{"id":"ac712a50-4bfe-4d40-bc51-ecefdc5c0cfb","arxiv_id":"2507.20043","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"A Liutex-based SGS eddy-viscosity model is shown to vanish near walls, follow a -10/3 spectral law, and predict periodic-hill reattachment within 6.9% error, matching or exceeding WALE.","lead":"This paper tests a 2022 subgrid-scale model that uses the rotational part of the velocity gradient to compute eddy viscosity, in turbulent channel flow and periodic hill flow. It reports that the model predicts separation points and near-wall Reynolds stresses at least as well as the WALE model, with better accuracy than Smagorinsky variants.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The paper states two mutually inconsistent near-wall scalings for the same model in §3.1 ('proportional to y' vs. 'proportional to y^2'); the abstract's O(y) claim is unsupported until the slope is measured and the contradiction resolved.","rationale":"The reader's weakest_assumption focuses on the fixed coefficient C_s=0.17, but the paper also contains a direct internal contradiction about the near-wall scaling of ν_t in the same section, which I consider more load-bearing: it makes the abstract's O(y) claim formally unsupported. The coefficient issue would require a sensitivity sweep to quantify, and the paper already concedes coefficients may need adjustment; it is a legitimate but secondary concern. The reader's rationale does mention the scaling contradiction, so my agreement is partial rather than full. A conditional verdict is still appropriate: the paper should be accepted only after the scaling slope is reported consistently and, ideally, a C_s sensitivity test is added. My finding therefore does not change the reader's conditional recommendation.","tokens_in":11738,"tokens_out":7601,"duration_ms":93691,"concrete_test":"From the G3 channel-flow run (or an independent reproduction with the same grid), extract the first 8-10 wall-normal values of ν_t/ν at y^+ in [0.5,5], and fit log(ν_t/ν) versus log(y^+); report the slope with uncertainty. If slope≈1, delete the 'proportional to y^2' sentence in §3.1; if slope≈2, change the abstract and Conclusion (2) to O(y^2); if neither, the scaling claim is unsupported. As an independent check, compute |R| from Eq. (9) on the Moser-Kim-Mansour Re_tau=395 DNS field and repeat the same fit.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing claim is the near-wall asymptotic behavior of the Liutex-based eddy viscosity. In §3.1, the paragraph describing Fig. 7 first states 'All eddy viscosities obtained from the present model approach zero near the wall, with an asymptotic trend proportional to y,' and then, a few sentences later, states 'The present model exhibits a vanishing tendency proportional to y^2, which is less accurate than that of WALE.' The abstract and Conclusion (2) repeat the O(y) version. These two statements cannot both describe the same G3 channel-flow result. Since no derivation of the scaling is given and no data or code are released, the reader cannot identify which statement is a typo and which is the actual behavior. This matters because 'exhibits an asymptotic behavior of O(y) near the walls' is an advertised headline result and is used to argue that the model is physically consistent. If the true slope is 2, the abstract and conclusions are wrong; if the true slope is 1, the §3.1 description is wrong. The coefficient-C_s issue raised by the reader is real but secondary: it affects magnitude and ranking, whereas this contradiction affects the correctness of the central physical statement and must be settled first.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper evaluates the Liutex-based subgrid-scale stress model of Ding et al. (2022) in two canonical flows: fully developed turbulent channel flow at Re_tau = 395 and periodic hill flow at Re = 10595. The authors employ OpenFOAM on three successively refined grids for each case, compare against Smagorinsky, Smagorinsky with Van Driest damping, and WALE, and validate against DNS (Moser et al., Krank et al.) and experiments (Rapp, Breuer). The central claims are: (i) the eddy viscosity from the Liutex model vanishes near the wall with an asymptotic behavior O(y); (ii) the power spectral density of |R| follows a -10/3 law in the dissipation range; (iii) in periodic hill flow the model predicts the reattachment point with 6.9% error, matching WALE and beating Smagorinsky variants; and (iv) it gives more accurate near-wall Reynolds stress than WALE at separation-core locations. The manuscript reports grid convergence and reasonable agreement with reference data, but it contains an unresolved internal contradiction about the near-wall scaling order that affects the headline physical-consistency argument.","tokens_in":12002,"tokens_out":4030,"duration_ms":47779,"significance":"If