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REVIEW 3 major objections 5 minor 53 references

Uncertainty Quantification of Drag Reduction over Superhydrophobic Surfaces by Unified Parameterizing Structure Spacing

T0 review · 3 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Spanwise spacing, not streamwise spacing, governs how much drag reduction varies across superhydrophobic surfaces.

desk verdict Solid DNS-based UQ study showing spanwise spacing dominates drag reduction on textured posts, but the Sobol ranking rests on an arbitrary Gaussian input assumption and the 'unified' framing oversells the coverage. read the letter →

arxiv 2509.01239 v1 pith:ZVB33DAO submitted 2025-09-01 physics.flu-dyn

Byeong-Cheon Kim , Kyoungsik Chang , Sang-Wook Lee , Hoai-Thanh Nguyen , Eun Seok Oh , Jaiyoung Ryu , Minjae Kim , Jaemoon Yoon This is my paper · ORCID
classification physics.flu-dyn
keywords superhydrophobicsurfacesdragreductionuncertaintyquantificationpolynomialchaosexpansionSobolsensitivityanalysisturbulentchannelflowmicrostructurespacingdirectnumericalsimulation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper aims to show that a single geometric axis—the spanwise gap between microscopic posts—controls how much a superhydrophobic surface's drag reduction is affected by manufacturing variability. The authors unify post-type, ridge-type, and transverse-ridge-type surfaces into one two-parameter family (d1, d2), run direct numerical simulations of turbulent channel flow at three Reynolds numbers, and fit a polynomial-chaos surrogate to the results. Their sensitivity analysis finds that the spanwise spacing d2 is the dominant input at every Reynolds number studied, with its sensitivity index roughly six to fourteen times larger than that of the streamwise spacing d1. If this holds, designers should treat the sideways spacing as the primary tolerance to control, and the same conclusion applies across the whole family of textured surfaces, not just one pattern. The paper also shows the resulting uncertainty in velocity and Reynolds stresses concentrates near the wall and shrinks as Reynolds number increases.

What carries the argument

The central device is the unified two-parameter post-spacing family (d1: streamwise gap, d2: spanwise gap), which turns the three standard superhydrophobic pattern types—posts, longitudinal ridges, transverse ridges—into continuous limiting cases of one geometry. The load-bearing machinery is a polynomial-chaos expansion surrogate trained on Latin-hypercube-selected DNS samples: it maps (d1,d2) to drag reduction, and its coefficients directly yield Sobol' sensitivity indices that decompose the variance into d1, d2, and interaction contributions. This lets a small number of expensive DNS runs (12–30 per Reynolds number) generate continuous response surfaces and uncertainty statements across t

What would settle it

Run two pairs of DNS cases at Re_tau=590: first hold d2 at its mean and vary d1 by ±0.33 times the mean value, then hold d1 at its mean and vary d2 by ±0.33 times the mean value. If the drag-reduction spread from varying d2 is not roughly fourteen times the spread from varying d1, the claimed dominance of spanwise spacing is refuted at that Reynolds number.

Watch

Extended reading notes

Core claim

The paper's central claim is a sensitivity ranking: for a post-type superhydrophobic surface with uncertain streamwise spacing d1 and spanwise spacing d2, the drag-reduction response is overwhelmingly more sensitive to d2. At Re_tau=180 the Sobol index (variance-based sensitivity measure) of d2 is about seven times that of d1; at Re_tau=590, about fourteen times. The interaction term grows with Reynolds number and exceeds the single d1 contribution at Re_tau=590. The paper links this to near-wall turbulence: uncertainty is largest in the viscous sublayer, the shear-stress component R12 is suppressed near the wall, and turbulence-anisotropy trajectories show weakened coherent structures that

Load-bearing premise

The ranking of spanwise over streamwise spacing rests on the unmeasured assumption that real manufacturing deviations in d1 and d2 are independent, bell-shaped, and fixed in size relative to the post width; if actual scatter is correlated or differently sized, the ranking could shift.

