rahul Deshpande, Woutijn J. Baars.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) A space-time contour of wall-pressure fluctuations, hih (U075U) tilit(b) Shtiilltt FIG. 1. (a) A space-time contour of wall-pressure fluctuations, [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) A conceptual representation of energy-containing ∆∆ [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) A conceptual representation of energy-containing scales in a zero-pressure gradient (ZPG) turbulent boundary llillRldb(b) Shif hlilid fbf ll FIG. 2. (a) A conceptual representation of energy-containing scales in a zero-pressure gradient (ZPG) turbulent boundary [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Setup for the TBL studies in the Delft University Boundary Layer Facility (DU-BLF, [ [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Wall-normal profile of the streamwise velocity variance, [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a,c) Space-time contour maps of Nu fluctuations at the () FIG. 5. Space-time contour maps of the wall-pressure fluctuations, [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Space-time correlation coefficient, [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (a) Premultiplied frequency and (b) streamwise wavenumber spectra of [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Isocontours of the [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. (a,b) Isocontours (in red) of space-time wall-pressure [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Caption here. Caption here. Caption here. Caption FIG. 10. (a-c) Average convection velocity, Uc,a, estimated fro [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. (a) Premultiplied frequency spectra of the raw measured wall-pressure time series for the four [PITH_FULL_IMAGE:figures/full_fig_p018_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. (a) Streamwise-spanwise and (d) space-time correlation of [PITH_FULL_IMAGE:figures/full_fig_p019_12.png] view at source ↗
read the original abstract

This study shows that the turbulent velocities most strongly correlated with outer-scaled ($\delta$-scaled) wall-pressure fluctuations beneath a zero-pressure-gradient boundary layer reside within the logarithmic region. Even though contributions from the wake region are present, they are found to be statistically less dominant than those from the logarithmic region. The findings are based on bespoke measurements using an array of 63 microphones spanning 5$\delta$ in the streamwise direction (where $\delta$ is the boundary layer thickness), which synchronously captures space-time $p_w$ data alongside streamwise velocity fluctuations ($u$) from a single hotwire probe at the array's downstream end. The array is designed to spatially filter $p_w$ signals to uncover outer-scale contributions, by accurately resolving the large-scale portion of the frequency-wavenumber $p_w$ spectrum while avoiding aliasing of small-scale energy. This design, and its effectiveness in anti-aliasing, is validated against previously published low-Reynolds-number simulation datasets of turbulent boundary layer flow. Present experiments span a friction Reynolds number range of $1400 \lesssim Re_{\tau} \lesssim 5200$, over which the large-scale energy in the boundary layer grows significantly. This growth is reflected in both the frequency-wavenumber $p_w$ spectrum and the space-time $p_w$ correlations, both of which show scaling trends reflective of the large-scale pressure field convecting at an outer-scaled velocity of $0.75U_\infty$, where $U_\infty$ is the freestream velocity. The linear coherence between streamwise velocity and large-scale $p_w$ is directly quantified through space-time $p_w$--$u$ correlations, which show increasing magnitudes across the inner region with rising $Re_{\tau}$.

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 manuscript reports experimental measurements in zero-pressure-gradient turbulent boundary layers (1400 ≲ Re_τ ≲ 5200) using a 63-microphone array spanning 5δ to isolate outer-scaled wall-pressure fluctuations p_w via spatial filtering of the frequency-wavenumber spectrum. Synchronous hot-wire measurements of streamwise velocity u at the array downstream end are used to compute space-time p_w–u correlations and linear coherence, leading to the claim that velocities most strongly correlated with outer-scaled p_w reside in the logarithmic region (with convection velocity ~0.75 U_∞), while wake-region contributions are statistically less dominant.

Significance. If the central observational claim holds after addressing validation concerns, the work provides direct experimental quantification of pressure-velocity coupling for large-scale structures, showing Re_τ-dependent growth of outer-scale energy and coherence trends. This could strengthen empirical support for log-layer dominance in outer-scaled pressure dynamics and aid development of predictive models for wall-pressure spectra in high-Re boundary layers.

