{"id":"e88f5534-70c8-4ff5-b965-dc5f0d1ff6c1","arxiv_id":"2505.23589","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"A threshold-free interface detection method based on uniform momentum zones is applied to DNS of a turbulent boundary layer, yielding consistent interface height statistics and sharper conditional profiles than TKE or vorticity thresholds.","lead":"This paper presents a new way to find the boundary between turbulent and non-turbulent fluid in a turbulent boundary layer, using velocity histograms to pick the interface without a manually chosen threshold. The method works on planar velocity data, so it could be used on experiments, and it gives interface statistics that match earlier studies.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central claim that uedge is the TNTI is unvalidated: the UMZ surface is 0.18δ below the vorticity-based interface, and the observed velocity jump is partly a selection effect of defining the interface as a velocity contour.","rationale":"The reader's weakest assumption concerned the existence of a clean local minimum in the velocity histogram. That is a real robustness issue, especially for low Reynolds numbers, high free-stream turbulence, or noisy PIV data. My concern is different and more immediately load-bearing: even when the histogram minimum exists and uedge is well defined, the paper does not establish that the resulting iso-contour is the turbulent/non-turbulent interface. The paper's own Fig. 5b shows a systematic 0.18δ offset from the vorticity-threshold interface, which is the standard physical definition of the TNTI. Because the interface thickness is only about 0.03δ, this offset is not a small calibration difference; it is a different surface. The conditional velocity jump, which is offered as evidence of mixing-layer-like dynamics, is partly built into the method, since a u=uedge contour will always separate higher-velocity from lower-velocity fluid in the conditional average. This makes the validation circular unless an independent reference interface is used. The method is promising and the sensitivity analysis is useful, but the central identification claim needs a direct test against an enstrophy-based or otherwise independently defined interface. The reader's conditional verdict already requires additional validation, so I do not change the verdict; I would make this specific equivalence check a condition for acceptance.","tokens_in":17173,"tokens_out":8262,"duration_ms":86782,"concrete_test":"On the same DNS fields, construct a reference TNTI from the enstrophy threshold selected at the saddle point of the joint PDF of |ω| and y/δ, as in Section VI, or from a threshold that maximizes the correlation between the resulting rotational mask and the UMZ mask. Compute the Jaccard overlap of the two binary turbulent-region masks and the mean and conditional separation between the two interfaces, stratified by y/δ and local interface orientation. If the overlap is high and the mean separation is much smaller than 0.18δ, the concern is resolved. If the UMZ contour consistently excludes a layer of rotational fluid of thickness about 0.18δ, then the UMZ-TNTI is an outer UMZ edge rather than the TNTI, and the central claim should be downgraded.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section III defines the TNTI as the iso-contour of uedge, the first local minimum below the freestream peak of the in-window velocity PDF. The physical interpretation in Sections IV–VII depends on this contour being the actual rotational/non-rotational boundary, but that correspondence is never independently validated. In Section VI, the UMZ-TNTI is compared with a vorticity-threshold TNTI chosen at the saddle point of the joint PDF of ω+ and y/δ (Fig. 4), and Fig. 5b shows a mean separation of 0.18δ, with the vorticity interface farther from the wall. Since the vorticity threshold is the standard marker of the TNTI in DNS, and since 0.18δ is roughly six interface thicknesses (δω/δ ≈ 0.03 from Fig. 10), the two surfaces cannot both be the same physical interface. The authors interpret the offset as a defect of vorticity thresholds, but no independent evidence, such as an enstrophy-based or Lagrangian identification, is offered to show that the UMZ contour is the correct one. The literature comparison in Table III is also selective: the two vorticity-based studies with higher yi/δ (Jiménez et al. and Eisma et al.) are set aside, leaving a range that brackets but does not verify the present values. Finally, the sharp velocity jump reported in Section VII A is partly a selection effect: defining the interface as a u=uedge iso-contour guarantees that the conditionally averaged streamwise velocity changes across it. The magnitude and shape of the jump are informative, but its existence cannot serve as independent confirmation that the detected surface is the TNTI. Thus the central claim rests on an unvalidated identification step.