the near-wall scaling and separation predictions are correct, the Liutex-based SGS model offers a physically motivated eddy-viscosity formulation with performance comparable to WALE and potentially better near-wall Reynolds-stress behavior in separated flows. The paper's strengths include systematic grid-convergence studies on three grids per case, validation against independent DNS and experimental data, and direct comparison with established SGS models. However, the central near-wall scaling claim is stated inconsistently (O(y) in the Abstract and Conclusion vs. O(y^2) in Section 3.1), and the model coefficient is inherited from Lilly's Smagorinsky value without sensitivity analysis. These issues must be resolved before the physical-consistency and superiority claims can be accepted. The contribution is of interest to the LES and turbulence-modeling community, but the current presentation does not yet support the advertised conclusions.","major_comments":[{"comment":"The paper contains two mutually inconsistent statements about the near-wall scaling of the Liutex-based eddy viscosity. The paragraph describing Fig. 7 first states that 'All eddy viscosities obtained from the present model approach zero near the wall, with an asymptotic trend proportional to y', but a few sentences later states that 'The present model exhibits a vanishing tendency proportional to y^2'. The Abstract and Conclusion (2) repeat the O(y) version. Since no analytic derivation or measured slope (e.g., a log-log fit of nu_t/nu vs y+) is provided, the reader cannot determine which statement is correct. Furthermore, the sentence preceding Fig. 7 asserts that the eddy viscosity must grow at least as the cubic power of y^+, which would make either O(y) or O(y^2) physically inaccurate relative to that criterion. This is load-bearing because the abstract advertises 'an asymptotic behavior of O(y) near the walls' as a central physical-consistency result. Please measure and report the actual scaling exponent, correct the Abstract/Conclusion or Section 3.1 accordingly, and clarify whether the scaling is derived or purely observational.","section":"§3.1, Fig. 7; Abstract; Conclusion (2)"},{"comment":"The model coefficient C_s is fixed at 0.17 for both channel flow and periodic hill flow, taken directly from Lilly's inertial-range value for the Smagorinsky model, with no sensitivity study. The paper itself admits in Section 4 that 'the model's coefficients may require adjustment for different flow conditions.' Because the quantitative comparisons (the 6.9% reattachment error, the Reynolds-stress ranking versus WALE, and the near-wall eddy-viscosity magnitude) all depend on this coefficient, the current evidence does not distinguish whether the reported performance reflects the physics of the Liutex velocity scale or merely a favorable coefficient choice. Please provide a sensitivity analysis over a plausible range of C_s (e.g., 0.1 to 0.2) or a dynamic/procedure-based determination of the coefficient, and discuss how the reattachment error and Reynolds-stress comparisons vary with C_s.","section":"§2.1, Eq. (10); §4; §3.2.1"}],"minor_comments":[{"comment":"The text refers to 'Fig. 3(c)' when discussing the |R| vortex-identification results; the relevant panel appears to be Fig. 2(c). Please check all figure cross-references.","section":"§3.1, Fig. 2 caption and text"},{"comment":"The captions for panels (b), (c), and (d) use 'y/h' but should be 'x/h' to match the streamwise locations discussed in the text.","section":"Fig. 12 caption"},{"comment":"The definition of g_ij^2 is introduced notationally but could be made more explicit: g_ij^2 = g_ik g_kj. Please define it unambiguously.","section":"Eq. (7)"},{"comment":"The abstract states that the model 'predicts velocity profiles more accurately than the Smagorinsky model, even when using Van Driest damping.' This is demonstrated only for the fine grid and at specific locations; please qualify the claim accordingly.","section":"Abstract and §3.1"},{"comment":"The -10/3 slope in the dissipation range is claimed visually but no quantitative fit or uncertainty is provided. Given that the slope is a stated result, please include a fitted line or reference to the fitting procedure.","section":"§3.1, Fig. 5"},{"comment":"The data availability statement says data are available from the corresponding author upon reasonable request. I recommend making the data and case files publicly available to support reproducibility, especially for the scaling-exponent measurement requested above.","section":"Data availability"}],"recommendation":"major_revision","confidential_remarks":"The internal contradiction between O(y) and O(y^2) in the near-wall scaling is the most serious issue and must be fixed before the paper can be considered for publication. The coefficient-sensitivity concern is also important because the central comparisons depend on an inherited Lilly constant. The paper is otherwise methodologically sound in its use of grid convergence and external validation, and the topic is within the journal's scope. I would also note that the -10/3 scaling claim relies heavily on prior Liutex-related publications and the present confirmation is qualitative; a more quantitative analysis would strengthen the paper."