Editorial extensions

If this is right

  • Manufacturing control should target spanwise spacing first; tightening d2 will reduce scatter in drag-reduction performance more than tightening d1.
  • The unified parameterization means design guidance transfers across post, ridge, and transverse-ridge surfaces rather than being limited to one pattern.
  • At higher Reynolds numbers, the same geometric uncertainty produces less variation in near-wall turbulence anisotropy, so superhydrophobic-surface performance becomes more predictable in high-speed regimes.
  • The growing interaction between d1 and d2 at high Reynolds numbers means the two spacings cannot be treated as independent design levers when Re_tau is large.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the assumed input distribution is unmeasured, repeating the analysis with correlated distributions estimated from profilometry could change the Sobol ranking; the 14-to-1 ratio is a property of that assumption as much as of the physics.
  • Since d2 is the dominant axis and ridge-type surfaces hold d1=0, ridge-type textures should exhibit less drag-reduction scatter under the same manufacturing noise than transverse-ridge textures, which vary d2 by construction.
  • A practical shortcut suggested by this result: for design exploration, treat d2 as the random variable and hold d1 at its nominal value; the surrogate would lose little accuracy while requiring fewer DNS runs.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper proposes a unified geometric parameterization of superhydrophobic surface (SHS) patterns in terms of streamwise and spanwise post spacings (d1, d2), with post width fixed. It performs direct numerical simulations (DNS) of turbulent channel flow at Re_tau = 180, 395, and 590 using NekRS, validates against Martell et al. for representative ridge, transverse-ridge, and post patterns, and builds polynomial chaos expansion (PCE) surrogates from Latin hypercube samples of d1 and d2. The central quantitative claim is that the spanwise spacing d2 dominates the uncertainty in drag reduction, with Sobol index ratios S_d2/S_d1 of roughly 6–14 across Reynolds numbers. The paper also presents uncertainty propagation for mean velocity, Reynolds stresses, and the barycentric anisotropy invariant map, and recommends controlling d2 for robust SHS design.

Significance. If the central claim holds, the paper provides a useful unified framework for comparing SHS geometries and identifies a practically important sensitivity ranking for manufacturing tolerance. The DNS methodology is standard and the validation against established literature is a clear strength. The PCE/LHS workflow is conventional and the use of LOO errors to select polynomial order is reasonable. However, the headline result is a Sobol-index ranking, which is a functional of the assumed input probability distribution. That distribution is chosen for convenience rather than based on physical or manufacturing data, and the quantity of interest (drag reduction) is never explicitly defined. These gaps make the quantitative ranking conditional on untested assumptions. The uncertainty propagation results and the qualitative insight that spanwise spacing matters more than streamwise spacing are plausible, but the paper needs additional robustness checks before the specific 6–14x claim can be accepted.

major comments (3)
  1. [Section II.C.3, Table III; Section IV.A] The Sobol indices S_d1 and S_d2, and hence the headline claim that d2 is 6–14 times more influential than d1, are functionals of the joint input distribution. The paper assumes independent Gaussian distributions for d1 and d2 with mean equal to the post width and sigma = 0.33mu, chosen only to avoid negative samples. No manufacturing tolerance data, physical correlation argument, or sensitivity analysis with respect to the distribution family or sigma is provided. If the true geometric variability is uniform, correlated, or of different magnitude, the variance decomposition and even the ranking could change. Please add a robustness study (e.g., uniform or truncated distributions, different sigma values, and a correlated case) or provide empirical justification for the Gaussian assumption. Without this, the quantitative dominance claim is conditional on an arbitrary input law.
  2. [Section IV.A] The quantity of interest, 'drag reduction,' is never explicitly defined in the manuscript. The reader cannot tell whether it is computed from the mean wall shear stress, the pressure-gradient imbalance, or a formula such as DR = (tau_0 - tau_SHS)/tau_0, nor whether it uses the top or bottom wall. Since Table IV and all Sobol indices are based on this QoI, the missing definition is load-bearing. Please state the exact formula and the averaging procedure used.
  3. [Section I and IV.A] The claimed 'unified' parameterization encompasses the full range 0 <= d_i <= 2w and includes ridge-type (d1=0) and transverse-ridge-type (d2=0) geometries. However, the UQ input distribution is centered at w = 0.1875h and the LHS samples are clustered around that mean; no samples at the boundaries d1=0 or d2=0 are included in the PCE training set. The response surface in Fig. 6 is extracted from the PCE surrogate, not from boundary DNS runs. Thus the evidence that the surrogate is accurate over the entire unified parameter space, and particularly at the ridge/transverse-ridge limits, is missing. Please either include boundary cases in the LHS design or explicitly assess extrapolation error at d=0.
minor comments (5)
  1. [Eq. (7)] The second row of the matrix appears to have a typo: it lists Ψ0(ξ0) instead of Ψ0(ξ1). Please correct.
  2. [Table III] The notation '±0.33μ' for standard deviation is misleading; standard deviation is positive. Use σ = 0.33μ.
  3. [Table I] The row label 'The number of cells, EN' is unclear; it seems to list total grid points. Please clarify notation and units.
  4. [Section IV.A / Fig. 6] The response surface is described as a third-order polynomial fit to 1000 surrogate samples, but this is separate from the PCE surrogate. Clarify the relationship between this visualization and the PCE model, and report the residual error of the response surface.
  5. [General] The phrase 'unified' is used broadly, but the study only varies d1 and d2 at a fixed post width w. Please state this limitation explicitly in the conclusion.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the d2-dominance ranking is an empirical, data-driven property of the DNS-trained PCE surrogate, not an artifact of the input definition or a fitted parameter.

