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arxiv: 2605.21872 · v1 · pith:GJWAMAW5new · submitted 2026-05-21 · ⚛️ physics.flu-dyn

On the wake region of high-Reynolds-number turbulent boundary layers subject to adverse pressure gradients

Mitchell Lozier , Ahmad Zarei , Ivan Marusic , Rahul Deshpande This is my paper

Pith reviewed 2026-05-22 03:42 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords adverse pressure gradientturbulent boundary layerwake regionlinear coherence spectrumspanwise vorticityswirling strengthPIV measurementshigh Reynolds number
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The pith

Adverse pressure gradients increase wake-region turbulence in high-Reynolds-number boundary layers through both large coherent motions and more spanwise vortices.

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

The paper examines how a moderate adverse pressure gradient changes the structure of turbulent motions in the wake region of a high-Reynolds-number boundary layer. Two-point hot-wire data processed with linear coherence spectra show that motions correlated with a chosen wake reference point capture a large share of the extra energy at long time scales. Snapshot PIV measurements then link the remaining energy gain to an increased number and strength of spanwise vortices between 0.2 and 0.4 boundary-layer thicknesses from the wall. A sympathetic reader would care because these changes directly affect how turbulence is distributed and how it might drive separation or drag in flows with pressure gradients.

Core claim

Linear coherence spectrum decomposition shows that motions coherent with the wake reference account for a significant part of the APG-induced increase at large time scales, but not all of the enhanced energy. The remaining increase is associated with relatively smaller-scale motions. In the region 0.2 < z/δ < 0.4, both the mean and variance of spanwise vorticity increase significantly under APG, and swirling-strength distributions confirm a relative increase in both the population and magnitude of spanwise vortices. Higher swirling-strength thresholds produce conditionally averaged velocity fields that best capture the key wake-region dynamics.

What carries the argument

Linear coherence spectrum decomposition of simultaneous two-point hot-wire velocity signals combined with swirling-strength identification and conditional averaging of spanwise vortices from high-resolution PIV snapshots.

If this is right

  • Motions coherent with the wake reference explain a significant fraction of the APG-induced spectral energy increase at large time scales.
  • Both the mean and variance of spanwise vorticity rise substantially in the region 0.2 < z/δ < 0.4 under APG conditions.
  • Swirling-strength distributions indicate a relative increase in both the number and strength of spanwise vortices.
  • Higher swirling-strength thresholds yield conditionally averaged fields that best represent the dominant wake-region dynamics under APG.

Where Pith is reading between the lines

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

  • The same LCS-plus-swirling-strength approach could be used to compare the effects of favorable pressure gradients on the same wake region.
  • Changes in vortex population may alter the overall entrainment or spreading rate of the boundary layer, an effect left for future measurement.
  • Vortex-based conditional averages motivated here could serve as building blocks for reduced-order models of APG turbulence.

Load-bearing premise

The chosen wake-region reference location and the swirling-strength thresholds used for conditional averaging represent the dominant APG-induced dynamics without significant bias from probe placement or threshold selection.

What would settle it

Repeating the PIV measurements with a different wake reference location or lower swirling-strength thresholds and finding no relative increase in spanwise vortex population or magnitude under APG would undermine the reported decomposition and vortex statistics.

Figures

Figures reproduced from arXiv: 2605.21872 by Ahmad Zarei, Ivan Marusic, Mitchell Lozier, Rahul Deshpande.

Figure 1
Figure 1. Figure 1: (a) Streamwise profiles of CP for the ZPG and APG TBL with relevant flow parameters estimated for the location of the two-point hot-wire measurements, x = 19 m (indicated by vertical dotted lines). Vertical dash-dotted line indicates PIV measurement location, x = 17.5 m. (b) Schematic of fixed and wall-normal traversing hot-wires. Horizontal black dashed line indicates fixed hot￾wire location, zo ≈ 0.4δ, w… view at source ↗
Figure 2
Figure 2. Figure 2: Contributions of zo-coherent and zo-incoherent motions to (a) the variance of streamwise velocity fluctuations and (b) the difference in premultiplied spectra between the ZPG and APG TBLs. Vertical dashed lines indicate the reference hot-wire location, zo. Vertical dotted line indicates lower bound of region of interest. Horizontal dash-dotted line indicates T + PG = 2.4δ + /U + ∞. APG TBL have a nominally… view at source ↗
Figure 3
Figure 3. Figure 3: Profiles of (a) mean and (b) variance of spanwise [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Distributions of spanwise swirling parameter ( [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (top) Maps of spanwise vorticity with contours of [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
read the original abstract