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a useful validation study of the 2022 Liutex-based SGS model, and the first to look at its near-wall scaling and periodic-hill separation behavior. The simulations are real: three grids with convergence trends, external DNS and experimental benchmarks, and the model comes out comparable to WALE and clearly better than Smagorinsky with Van Driest on reattachment. But there is a genuine internal contradiction in the headline near-wall claim that must be fixed before the result can be trusted.\n\nWhat's new: the paper reports the near-wall decay of the model's eddy viscosity and shows a 6.9% reattachment-point error on periodic hills, matching WALE and beating Smagorinsky. The -10/3 PSD scaling of Liutex in the dissipation range was already reported by Xu et al. and Yan et al. (with co-authors of this paper), so that part is confirmatory rather than new. The validation is solid: grid convergence is shown for both flows, and the comparisons use Moser's DNS for channel flow and the Rapp/Breuer experiments and Krank DNS for periodic hills. The Reynolds-stress improvement over WALE in the separation core is a real, if modest, observation.\n\nThe soft spot is not minor. In Section 3.1, the paragraph describing Fig. 7 first says the eddy viscosity approaches zero near the wall with an asymptotic trend proportional to y, and then, a few sentences later, says the present model exhibits a vanishing tendency proportional to y^2, which is less accurate than that of WALE. The abstract and Conclusion (2) repeat the O(y) version. These cannot both be true. Since no data or code are released, the reader cannot tell which statement is a typo. That matters because the near-wall scaling is an advertised headline result and is used to argue physical consistency. The O(y^2) version would actually contradict the abstract.\n\nThe fixed coefficient C_s = 0.17 is a secondary concern. The authors inherit Lilly's value, and they admit in Section 4 that coefficients may need adjustment per flow. That leaves open the possibility that the 6.9% reattachment error and the Reynolds-stress comparisons partly reflect coefficient choice, not the velocity-scale physics. Still, the paper does not fit anything: C_s is not tuned here, and the external validation makes the results meaningful.\n\nWho this is for: LES practitioners interested in alternative velocity scales for SGS models. It deserves a serious referee because the simulations are substantive and the model's behavior is worth documenting, but the referee should insist on resolving the y vs y^2 contradiction and on a sensitivity check for C_s. I would not cite it in its current form.","headline":"Useful validation of the Liutex SGS model with solid simulations, but the near-wall scaling claim is internally contradictory (O(y) vs O(y^2)) and must be resolved before the headline result is credible.","tokens_in":12535,"tokens_out":2561,"would_cite":false,"duration_ms":27734,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A rotation-based eddy-viscosity model predicts separated hill flow within 6.9% of experiment.","keywords":["large eddy simulation","subgrid-scale stress model","Liutex velocity scale","rigid rotation","eddy viscosity","near-wall scaling","flow separation","periodic hill flow"],"falsifier":"Rerun the periodic-hill case with $C_s=0.10$, $0.17$, and $0.25$ on the same grids and record the reattachment location; if reattachment moves by much more than the reported 6.9% error as $C_s$ changes, the claimed accuracy is a coefficient effect, not a property of the rotation-based velocity scale.","tokens_in":11556,"feed_emoji":"🌀","tokens_out":15064,"duration_ms":136846,"temperature":0.7,"pith_summary":"Large-eddy simulations need a rule for the unresolved small scales, and most rules either add too much dissipation near walls or rely on damping functions and calibrated constants. This paper argues that a 2022 subgrid-scale stress model, which sets its velocity scale to the magnitude of the Liutex vector (twice the local angular velocity of rigid rotation), avoids that problem: in turbulent channel flow its eddy viscosity vanishes toward the wall and stays in the $10^{-2}$ to $10^{-4}$ range, like the WALE model. In periodic-hill flow the model predicts the reattachment point with a 6.9% error, matching WALE and beating