full rationale

The paper's derivation chain is: choose a Gaussian input distribution for d1 and d2 (with equal means and equal standard deviations), generate LHS samples, run DNS at those samples, fit a PCE surrogate to the drag-reduction outputs, and then compute Sobol indices from the PCE coefficients. Nothing in this chain defines d2 as more influential by construction. Both inputs are assigned the same Gaussian law, so the input distribution is symmetric; the observed asymmetry in Sobol indices (Sd2 >> Sd1) must therefore come from the DNS-evaluated response surface, not from the parameterization or distribution. The standard deviation σ=0.33μ is a modeling assumption intended to keep samples non-negative, not a parameter fitted to the QoI, so this does not amount to a fitted input being renamed as a prediction. The PCE surrogate is cross-validated with leave-one-out errors, and the DNS setup is validated against external reference data (Martell et al., refs. 15 and 24). The authors' self-citations (refs. 17, 26, 47) appear only as supporting mentions in literature context or grid-resolution comparisons; they are not load-bearing for the central UQ claim. Thus the central ranking of d2 over d1 is an empirical result conditional on the stated input assumptions, not an equivalence to the paper's inputs by construction.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The UQ framework rests on two hand-chosen distribution parameters and several idealized modeling assumptions (flat shear-free interface, Gaussian inputs). No physical entities are newly postulated; the parameterization is a geometric re-parameterization of existing patterns. The free parameters (mu, sigma) directly control the uncertainty magnitude and therefore the Sobol index ranking.

free parameters (2)
  • Gaussian mean for d1 and d2 = 0.1875h (post width)
    Chosen equal to the post width, not measured from any physical sample; defines the center of the UQ distribution.
  • Gaussian standard deviation sigma = 0.33 * mu
    Set to 0.33 times the mean to keep samples non-negative; arbitrary and not based on empirical manufacturing variability.
assumptions (4)
  • domain assumption Flat, shear-free air-water interface over the slip regions, with no meniscus deformation or wettability transition
    Introduced in Section II.B and Fig. 1 as a modeling idealization; the entire DNS setup relies on this boundary condition to represent the SHS.
  • standard math Incompressible constant-property Navier-Stokes equations with periodic streamwise/spanwise boundaries and constant pressure-gradient forcing
    Standard channel-flow DNS formulation; stated in Section II.A and II.B.
  • domain assumption The relation tau_w = (2/Ly)(dP/dx) is used to set the friction Reynolds number
    Invoked in Section II.B; this relation is exact for symmetric no-slip channels but only approximate when the bottom wall is an SHS with different shear, potentially affecting the Re_tau values reported.
  • domain assumption Input spacings d1 and d2 follow independent Gaussian distributions
    Stated in Section II.C.3; this is the load-bearing distribution for all UQ results and has no empirical justification.