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a new way to identify the turbulent/non-turbulent interface (TNTI) in a zero-pressure-gradient turbulent boundary layer using the uniform momentum zone (UMZ) concept. For each spanwise plane and each sliding window of size 1δ × 2δ, the streamwise velocity histogram is used to find the local minimum uedge adjacent to the free-stream peak, and the iso-contour u = uedge is declared the TNTI. The method is applied to the DNS data of Sillero et al. at Reτ ≈ 1,000–2,000. The paper reports geometric properties (interface-height PDF, intermittency), a sensitivity study of the streamwise window length, comparisons with TKE- and vorticity-threshold interfaces, and conditionally averaged mean velocity, Reynolds stress, and vorticity profiles relative to the detected interface. The central claims are that the method is threshold-free, scales with δ, agrees with non-vorticity-based experiments, and produces sharper conditional velocity and vorticity profiles than threshold-based methods.","tokens_in":17609,"tokens_out":3725,"duration_ms":38357,"significance":"If the method is valid, it is attractive because it uses only planar streamwise velocity and could be applied directly to experimental PIV data, avoiding the need to choose threshold levels that are Reynolds-number dependent. The paper is grounded in a well-established DNS dataset, and the demonstration that the detected interface height is only weakly sensitive to the streamwise window size is a useful robustness result. However, the central identification claim is not yet independently validated: the detected UMZ contour is on average 0.18δ below a standard vorticity-based TNTI, and the reported velocity jump across the interface is partly a selection effect of defining the interface as a streamwise-velocity iso-contour. The paper therefore presents a promising method whose physical interpretation as the TNTI requires additional evidence before its statistical results can be taken as definitive.","major_comments":[{"comment":"The difference between the UMZ-TNTI and the vorticity-threshold TNTI is 0.18δ on average, which is about six times the interface thickness δω/δ reported in Fig. 10. Because the vorticity threshold is the standard marker of the rotational/non-rotational boundary in DNS, this offset means that the two surfaces cannot both be the same physical interface. The paper interprets the offset as a deficiency of vorticity thresholds, but no independent identification (e.g., based on enstrophy, Lagrangian trajectories, or a passive scalar) is provided to show that the UMZ contour is the correct TNTI. This is load-bearing because all conditional statistics in Section VII are conditioned on this contour.","section":"Section VI, Fig. 5"},{"comment":"The sharp velocity jump D[U] is to a substantial degree a selection effect: because the interface is defined as the u = uedge iso-contour, the conditionally averaged streamwise velocity must change across it. The magnitude and shape of the jump are informative, but the paper also uses this jump as evidence that the UMZ method 'fits better with the conceptual model of the TNTI' (Section VII A). That reasoning is circular. The authors should quantify what velocity jump would be obtained for an arbitrary contour with the same height distribution, or provide an independent marker of the turbulent/non-turbulent boundary, before using D[U] as evidence for the correctness of the method.","section":"Section VII A, Figs. 6–8"},{"comment":"Equation (7) is not a parameter-free prediction: a1 and a2 are the linear-fit parameters obtained in Fig. 9. The statement in the text that Eq. (7) 'shows good agreement with the data points, as expected' is therefore a fit to the data rather than an independent validation of the δω/δ ~ 1/(a1 Reτ + a2) scaling. The collapse claim based on this equation should be reframed accordingly, and the fit parameters and their uncertainties should be reported.","section":"Section VII, Eqs. (7), Figs. 9–10"},{"comment":"The paper describes the method as 'threshold-free,' but it actually relies on several hand-chosen rules: the sliding-window height of 2δ, the definition of the interface height as the lower envelope of the interface contour, the removal of closed pockets, and the histogram bin width and local-minimum detection procedure. The sensitivity analysis in Section V varies only the streamwise window length Lx. Since the claimed advantage over TKE- and vorticity-based methods is the absence of arbitrary thresholds, the authors should demonstrate that the results are insensitive to the histogram bin width, the window height, and the pocket-removal rule, or explicitly state these as parameters of the method.","section":"Section III and Section V"},{"comment":"The method assumes that, in every sliding window, the streamwise velocity histogram has a clean local minimum between the free-stream peak and the turbulent region. This assumption is demonstrated only for the present DNS at Reτ ≈ 1,000–2,000. At lower Reynolds numbers, in flows with significant free-stream turbulence, or with experimental noise, the free-stream peak may merge with the turbulent distribution and uedge may become ill-defined or jump discontinuously. The paper should either demonstrate robustness of the local-minimum criterion across a wider parameter range or clearly