the classical strain-rate-based model's 14.0%. The paper also reports that near-wall Reynolds stresses in the separation core are closer to experiment for the rotation-based model than for WALE. A sympathetic reader would care because this suggests a single rotation-based quantity can handle the near-wall and separated-flow parts of the subgrid problem without extra damping.","feed_headline":"Rotation-based eddy viscosity hits 6.9% reattachment error","feed_subtitle":"With rigid rotation as its velocity scale, near-wall eddy viscosity dies out naturally, with no damping function.","key_machinery":"The load-bearing object is the Liutex vector $\\mathbf{R}$, the rigid-rotation part of the velocity-gradient field; its magnitude $|\\mathbf{R}|$ replaces the strain-rate magnitude in the classical eddy-viscosity formula, giving $\\nu_t=(C_s\\Delta)^2|\\mathbf{R}|$ with $C_s=0.17$. Because rigid rotation is zero in pure shear, the formula has a built-in wall behavior: the viscous sublayer is nearly pure shear, so $\\nu_t$ dies out there without a damping function. The paper uses this mechanism to explain the near-wall scaling, the correlation between eddy viscosity and visualized vortex structures, and the model's ability to predict separated-flow reattachment; the $-10/3$ dissipation-range spectrum of $|\\mathbf{R}|$ is offered as evidence that the velocity scale has the correct small-scale content.","core_discovery":"The central claim is that the 2022 rotation-based SGS model---$\\nu_t = (C_s \\Delta)^2 |\\mathbf{R}|$, with $\\mathbf{R}$ the Liutex vector (twice the local angular velocity of rigid rotation)---has the near-wall and separated-flow behavior that standard closures lack. In channel flow at $Re_\\tau=395$, the paper reports that $\\nu_t$ vanishes near the wall, with an asymptotic trend given as $O(y)$ in the abstract and as $O(y^2)$ in the conclusions, that the dimensionless eddy viscosity sits in the $10^{-2}$ to $10^{-4}$ range like WALE's, and that the power spectrum of $|\\mathbf{R}|$ follows a $-10/3$ slope in the dissipation range; mean velocity profiles on fine grids match DNS. In periodic-hill flow at $Re_H=10595$, the model places reattachment at $x/h=4.5$, a 6.9% error against the experimental 4.21, the same as WALE and much better than the classical strain-rate-based model's 14.0%. At the separation core ($x/h=2$), the model's Reynolds-stress components are closer to experiment than WALE's in the near-wall region; downstream of reattachment the paper acknowledges its Reynolds stress is less developed. The paper also states that the model coefficient may need adjustment for other flow conditions.","pith_inferences":["The paper does not test this, but if the 6.9% reattachment error survives when $C_s$ is dynamic rather than fixed at 0.17, that would show the Liutex velocity scale, not the coefficient, carries the improvement.","A natural extension the paper does not attempt is homogeneous isotropic turbulence: comparing the $|\\mathbf{R}|$ spectrum with the dissipation spectrum would test whether $|\\mathbf{R}|$ is a local proxy for $\\epsilon^{1/3}$, the spectral justification for using $\\Delta^2|\\mathbf{R}|$ as an eddy viscosity.","The paper does not claim this, but the near-wall advantage at the separation core could be probed at higher Reynolds numbers or on a geometrically different separation such as a bluff body or airfoil, which would show whether the effect is tied to the periodic-hill case.","The paper's own note that coefficients may need adjustment implies a practical next step: a two-parameter calibration against wall-resolved DNS to separate the velocity scale's contribution from the constant's contribution."],"forward_implications":["The rotation-based closure would give a fixed-coefficient SGS model that needs neither a wall-damping function nor a dynamic procedure in channel and separated flows.","For separated-flow geometries like periodic hills, backward-facing steps, or stalled airfoils, reattachment points would typically be predicted with roughly half the error of the classical strain-rate-based model.","Near-wall Reynolds-stress predictions at a separation core would improve over WALE, which matters for surface loads and heat-transfer predictions in separated regions.","Because the same $|\\mathbf{R}|$ field both identifies vortices and sets eddy viscosity, simulation workflows could use one computed quantity for visualization and closure.","The $-10/3$ spectral behavior suggests $|\\mathbf{R}|$ could serve as a direct, resolved-scale proxy for the dissipation-range cascade in LES grids."],"supporting_citations":[{"why":"Proposes the rotation-based (Liutex) subgrid-scale stress model; supplies the eddy-viscosity formula being tested.","marker":"[13]"},{"why":"Defines the Liutex vector as the rigid-rotation part of the velocity