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Cite this review

Pith. "Pith review of Uncertainty Quantification of Drag Reduction over Superhydrophobic Surfaces by Unified Parameterizing Structure Spacing." pith.science (2026). https://pith.science/paper/ZVB33DAO

@misc{pith2026250901239,
  author       = {Pith},
  title        = {Pith review of: Uncertainty Quantification of Drag Reduction over Superhydrophobic Surfaces by Unified Parameterizing Structure Spacing},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZVB33DAO}},
  note         = {Machine review of arXiv:2509.01239}
}
abstract

Superhydrophobic surfaces (SHS) have demonstrated significant potential in reducing turbulent drag by introducing slip conditions through micro-structured geometries. While previous studies have examined individual SHS configurations such as post-type, ridge-type, and transverse ridge-type surfaces, a unified analysis that connects these patterns through geometric parameterization remains limited. In this study, we propose a systematic framework to explore the drag reduction characteristics by varying the streamwise and spanwise spacing ($d_1, d_2$) of post-type patterns, effectively encompassing a range of SHS geometries. High-fidelity direct numerical simulations (DNS) were performed using NekRS, a GPU-accelerated spectral element solver, to resolve incompressible turbulent channel flows over these SHSs. To account for variability in the geometric parameters and quantify their influence, we construct a surrogate model based on polynomial chaos expansion (PCE) using Latin hypercube sampling (LHS) method. The resulting model enables efficient uncertainty quantification (UQ) and sensitivity analysis, revealing the relative importance of $d_1$ and $d_2$ in drag reduction performance. This unified UQ framework provides both predictive capability and design guidance for optimizing SHS configurations under uncertain geometric conditions.

Figures

Figures reproduced from arXiv: 2509.01239 by the authors.

Figure 1
Figure 1. FIG. 1. Schematic diagram of the various superhydrophobic structure patterns created by the parameterized structure spacing ( [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The procedure of uncertainty quantification for two input random variables ( [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Validation of DNS results according to the SHS type and shear Reynolds number. (A-E) velocity profile, (F-J) Reynolds stress profile. [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Graph of drag reduction according to the dimensionless slip [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. The barycentric anisotropy invariant map for representative cases( [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. The response surface of drag reduction according to the two [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. The uncertainty propagation of the velocity profile according to the shear Reynolds number( [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. The uncertainty propagation of the Reynolds shear stress( [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. The Sobol’ indices of the Reynolds shear stress( [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. The uncertainty propagation of the barycentric anisotropy invariant map according to the shear Reynolds number( [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]

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Works this paper leans on

53 extracted references · 47 canonical work pages

  1. [1]

    merlin.mbs aapmrev4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked

    FUNCTION id.bst "merlin.mbs aapmrev4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked" ENTRY address archive archivePrefix author bookaddress booktitle chapter collaboration doi edition editor eid eprint howpublished institution isbn issn journal key language month note number organization pages primaryClass publisher school SLACcitation series title translat...

    2010

  2. [2]

    merlin.mbs aipauth4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked

    FUNCTION id.bst "merlin.mbs aipauth4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked" ENTRY address archive archivePrefix author bookaddress booktitle chapter collaboration doi edition editor eid eprint howpublished institution isbn issn journal key language month note number organization pages primaryClass publisher school SLACcitation series title translat...

    2010

  3. [3]

    merlin.mbs aipnum4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked

    FUNCTION id.bst "merlin.mbs aipnum4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked" ENTRY address archive archivePrefix author bookaddress booktitle chapter collaboration doi edition editor eid eprint howpublished institution isbn issn journal key language month note number organization pages primaryClass publisher school SLACcitation series title translati...

    2010

  4. [4]

    author author J. P. \ Rothstein ,\ 10.1146/annurev-fluid-121108-145558 journal journal Annual Review of Fluid Mechanics \ volume 42 ,\ pages 89 ( year 2010 ) NoStop

    work page doi:10.1146/annurev-fluid-121108-145558 2010

  5. [5]

    Lee , author C.-H

    author author C. Lee , author C.-H. \ Choi , \ and\ author C.-J. \ Kim ,\ @noop journal journal Experiments in Fluids \ volume 57 ,\ pages 1 ( year 2016 ) NoStop

    work page 2016

  6. [6]

    Park , author C.-H

    author author H. Park , author C.-H. \ Choi , \ and\ author C.-J. \ Kim ,\ @noop journal journal Experiments in Fluids \ volume 62 ,\ pages 1 ( year 2021 ) NoStop

    work page 2021

  7. [7]

    Luo \ and\ author Z

    author author J. Luo \ and\ author Z. Guo ,\ @noop journal journal Nanoscale \ volume 16 ,\ pages 16404 ( year 2024 ) NoStop

    work page 2024

  8. [8]