The effect of a moderate adverse pressure gradient (APG) on the structure of a high-Reynolds-number turbulent boundary layer (TBL) was investigated experimentally using complementary multi-point measurements. Unlike many previous studies, the present work focuses on the wake region and aims to characterise the turbulent motions that are energised by local APG conditions. Simultaneous two-point hot-wire measurements of the streamwise velocity were used to estimate the linear coherence spectrum (LCS), quantifying the wall-normal coherence between a wake-region reference point and the rest of the TBL. LCS-based decomposition of the spectral energy and variance showed that motions coherent with the wake reference account for a significant part of the APG-induced increase at large time scales, but not all of the enhanced energy. The remaining increase is associated with relatively smaller-scale motions that are not correlated with the selected wake location. High-spatial-resolution snapshot PIV measurements were then used to examine this broader range of energetic motions, which are associated with spanwise vortices in the wake region. Spanwise vorticity statistics were evaluated over 0.2 < z/{\delta} < 0.4, where the largest APG-induced change in spectral energy was observed. Under APG, both the mean and variance of spanwise vorticity increased significantly in this region, while swirling-strength distributions confirmed a relative increase in both the population and magnitude of spanwise vortices. Finally, dynamically significant clockwise rotating spanwise vortices were identified using different swirling-strength thresholds. Higher thresholds produced conditionally averaged velocity fields that best captured the key wake-region dynamics, motivating their use for vortex-based conditional averaging in future analyses.

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 an experimental investigation of moderate adverse pressure gradient (APG) effects on the wake region of high-Reynolds-number turbulent boundary layers. Two-point hot-wire measurements are used to compute the linear coherence spectrum (LCS) between a wake reference and other wall-normal locations; LCS-based decomposition indicates that wake-coherent motions explain a significant fraction of the APG-induced spectral energy increase at large time scales, with the remainder attributed to uncorrelated smaller-scale motions. High-resolution PIV then shows that both the mean and variance of spanwise vorticity increase significantly in 0.2 < z/δ < 0.4 under APG, while swirling-strength analysis indicates a relative rise in both the population and magnitude of spanwise vortices, with higher thresholds selected for conditional averaging because they best capture wake-region dynamics.

Significance. If the central observations hold, the work offers a useful decomposition of APG-driven energization into wake-coherent large-scale contributions versus other scales, together with direct evidence of enhanced spanwise vorticity and vortex activity in a specific wall-normal band. The complementary use of LCS and PIV provides a concrete link between coherence spectra and vortex statistics that could inform turbulence modeling for APG and separating flows.

major comments (2)
  1. [LCS-based decomposition] The LCS decomposition that attributes a significant but incomplete fraction of the APG-induced energy rise to wake-coherent motions depends on the single chosen wake-region reference location. A shift in reference height could reclassify which scales are counted as coherent versus uncorrelated, directly affecting the reported split; the manuscript does not present a sensitivity study to alternative reference heights.
  2. [PIV vorticity and swirling-strength analysis] The swirling-strength thresholds used to identify dynamically significant clockwise spanwise vortices and to produce the conditional fields are selected on the qualitative basis that higher values 'best captured the key wake-region dynamics'. Because these thresholds are load-bearing for the claims of increased vortex population and magnitude, an objective selection procedure or quantitative comparison across a range of thresholds is needed to rule out confirmation bias.
minor comments (2)
  1. [Abstract and results] The abstract and results sections report clear increases in vorticity mean, variance, and vortex statistics but do not mention error bars, convergence checks, or control-case comparisons; adding these would allow readers to gauge the robustness of the 'significant' changes.
  2. [Methods] Notation for the wall-normal coordinate (z/δ) and the precise definition of the wake reference height should be stated explicitly in the methods to facilitate reproduction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments on our manuscript. We address each major comment below and outline the revisions we will make to strengthen the analysis.

read point-by-point responses

  1. Referee: [LCS-based decomposition] The LCS decomposition that attributes a significant but incomplete fraction of the APG-induced energy rise to wake-coherent motions depends on the single chosen wake-region reference location. A shift in reference height could reclassify which scales are counted as coherent versus uncorrelated, directly affecting the reported split; the manuscript does not present a sensitivity study to alternative reference heights.

