pith. sign in

arxiv: 2605.23166 · v1 · pith:DVHI6CARnew · submitted 2026-05-22 · ⚛️ physics.flu-dyn · physics.geo-ph

Free surfaces in turbulence -- A unified framework from water surfaces to elastic solids

Giulio Foggi Rota , Andrea Mazzino , Marco Edoardo Rosti This is my paper

Pith reviewed 2026-05-25 03:40 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn physics.geo-ph
keywords free surfacesturbulencedeformable interfaceslinear responseair-water interfaceelastic solidsocean surfaceturbulence-induced waves
0
0 comments X

The pith

A linear theory of turbulent pressure fluctuations unifies the response of deformable surfaces from water to elastic solids, predicting whether the interface follows the flow or develops its own dynamics.

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

The paper develops a linear framework describing how pressure fluctuations from turbulent flow deform a free surface. It distinguishes two regimes: one in which the surface is enslaved to the underlying turbulence and another in which intrinsic surface dynamics appear. Nonlinear simulations of air-water interfaces and rubber layers match the linear predictions and show no wave turbulence, while aerial ocean measurements also align with the same regimes.

Core claim

A linear theory that excludes nonlinear wave-wave interactions describes the response of a deformable surface to pressure fluctuations from a turbulent flow. The theory predicts distinct regimes depending on whether intrinsic surface dynamics emerge or the interface remains enslaved by the flow. Fully nonlinear simulations of realistic air-water and rubber interfaces reproduce the predicted regimes without developing wave turbulence, and the same predictions match observations of the ocean surface.

What carries the argument

Linear response of a deformable surface to turbulent pressure fluctuations, which determines whether the interface is flow-enslaved or exhibits intrinsic dynamics.

If this is right

  • The same linear framework applies to both fluid interfaces and elastic solid surfaces exposed to turbulence.
  • Realistic conditions favor turbulence-induced waves over intrinsic wave-turbulence cascades.
  • Surface statistics can be predicted directly from the statistics of turbulent pressure without solving the full nonlinear surface problem.
  • Ocean-surface measurements can be interpreted within the enslaved or intrinsic regime depending on local flow and surface parameters.

Where Pith is reading between the lines

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

  • The boundary between the two regimes may be mapped by varying surface tension, elasticity, or flow Reynolds number in controlled experiments.
  • The framework could be tested on other deformable boundaries, such as thin films or biological membranes in flow.
  • If the linear regime holds more generally, many existing wave-turbulence models may overstate the role of nonlinear cascades in realistic turbulent environments.

Load-bearing premise

Nonlinear wave-wave interactions can be neglected so that pressure fluctuations alone drive a linear surface response even when the simulations allow nonlinearity.

What would settle it

Detection of clear nonlinear wave-turbulence signatures, such as an energy cascade across scales, in either the simulations or ocean-surface data that the linear predictions cannot reproduce.

Figures

Figures reproduced from arXiv: 2605.23166 by Andrea Mazzino, Giulio Foggi Rota, Marco Edoardo Rosti.

Figure 1
Figure 1. Figure 1: Interplay between flow turbulence and surface waves. We visualise the multiphase air–water flow over a smooth bed, as captured by our fully resolved nonlinear simulations. Turbulence develops in the water due to friction at the bed and spreads towards the surface, agitated by pressure fluctuations. Surface waves develop and propagate, perturbing the overlying wind through the formation of hairpin-like vort… view at source ↗
Figure 2
Figure 2. Figure 2: Water surface dynamics in turbulence. We consider the surface separating a flowing water layer from the air above (figure 1) and confirm the fully turbulent nature of the flow inspecting the streamwise spectra of the turbulent kinetic energy (panel 𝑎) and of the pressure below the water surface (panel 𝑏), closely matching Kolmogorov’s predictions (Kolmogorov 1941). We thus assess wave propagation at the su… view at source ↗
Figure 3
Figure 3. Figure 3: Elastic solid surface in turbulence. We consider a thick layer of rubber coating the bottom wall of a turbulent channel flow, as investigated in a previous work from our group (Koseki et al. 2025). We thus compute the elevation (panel 𝑎) and vertical velocity spectra (panel 𝑏) of the solid surface along the streamwise direction. Remarkable agreement is found with our theoretical predictions in the regime w… view at source ↗
Figure 4
Figure 4. Figure 4: Displacement spectrum from aerial measurements of the oceanic surface compared to analytical predictions. Measurements from literature (Hwang et al. 2000; Zhou et al. 2015; Bondur et al. 2016; Lenain & Melville 2017) are shown in colour, while the black dashed line denotes our theoretical prediction, and the black dotted line the prediction from wave turbulence. All spectra (including those compensated wit… view at source ↗
Figure 5
Figure 5. Figure 5: Frequency ratio between intrinsic surface dynamics and turbulent flow dynamics. 𝛿 = 𝜔0/𝜔𝑡 > 0 at all streamwise wavenumbers 𝜅𝑥 , confirming the placement of the reported air–water simulation in the regime where intrinsic surface dynamics are faster than the surrounding flow turbulence, and are thus able to emerge. Appendix B. Equivalence of isotropic and one-dimensional elevation spectra We show here that,… view at source ↗
read the original abstract