    Chen , author S

    author author L. Chen , author S. Wang , author J. Ding , author Y. Wang , author P. Bennett , author J. Cheng , author Q. Yang , \ and\ author D. Liu ,\ @noop journal journal Ocean Engineering \ volume 269 ,\ pages 113440 ( year 2023 ) NoStop

    work page 2023

Show all 53 references
  1. [9]

    Wang , author H

    author author H. Wang , author H. Lu , \ and\ author W. Zhao ,\ @noop journal journal Physics of Fluids \ volume 35 ( year 2023 ) NoStop

    2023

  2. [10]

    Cassie \ and\ author S

    author author A. Cassie \ and\ author S. Baxter ,\ @noop journal journal Transactions of the Faraday society \ volume 40 ,\ pages 546 ( year 1944 ) NoStop

    1944

  3. [11]

    Dunn , author T

    author author A. Dunn , author T. J. \ Wasley , author J. Li , author R. W. \ Kay , author J. Stringer , author P. J. \ Smith , author E. Esenturk , author C. Connaughton , author J. D. \ Shephard , et al. ,\ @noop journal journal Applied Surface Science \ volume 365 ,\ pages ...

    2016

  4. [12]

    author author C. W. \ Berendsen , author M. S kere n , author D. Najdek , \ and\ author F. C ern \`y ,\ @noop journal journal Applied Surface Science \ volume 255 ,\ pages 9305 ( year 2009 ) NoStop

    2009

  5. [13]

    Qian \ and\ author Z

    author author B. Qian \ and\ author Z. Shen ,\ @noop journal journal Langmuir \ volume 21 ,\ pages 9007 ( year 2005 ) NoStop

    2005

  6. [14]

    Park , author H

    author author H. Park , author H. Park , \ and\ author J. Kim ,\ @noop journal journal Physics of Fluids \ volume 25 ( year 2013 ) NoStop

    2013

  7. [15]

    T \"u rk , author G

    author author S. T \"u rk , author G. Daschiel , author A. Stroh , author Y. Hasegawa , \ and\ author B. Frohnapfel ,\ @noop journal journal Journal of fluid mechanics \ volume 747 ,\ pages 186 ( year 2014 ) NoStop

    2014

  8. [16]

    Jelly , author S

    author author T. Jelly , author S. Jung , \ and\ author T. Zaki ,\ @noop journal journal Physics of Fluids \ volume 26 ( year 2014 ) NoStop

    2014

  9. [17]

    author author H. J. \ Im \ and\ author J. H. \ Lee ,\ @noop journal journal Physics of Fluids \ volume 29 ( year 2017 ) NoStop

    2017

  10. [18]

    author author M. B. \ Martell , author J. P. \ Rothstein , \ and\ author J. B. \ Perot ,\ @noop journal journal Physics of Fluids \ volume 22 ( year 2010 ) NoStop

    2010

  11. [19]

    Seo \ and\ author A

    author author J. Seo \ and\ author A. Mani ,\ @noop journal journal Physics of Fluids \ volume 28 ( year 2016 ) NoStop

    2016

  12. [20]

    \ Nguyen , author S.-W

    author author H.-T. \ Nguyen , author S.-W. \ Lee , author J. Ryu , author M. Kim , author J. Yoon , \ and\ author K. Chang ,\ @noop journal journal Scientific Reports \ volume 14 ,\ pages 12053 ( year 2024 ) NoStop

    2024

  13. [21]

    Seo \ and\ author A

    author author J. Seo \ and\ author A. Mani ,\ @noop journal journal Physical Review Fluids \ volume 3 ,\ pages 044601 ( year 2018 ) NoStop

    2018

  14. [22]

    Xiu ,\ @noop journal journal Communications in computational physics \ volume 2 ,\ pages 293 ( year 2007 ) NoStop

    author author D. Xiu ,\ @noop journal journal Communications in computational physics \ volume 2 ,\ pages 293 ( year 2007 ) NoStop

    2007

  15. [23]

    Xiu \ and\ author J

    author author D. Xiu \ and\ author J. S. \ Hesthaven ,\ @noop journal journal SIAM Journal on Scientific Computing \ volume 27 ,\ pages 1118 ( year 2005 ) NoStop

    2005

  16. [24]

    author author M. O. \ Deville , author P. F. \ Fischer , \ and\ author E. H. \ Mund ,\ @noop title High-order methods for incompressible fluid flow ,\ Vol. volume 9 \ ( publisher Cambridge university press ,\ year 2002 ) NoStop

    2002

  17. [25]

    Fischer , author S

    author author P. Fischer , author S. Kerkemeier , author M. Min , author Y.-H. \ Lan , author M. Phillips , author T. Rathnayake , author E. Merzari , author A. Tomboulides , author A. Karakus , author N. Chalmers , et al. ,\ @noop journal journal Parallel Computing \ volume 1...