major comments (2)
  1. [Methods / array validation] Validation of array design (described in the methods and results sections): the anti-aliasing and spatial-filtering performance that isolates the large-scale portion of the p_w spectrum is demonstrated solely against low-Re_τ DNS datasets. At the experimental upper limit (Re_τ ≈ 5200), where large-scale energy has grown substantially and the frequency-wavenumber spectrum has evolved, the same microphone spacing and processing may permit unresolved small-scale energy to alias into the retained outer-scale band. This directly affects the reliability of the p_w–u coherence peaks used to locate the strongest correlation in the log region.
  2. [Results / coherence analysis] Space-time correlation and coherence analysis (results section): the reported increase in p_w–u coherence magnitudes across the inner region with rising Re_τ is presented without quantitative error bars, uncertainty estimates from finite sampling, or explicit criteria for data exclusion (e.g., outlier rejection or convergence checks). Because the hot-wire is traversed in y to identify the peak-coherence wall-normal location, any residual aliasing or statistical variability could systematically shift the apparent location of strongest correlation.
minor comments (2)
  1. [Abstract / results] The abstract states that the array 'accurately resolves the large-scale portion... while avoiding aliasing,' but the corresponding figure or table showing the filtered spectrum at the highest Re_τ is not cross-referenced in the text.
  2. [Results] Notation for the outer-scaled convection velocity (0.75 U_∞) should be defined consistently with the frequency-wavenumber spectrum plots to avoid ambiguity when comparing across Re_τ.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed and constructive review of our manuscript. We address each major comment below in a point-by-point manner and indicate where revisions will be incorporated.

read point-by-point responses

  1. Referee: [Methods / array validation] Validation of array design (described in the methods and results sections): the anti-aliasing and spatial-filtering performance that isolates the large-scale portion of the p_w spectrum is demonstrated solely against low-Re_τ DNS datasets. At the experimental upper limit (Re_τ ≈ 5200), where large-scale energy has grown substantially and the frequency-wavenumber spectrum has evolved, the same microphone spacing and processing may permit unresolved small-scale energy to alias into the retained outer-scale band. This directly affects the reliability of the p_w–u coherence peaks used to locate the strongest correlation in the log region.

    Authors: We appreciate the referee's concern regarding the array validation. The microphone spacing and spatial-filtering approach were selected to resolve outer-scaled wavenumbers based on the frequency-wavenumber spectra from available low-Re_τ DNS, where the large-scale content is well-characterized. We agree that direct validation at Re_τ ≈ 5200 is not provided and that spectral evolution could introduce some aliasing risk. In the revised manuscript we will add a dedicated discussion paragraph quantifying the expected aliasing contribution using the observed Re_τ-dependent growth of outer-scale energy and the measured convection velocity; this will include a sensitivity estimate showing that any residual small-scale leakage remains below the coherence threshold used for peak identification. New high-Re DNS validation is outside the scope of the present experimental work. revision: partial

  2. Referee: [Results / coherence analysis] Space-time correlation and coherence analysis (results section): the reported increase in p_w–u coherence magnitudes across the inner region with rising Re_τ is presented without quantitative error bars, uncertainty estimates from finite sampling, or explicit criteria for data exclusion (e.g., outlier rejection or convergence checks). Because the hot-wire is traversed in y to identify the peak-coherence wall-normal location, any residual aliasing or statistical variability could systematically shift the apparent location of strongest correlation.

    Authors: We agree that the coherence results would benefit from explicit uncertainty quantification. The space-time correlations were formed from long-time records, yet error bars and convergence criteria were omitted in the original submission. In the revised version we will add uncertainty estimates obtained via block-bootstrapping of the finite ensemble and will state the convergence threshold (e.g., change in coherence < 5 % when doubling record length). We will also document the outlier-rejection rule (coherence values exceeding three standard deviations from the local mean) and confirm that the wall-normal location of maximum coherence remains within the logarithmic region even after these checks. These additions will directly address the possibility of systematic shifts in the reported peak location. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental correlations rest on direct measurements

full rationale

The manuscript is an experimental study that reports direct space-time correlations between outer-scaled wall-pressure fluctuations (measured with a 63-microphone array) and streamwise velocity (measured with a hot-wire). No derivations, fitted parameters renamed as predictions, or self-referential definitions appear in the presented results. The array design is validated against independent low-Re DNS datasets from the literature; this constitutes external benchmarking rather than a load-bearing step that reduces to the present paper's own inputs. The central claim—that peak coherence occurs in the logarithmic region—follows from the measured coherence functions and is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Experimental paper; central claim rests on standard fluid-dynamics measurement assumptions and the zero-pressure-gradient condition rather than new theoretical constructs.

axioms (1)
  • domain assumption The boundary layer is zero-pressure-gradient and canonical.
    Stated explicitly in the abstract as the flow configuration under study.

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