state this limitation as a condition of applicability.","section":"Section III"}],"minor_comments":[{"comment":"The comparison with previous work excludes the two vorticity-based studies (Jiménez et al. and Eisma et al.) when concluding that the measured yi/δ is consistent with the literature. Since the paper's main discrepancy is precisely with vorticity-based detection, the table should include those points in the comparison and discuss what the scatter implies for the validation of the method.","section":"Table III"},{"comment":"The caption of Fig. 10 appears to be a copy of the caption of Fig. 9; it describes the maximum velocity gradient, while the plotted quantity is δω/δ. This should be corrected.","section":"Fig. 10"},{"comment":"The notation in Eq. (5) is inconsistent with the rest of the paper: U and V are used for mean quantities, but the equation is presented as a conditional balance. Please clarify whether these are ensemble-mean or conditionally averaged quantities and define all terms.","section":"Section VII A, Eq. (5)"},{"comment":"The bin width used to construct the velocity histogram is not specified. Since uedge is defined by a local minimum of this histogram, the bin width is a parameter of the method and should be reported.","section":"Section III and Fig. 1"},{"comment":"The statement that 'the intermittency profiles exhibit negligible variation across Reynolds numbers' should be supported by quantitative measures, since the profiles in Fig. 3(a) are shown only for station 1 and the text says stations 2 and 3 follow the same trend.","section":"Section V"}],"recommendation":"major_revision","confidential_remarks":"The paper introduces a practically attractive detection scheme and uses a high-quality DNS dataset, but the referee report identifies two load-bearing issues: the lack of independent validation of the UMZ contour as the true TNTI, and the partly circular use of the velocity jump as evidence for the method. These issues can be addressed with additional analyses rather than requiring a new dataset, so major revision is appropriate. I would also encourage the editor to request that the authors report histogram-binning parameters and fit uncertainties, as these are needed for reproducibility."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should read this one. The core idea—using the first local minimum next to the free-stream peak in a sliding-window velocity histogram as the TNTI—is genuinely new and worth taking seriously. It is threshold-free, works on planar streamwise velocity data, and the authors demonstrate it on a well-verified DNS dataset at three Reynolds numbers. The window-size sensitivity analysis is a nice practical touch, and the conditional statistics are carefully presented. The claim that the method gives sharper velocity and vorticity gradients than TKE- or vorticity-threshold methods is believable, partly because the definition builds that sharpness in.\n\nThe soft spots are real but should not kill the paper. The identification step is never independently validated: the UMZ surface sits 0.18δ below the vorticity-based interface, which is roughly six interface thicknesses, and the paper offers no independent marker (enstrophy, Lagrangian tracking, scalar) to show which surface is the true TNTI. The velocity jump across the interface is partly a selection effect—if you define the interface as a u = uedge contour, you guarantee a streamwise velocity change across it. The magnitudes and shapes are still informative, but they cannot serve as confirmation that the detected surface is the TNTI. The scaling in Eq. (7) is a fit with fitted constants a1, a2; calling it a collapse is fine, but it is not a prediction. There are also no error bars on the conditional statistics, and the method's robustness outside Reτ = 1000–2000, or with noisy PIV data, is unshown. The comparison with prior work is a bit selective, though the discussion of why vorticity thresholds are problematic is fair.\n\nThat said, the paper is clearly reasoned, the authors know the literature, and the method is a plausible step forward for entrainment and mixing-layer studies. It deserves peer review, but it needs revision: code or detailed algorithmic pseudocode, uncertainty quantification, an independent check of the interface position (even a simple enstrophy-based comparison would help), and a toned-down claim about experimental applicability until PIV validation appears. I would bring it to a reading group and would cite it if they fix the validation gap. Send it to referees, but expect them to push for the missing evidence.","headline":"A genuinely new threshold-free TNTI detector with real promise, but the paper has not yet shown that its interface is the actual turbulent/non-turbulent boundary rather than a convenient velocity contour.","tokens_in":18093,"tokens_out":886,"would_cite":true,"duration_ms":10267,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The turbulent/non-turbulent interface of a boundary layer can be identified as the velocity contour at the first histogram valley next to the free-stream peak, with no threshold required.","keywords":["turbulent/non-turbulent