    2022

  18. [26]

    author author P. F. \ Fischer , author J. W. \ Lottes , \ and\ author S. G. \ Kerkemeier ,\ @noop title nek5000 web page , \ howpublished https://nek5000.mcs.anl.gov/ ( year 2008 ) NoStop

    2008

  19. [27]

    author author M. B. \ Martell , author J. B. \ Perot , \ and\ author J. P. \ Rothstein ,\ @noop journal journal Journal of Fluid Mechanics \ volume 620 ,\ pages 31 ( year 2009 ) NoStop

    2009

  20. [28]

    Rezaeiravesh , author R

    author author S. Rezaeiravesh , author R. Vinuesa , \ and\ author P. Schlatter ,\ @noop journal journal Computers & Fluids \ volume 227 ,\ pages 105024 ( year 2021 ) NoStop

    2021

  21. [29]

    \ Kim , author K

    author author B.-C. \ Kim , author K. Chang , author S.-W. \ Lee , author J. Ryu , author M. Kim , \ and\ author J. Yoon ,\ @noop journal journal arXiv preprint arXiv:2504.07377 \ ( year 2025 ) NoStop

    2025 arXiv

  22. [30]

    author author S. B. \ Pope \ and\ author S. B. \ Pope ,\ @noop title Turbulent flows \ ( publisher Cambridge university press ,\ year 2000 ) NoStop

    2000

  23. [31]

    Fischer ,\ @noop title Implementation considerations for the oifs/characteristics approach to convection problems , \ type Tech

    author author P. Fischer ,\ @noop title Implementation considerations for the oifs/characteristics approach to convection problems , \ type Tech. Rep. \ ( institution Argonne National Laboratory ,\ year 2003 ) NoStop

    2003

  24. [32]

    Hosder , author R

    author author S. Hosder , author R. Walters , \ and\ author M. Balch ,\ in\ @noop booktitle 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference \ ( year 2007 )\ p.\ pages 1939 NoStop

    2007

  25. [33]

    author author J. C. \ Helton \ and\ author F. J. \ Davis ,\ @noop journal journal Reliability Engineering & System Safety \ volume 81 ,\ pages 23 ( year 2003 ) NoStop

    2003

  26. [34]

    Xiu ,\ doi:10.1515/9781400835348 title A Spectral Method Approach \ ( publisher Princeton University Press ,\ address Princeton ,\ year 2010 ) NoStop

    author author D. Xiu ,\ doi:10.1515/9781400835348 title A Spectral Method Approach \ ( publisher Princeton University Press ,\ address Princeton ,\ year 2010 ) NoStop

    2010 doi

  27. [35]

    Marelli \ and\ author B

    author author S. Marelli \ and\ author B. Sudret ,\ title Uqlab: A framework for uncertainty quantification in matlab , \ in\ 10.1061/9780784413609.257 booktitle Vulnerability, Uncertainty, and Risk \ ( publisher ASCE ,\ year 2014 )\ pp.\ pages 2554--2563 ,\ http://arxiv.org/a...

    2014 doi

  28. [36]

    Fukagata , author N

    author author K. Fukagata , author N. Kasagi , \ and\ author P. Koumoutsakos ,\ @noop journal journal Physics of fluids \ volume 18 ( year 2006 ) NoStop

    2006

  29. [37]

    Busse \ and\ author N

    author author A. Busse \ and\ author N. Sandham ,\ @noop journal journal Physics of Fluids \ volume 24 ( year 2012 ) NoStop

    2012

  30. [38]

    Jung , author H

    author author T. Jung , author H. Choi , \ and\ author J. Kim ,\ @noop journal journal Journal of Fluid Mechanics \ volume 790 ,\ pages R1 ( year 2016 ) NoStop

    2016

  31. [39]