gradient; this is the paper's velocity scale.","marker":"[12]"},{"why":"Introduces the WALE model, the main near-wall-behavior baseline the present model is compared against.","marker":"[10]"},{"why":"Introduces the classical strain-rate-based eddy-viscosity model; its results are the primary baseline for velocity-profile and reattachment comparisons.","marker":"[2]"},{"why":"Derives the inertial-range coefficient 0.17 that the present model uses unchanged as C_s.","marker":"[14]"},{"why":"Provides the DNS channel-flow data at Re_tau=395 used to validate mean velocity profiles.","marker":"[31]"},{"why":"Provides the DNS periodic-hill data at Re_H=10595 used to validate skin friction and reattachment.","marker":"[32]"},{"why":"Provides the experimental reattachment location x/h=4.21 that defines the reported 6.9% and 14.0% errors.","marker":"[33]"},{"why":"Provides experimental mean-velocity and Reynolds-stress profiles used for the periodic-hill comparisons.","marker":"[34]"}],"fun_headline_variants":["Rotation-based eddy viscosity: 6.9% reattachment error","Rotation-based SGS model improves separation prediction to 6.9% error","No damping needed: rotation-based model predicts reattachment well","Rotation-based model: near-wall decay and 6.9% separation error","Liutex-based eddy viscosity: natural decay, improved separation"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The entire comparison rests on the fixed coefficient $C_s=0.17$ being the right weight for the Liutex velocity scale; if that constant has to be retuned for each flow, the reported 6.9% error and Reynolds-stress gains could be artifacts of the chosen number rather than of using rigid rotation.","fun_headline_variants_meta":{"raw":{"variants":["Rotation-based eddy viscosity: 6.9% reattachment error","Rotation-based SGS model improves separation prediction to 6.9% error","No damping needed: rotation-based model predicts reattachment well","Rotation-based model: near-wall decay and 6.9% separation error","Liutex-based eddy viscosity: natural decay, improved separation"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00055,"raw_usage":{"total_tokens":2707,"prompt_tokens":1110,"completion_tokens":1597,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":726,"completion_tokens_details":{"reasoning_tokens":1504}},"tokens_in":726,"tokens_out":1597,"duration_ms":14534,"temperature":1.0,"reasoning_tokens":1504,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T13:50:30.131509+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Rerun the periodic-hill case with $C_s=0.10$, $0.17$, and $0.25$ on the same grids and record the reattachment location; if reattachment moves by much more than the reported 6.9% error as $C_s$ changes, the claimed accuracy is a coefficient effect, not a property of the rotation-based velocity scale.","supporting_citations":[{"cited_title":"A Liutex-based subgrid stress model for large-eddy simulation[J]","cited_arxiv_id":null,"evidence_quote":"Proposes the rotation-based (Liutex) subgrid-scale stress model; supplies the eddy-viscosity formula being tested."},{"cited_title":"Definitions of vortex vector and vortex[J]","cited_arxiv_id":null,"evidence_quote":"Defines the Liutex vector as the rigid-rotation part of the velocity gradient; this is the paper's velocity scale."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the WALE model, the main near-wall-behavior baseline the present model is compared against."},{"cited_title":"Smagorinsky, General circulation experiments with the primitive equations: I","cited_arxiv_id":null,"evidence_quote":"Introduces the classical strain-rate-based eddy-viscosity model; its results are the primary baseline for velocity-profile and reattachment comparisons."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Derives the inertial-range coefficient 0.17 that the present model uses unchanged as C_s."},{"cited_title":"Direct numerical simulation of turbulent channel flow up to Re= 590[J]","cited_arxiv_id":null,"evidence_quote":"Provides the DNS channel-flow data at Re_tau=395 used to validate mean velocity profiles."},{"cited_title":"Direct Numerical Simulation of Flow over Periodic Hills up to ReH = 10, 595 [J]","cited_arxiv_id":null,"evidence_quote":"Provides the DNS periodic-hill data at Re_H=10595 used to validate skin friction and reattachment."},{"cited_title":"Flow over periodic hills: an experimental study[J]","cited_arxiv_id":null,"evidence_quote":"Provides the experimental reattachment location x/h=4.21 that defines the reported 6.9% and 14.0% errors."},{"cited_title":"Flow over periodic hills–numerical and experimental study in a wide range of Reynolds numbers[J]","cited_arxiv_id":null,"evidence_quote":"Provides experimental mean-velocity and Reynolds-stress profiles used for the periodic-hill comparisons."}],"review_version":1}