interface","uniform momentum zones","zero-pressure-gradient turbulent boundary layer","threshold-free detection","conditional statistics","intermittency","direct numerical simulation","particle image velocimetry"],"falsifier":"Take a ZPG-TBL DNS or experiment below $Re_\\tau \\approx 1{,}000$ or with elevated free-stream turbulence and compute the sliding-window histogram; if the first local minimum beside the free-stream peak is absent, or the resulting $u_{edge}$ contour jumps discontinuously while a vorticity- or TKE-based interface remains smooth, the central claim fails for that regime.","tokens_in":16978,"feed_emoji":"🌊","tokens_out":5908,"duration_ms":49970,"temperature":0.7,"pith_summary":"This paper tries to establish that the turbulent/non-turbulent interface in a zero-pressure-gradient turbulent boundary layer can be located without arbitrary thresholds: it is the streamwise-velocity iso-contour whose value is the first local minimum beside the free-stream peak in the local velocity histogram. That would matter because existing TKE- and vorticity-based detections rely on user-chosen thresholds that vary with Reynolds number and dataset, complicating comparisons across simulations and experiments. Using DNS at Reynolds numbers from about 1,045 to 1,965, the authors show the detected interface height scales with the local boundary layer thickness, gives error-function-like intermittency profiles, and yields conditional velocity and vorticity profiles with sharper gradients than TKE-based interfaces. If the method holds, it gives a consistent, experiment-friendly way to identify the interface from planar velocity data alone.","feed_headline":"Turbulent interface found by a velocity histogram valley","feed_subtitle":"A UMZ-based method pins the interface to a velocity-histogram valley, needing only planar PIV data and no tuned threshold.","key_machinery":"The carrying object is the uniform momentum zone (UMZ) concept: the boundary layer is viewed as a stack of nearly uniform-momentum layers separated by thin shear layers, so the streamwise velocity histogram inside a sliding window has peaks for each zone and valleys at the edges between them. The first valley on the free-stream side of the histogram defines the edge velocity $u_{edge}$, and the iso-contour at $u_{edge}$ is declared the turbulent/non-turbulent interface. This replaces an externally set threshold with an internally defined feature of the velocity PDF, which is why the method is called threshold-free; the derived vorticity thickness $\\delta_\\omega = D[\\tilde U]/(\\mathrm{d}\\tilde U/\\mathrm{d}\\tilde y)_{\\max}$ then supplies the length scale that collapses the conditional statistics.","core_discovery":"The central claim is that the turbulent/non-turbulent interface in a ZPG-TBL is a uniform-momentum-zone edge: the iso-contour of the streamwise velocity $u_{edge}$, defined as the first local minimum adjacent to the free-stream peak in the velocity histogram of a sliding $1\\delta \\times 2\\delta$ window. Removing closed pocket boundaries and taking the lower envelope as the interface height, the method detects an interface whose mean height $y_i/\\delta \\approx 0.74\\text{--}0.77$ and standard deviation $\\sigma(y_i)/\\delta \\approx 0.16\\text{--}0.17$ across $Re_\\tau \\approx 1{,}045\\text{--}1{,}965$, matching non-vorticity-based measurements from the literature. The interface scales with $\\delta$, is nearly insensitive to streamwise window length between $0.25\\delta$ and $3\\delta$, and produces conditional mean-velocity profiles with a sharp mixing-layer-like jump; the jump is about 50% larger than that from a local-TKE threshold method, while a vorticity-threshold interface lies on average $0.18\\delta$ farther from the wall. When the conditional profiles are normalized by the interface velocity jump $D[\\tilde U]$ and the vorticity thickness $\\delta_\\omega$, mean velocity and vorticity profiles collapse across Reynolds numbers.","pith_inferences":["The same histogram-valley logic could be extended to other shear flows, such as jets, wakes, and mixing layers, wherever a free-stream peak is identifiable, potentially giving a unified threshold-free TNTI definition.","The method's robustness has a testable boundary: at lower Reynolds numbers, higher free-stream turbulence, or noisy experimental data, the free-stream peak may merge with the turbulent distribution, making $u_{edge}$ ill-defined; the paper demonstrates the minimum only for $Re_\\tau \\approx 1{,}000\\text{--}2{,}000$.","Because the $u_{edge}$ distribution is negatively skewed while interface heights are nearly Gaussian, the velocity-valley-to-interface mapping is smooth in this dataset; examining that mapping under measurement noise would clarify the practical resolution limits of the method."],"forward_implications":["TNTI detection becomes threshold-free and Reynolds-number-consistent across $Re_\\tau \\approx 1{,}045\\text{--}1{,}965$, with mean interface height $y_i/\\delta \\approx 0.74\\text{--}0.77$ and standard deviation $\\sigma(y_i)/\\delta \\approx 0.16\\text{--}0.17$.","Because only planar streamwise velocity is required, the