    Park , author G

    author author H. Park , author G. Sun , et al. ,\ @noop journal journal Journal of Fluid Mechanics \ volume 747 ,\ pages 722 ( year 2014 ) NoStop

    2014

  32. [40]

    Xu , author A

    author author M. Xu , author A. Grabowski , author N. Yu , author G. Kerezyte , author J.-W. \ Lee , author B. R. \ Pfeifer , \ and\ author C.-J. \ Kim ,\ @noop journal journal Physical Review Applied \ volume 13 ,\ pages 034056 ( year 2020 ) NoStop

    2020

  33. [41]

    Xu , author N

    author author M. Xu , author N. Yu , author J. Kim , et al. ,\ @noop journal journal Journal of Fluid Mechanics \ volume 908 ,\ pages A6 ( year 2021 ) NoStop

    2021

  34. [42]

    Srinivasan , author J

    author author S. Srinivasan , author J. A. \ Kleingartner , author J. B. \ Gilbert , author R. E. \ Cohen , author A. J. \ Milne , \ and\ author G. H. \ McKinley ,\ @noop journal journal Physical review letters \ volume 114 ,\ pages 014501 ( year 2015 ) NoStop

    2015

  35. [43]

    Ahn , author S

    author author S. Ahn , author S. Jo , author W. Song , author H. Lee , author G. Ku , author M. Kim , author D. R. \ Kim , \ and\ author S. Song ,\ @noop journal journal International Journal of Heat and Fluid Flow \ volume 114 ,\ pages 109805 ( year 2025 ) NoStop

    2025

  36. [44]

    author author J. L. \ Lumley \ and\ author G. R. \ Newman ,\ @noop journal journal Journal of Fluid Mechanics \ volume 82 ,\ pages 161 ( year 1977 ) NoStop

    1977

  37. [45]

    Emory \ and\ author G

    author author M. Emory \ and\ author G. Iaccarino ,\ @noop journal journal Center for Turbulence Research Annual Research Briefs \ ,\ pages 123 ( year 2014 ) NoStop

    2014

  38. [46]

    Hoyas \ and\ author J

    author author S. Hoyas \ and\ author J. Jim \'e nez ,\ @noop journal journal Physics of fluids \ volume 18 ( year 2006 ) NoStop

    2006

  39. [47]

    Watanabe , author H

    author author S. Watanabe , author H. Mamori , \ and\ author K. Fukagata ,\ @noop journal journal Fluid Dynamics Research \ volume 49 ,\ pages 025501 ( year 2017 ) NoStop

    2017

  40. [48]

    Elboth , author B

    author author T. Elboth , author B. A. \ Pettersson Reif , author . Andreassen , \ and\ author M. B. \ Martell ,\ @noop journal journal Geophysics \ volume 77 ,\ pages P1 ( year 2012 ) NoStop

    2012

  41. [49]

    Min \ and\ author J

    author author T. Min \ and\ author J. Kim ,\ @noop journal journal Physics of Fluids \ volume 16 ,\ pages L55 ( year 2004 ) NoStop

    2004

  42. [50]

    author author H. T. \ Nguyen , author K. Chang , author S.-W. \ Lee , author J. Ryu , \ and\ author M. Kim ,\ @noop journal journal Energies \ volume 15 ,\ pages 6645 ( year 2022 ) NoStop

    2022

  43. [51]

    Offermans ,\ @noop title Gather-scatter library in nek5000: Documentation of the gs library developed by james lottes , \ type Tech

    author author N. Offermans ,\ @noop title Gather-scatter library in nek5000: Documentation of the gs library developed by james lottes , \ type Tech. Rep. \ ( institution Report ,\ year 2017 ) NoStop

    2017

  44. [52]

    merlin.mbs apsrev4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked

    FUNCTION id.bst "merlin.mbs apsrev4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked" ENTRY address archive archivePrefix author bookaddress booktitle chapter collaboration doi edition editor eid eprint howpublished institution isbn issn journal key language month note number orga...

    2010

  45. [53]

    merlin.mbs apsrmp4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked

    FUNCTION id.bst "merlin.mbs apsrmp4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked" ENTRY address archive archivePrefix author bookaddress booktitle chapter collaboration doi edition editor eid eprint howpublished institution isbn issn journal key language month note number orga...

    2010

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.