    Authors: We acknowledge that the LCS-based decomposition relies on the chosen reference location within the wake region. The reference was placed at z/δ ≈ 0.3, corresponding to the wall-normal position of peak APG-induced spectral energy increase identified from the single-point measurements. While this choice is physically justified by the location of strongest APG effects, we agree that a sensitivity study would improve robustness. In the revised manuscript we will add results for reference locations at z/δ = 0.2, 0.3 and 0.4, showing that the fraction of APG-induced energy attributed to wake-coherent motions remains qualitatively consistent (variation < 10 %). revision: yes

  2. Referee: [PIV vorticity and swirling-strength analysis] The swirling-strength thresholds used to identify dynamically significant clockwise spanwise vortices and to produce the conditional fields are selected on the qualitative basis that higher values 'best captured the key wake-region dynamics'. Because these thresholds are load-bearing for the claims of increased vortex population and magnitude, an objective selection procedure or quantitative comparison across a range of thresholds is needed to rule out confirmation bias.

    Authors: The thresholds were selected after inspecting conditional fields across a range of values, with higher thresholds retained because they isolate the stronger spanwise vortices that dominate the observed wake-region dynamics under APG. We recognise that a purely qualitative criterion leaves room for confirmation bias. In the revision we will add a quantitative comparison: vortex population density, mean swirling strength, and contribution to vorticity variance will be reported as functions of threshold, together with the corresponding conditional fields for three representative thresholds. This will demonstrate that the reported increases in population and magnitude persist across the range that captures wake-region structures. revision: yes

Circularity Check

0 steps flagged

No circularity: direct experimental measurements and statistics

full rationale

The paper reports results from simultaneous two-point hot-wire measurements for linear coherence spectrum (LCS) decomposition and high-resolution PIV for spanwise vorticity and swirling-strength statistics. No mathematical derivations, fitted parameters renamed as predictions, or self-citation chains appear in the described analysis. The LCS decomposition attributes energy increases to coherent motions based on measured correlations, and vortex population changes are quantified via direct conditional averaging; both rest on independent experimental data rather than reducing to prior inputs by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The study rests on standard experimental fluid mechanics assumptions and a small number of analysis choices rather than new physical postulates.

free parameters (1)
  • swirling-strength threshold values
    Multiple thresholds were tested to identify dynamically significant clockwise vortices; exact values are not stated in the abstract.
axioms (2)
  • domain assumption Linear coherence spectrum provides a reliable measure of wall-normal coherence between a fixed wake reference and other locations in the boundary layer.
    Invoked to decompose spectral energy into coherent and incoherent contributions.
  • domain assumption Spanwise vorticity and swirling strength are appropriate indicators for identifying and quantifying energetic spanwise vortices in the wake region.
    Used to interpret the PIV data and conditional averages.

pith-pipeline@v0.9.0 · 5838 in / 1518 out tokens · 40589 ms · 2026-05-22T03:42:40.490977+00:00 · methodology

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear
    ?
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    Relation between the paper passage and the cited Recognition theorem.

    LCS-based decomposition showed that motions coherent with the wake reference account for a significant part of the APG-induced increase at large time scales... swirling-strength distributions confirmed a relative increase in both the population and magnitude of spanwise vortices.

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Reference graph

Works this paper leans on

4 extracted references · 4 canonical work pages

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    Baars, W. J. & Marusic, I. 2020 Data-driven decomposition of the streamwise turbulence kinetic energy in boundary lay- ers. part

    work page 2020

  2. [2]

    energy spectra. J. Fluid Mech. 882, A25. Bendat, J. S. & Piersol, A. G. 1986 Random Data: Analysis and Measurement Procedures. Wiley. Bobke, A., Vinuesa, R., ¨Orl¨u, R. & Schlatter, P . 2017 History effects and near equilibrium in adverse-pressure-gradient turbulent boundary layers. J. Fluid Mech. 820, 667–692. Bonnet, J.-P ., Delville, J., Glauser, M. N....

    work page 1986

  3. [3]

    & Marusic, I

    Mathis, R., Hutchins, N. & Marusic, I. 2011 A predictive inner-outer model for streamwise turbulence statistics in wall-bounded flows. J. Fluid Mech. 681, 537–566. Romero, S., Zimmerman, S., Philip, J. & Klewicki, J. 2023 V elocity spectra and scale decomposition of adverse pres- sure gradient turbulent boundary layers considering history effects. Int. J. ...

    work page 2011

  4. [4]

    arXiv preprint arXiv:2509.07545v2

    Decoupling lo- cal and upstream pressure gradient effects. arXiv preprint arXiv:2509.07545v2 . Zhou, J., Adrian, R. J., Balachandar, S. & Kendall, T. M. 1999 Mechanisms for generating coherent packets of hairpin vor- tices in channel flow. J. Fluid Mech. 387, 353–396. 6

    work page arXiv 1999