method transfers directly to experimental PIV without tuning a threshold or relying on resolved vorticity.","The UMZ-TNTI interface gives a sharper velocity jump across the interface: $D[\\tilde U]/u_\\tau$ is about 50% larger than the local-TKE interface, and the maximum gradient $\\delta/u_\\tau\\,\\mathrm{d}\\tilde U/\\mathrm{d}\\tilde y|_{\\max}$ grows linearly with $Re_\\tau$.","Conditional mean and fluctuating vorticity profiles collapse better across Reynolds numbers when scaled by the interface velocity jump and vorticity thickness than for TKE-based interfaces.","Reynolds stresses respond anisotropically across the interface: streamwise fluctuations change most, wall-normal moderately, and spanwise least."],"supporting_citations":[{"why":"Supplies the UMZ identification method based on streamwise velocity PDFs that the $u_{edge}$ valley detection builds on.","marker":"[15]"},{"why":"First identified uniform momentum zones in a turbulent boundary layer, the concept the method exploits.","marker":"[14]"},{"why":"Showed velocity jumps exist across UMZ boundaries and proposed scaling window sizes with $\\delta$, the basis for the sliding-window design.","marker":"[21]"},{"why":"Provides the local-TKE threshold-based TNTI detection used as the main comparison baseline.","marker":"[13]"},{"why":"Established the vorticity-threshold saddle-point criterion and the analysis of turbulent/non-turbulent pockets; supplies the vorticity comparison.","marker":"[9]"},{"why":"Supplies the DNS dataset of the ZPG-TBL at $Re_\\tau \\approx 1{,}000\\text{--}2{,}000$ used throughout.","marker":"[22]"},{"why":"Introduced intermittency profiles and the laminar superlayer concept, against which interface statistics are benchmarked.","marker":"[2]"},{"why":"Documented the velocity jump across the TNTI in wakes, the jump the UMZ-TNTI method reproduces more sharply.","marker":"[3]"}],"fun_headline_variants":["Velocity histogram valley pins turbulent interface","Uniform momentum zones find boundary layer edge","Threshold-free method spots turbulent interface","Histogram-based interface detection for ZPG boundary layers","UMZ concept yields mixing-layer-like turbulent edge"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that in every sliding window the streamwise velocity histogram has a clear local minimum between the free-stream peak and the turbulent region, and that the corresponding iso-velocity contour is the turbulent/non-turbulent interface.","fun_headline_variants_meta":{"raw":{"variants":["Velocity histogram valley pins turbulent interface","Uniform momentum zones find boundary layer edge","Threshold-free method spots turbulent interface","Histogram-based interface detection for ZPG boundary layers","UMZ concept yields mixing-layer-like turbulent edge"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000438,"raw_usage":{"total_tokens":2323,"prompt_tokens":1140,"completion_tokens":1183,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":756,"completion_tokens_details":{"reasoning_tokens":1119}},"tokens_in":756,"tokens_out":1183,"duration_ms":9461,"temperature":1.0,"reasoning_tokens":1119,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T12:42:29.200446+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a ZPG-TBL DNS or experiment below $Re_\\tau \\approx 1{,}000$ or with elevated free-stream turbulence and compute the sliding-window histogram; if the first local minimum beside the free-stream peak is absent, or the resulting $u_{edge}$ contour jumps discontinuously while a vorticity- or TKE-based interface remains smooth, the central claim fails for that regime.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the UMZ identification method based on streamwise velocity PDFs that the $u_{edge}$ valley detection builds on."},{"cited_title":"14a shows that ˜w′w′ follows a similar trend above, within, and below the TNTI, without sharp changes","cited_arxiv_id":null,"evidence_quote":"First identified uniform momentum zones in a turbulent boundary layer, the concept the method exploits."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Showed velocity jumps exist across UMZ boundaries and proposed scaling window sizes with $\\delta$, the basis for the sliding-window design."},{"cited_title":"Chauhan, J","cited_arxiv_id":null,"evidence_quote":"Provides the local-TKE threshold-based TNTI detection used as the main comparison baseline."},{"cited_title":"Borrell and J","cited_arxiv_id":null,"evidence_quote":"Established the vorticity-threshold saddle-point criterion and the analysis of turbulent/non-turbulent pockets; supplies the vorticity comparison."},{"cited_title":"Thavamani, C","cited_arxiv_id":null,"evidence_quote":"Supplies the DNS dataset of the ZPG-TBL at $Re_\\tau \\approx 1{,}000\\text{--}2{,}000$ used throughout."},{"cited_title":"Corrsin and A","cited_arxiv_id":null,"evidence_quote":"Introduced intermittency profiles and the laminar superlayer concept, against which interface statistics are benchmarked."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Documented the velocity jump across the TNTI in wakes, the jump the UMZ-TNTI method reproduces more sharply."}],"review_version":1}