What do the ocean surface and a swaying flag have in common? Both are deformable surfaces exhibiting chaotic motion when exposed to turbulent flows. Whether such motion is primarily driven by flow turbulence or by nonlinear dynamics intrinsic to the surface remains debated. Surface waves can interact nonlinearly and transfer energy across scales through the cascade of wave turbulence, a behaviour observed at interfaces between otherwise quiescent fluids and in controlled laboratory experiments. They can as well induce turbulent motions in the neighbouring fluids (wave-induced-turbulence), provided the local Reynolds number is large enough. Realistic environments, however, are more complex and typically involve the simultaneous presence of wave turbulence and wave-induced-turbulence with turbulence-induced-waves, the dynamic relevance of which remains unclear. Here we develop a theoretical framework describing the response of a deformable surface to pressure fluctuations generated by a turbulent flow, and validate it using numerical simulations of the air-water interface in quasi-realistic conditions, complemented by simulations of a deformable rubber layer. Our linear theory, which excludes nonlinear wave-wave interactions, predicts distinct dynamical regimes depending on whether intrinsic surface dynamics emerge or whether the interface is enslaved by flow turbulence. Remarkably, although our fully resolved and nonlinear simulations do not inhibit the onset of wave turbulence, we do not observe it. Instead, we find strong agreement with theoretical predictions in both regimes. We find notable agreement between our predictions and aerial surveys of the ocean surface, highlighting the need for further measurements to distinguish among wave turbulence and turbulence-induced-waves.

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 develops a linear theoretical framework describing the response of deformable free surfaces (air-water interfaces and elastic solids) to pressure fluctuations from turbulent flows, explicitly excluding nonlinear wave-wave interactions. It predicts two regimes: one in which intrinsic surface dynamics emerge and one in which the interface is enslaved to the flow. The framework is tested against fully nonlinear simulations of the air-water interface under quasi-realistic conditions and of a deformable rubber layer; both show agreement with the linear predictions. Additional support is claimed from aerial ocean-surface surveys. The central claim is that the linear, pressure-driven description suffices even when the simulations permit (but do not exhibit) wave turbulence.

Significance. If the central claim holds, the work supplies a unified, parameter-light description that spans fluid and solid interfaces and indicates when turbulence-induced waves dominate over intrinsic wave dynamics. The multi-system validation (air-water, rubber) and the ocean-data comparison are positive features. The absence of free parameters in the linear derivation and the direct confrontation with nonlinear simulations are also strengths. However, the significance is tempered by the need for clearer quantitative validation and regime-boundary tests.

major comments (2)
  1. [Simulations section] Simulations section (and associated figures): the claim that 'fully resolved and nonlinear simulations do not inhibit the onset of wave turbulence' yet exhibit 'strong agreement with theoretical predictions' is load-bearing for the decision to drop nonlinear wave-wave terms. No quantitative diagnostics are provided for wave steepness, nonlinear interaction time scales relative to simulation duration, or spectral signatures of an energy cascade; without these it is impossible to determine whether the observed agreement reflects genuine linear dominance or simply that the nonlinear regime was not reached.
  2. [Ocean-data comparison] Ocean-data comparison paragraph: the reported 'notable agreement' with aerial surveys is presented as supporting evidence for the two-regime picture, yet no error bars, quantitative metrics (e.g., spectral slopes, regime classification criteria), or discussion of how the data distinguish turbulence-induced waves from wave turbulence are supplied. This weakens the external-validation component of the central claim.
minor comments (2)
  1. [Abstract] Abstract: quantitative validation details, error analysis, and explicit regime-boundary criteria are absent; these should be added to allow readers to assess the strength of the reported agreement.
  2. [Theory section] Notation: the distinction between 'intrinsic surface dynamics' and 'enslaved interface' should be defined with a clear, non-dimensional threshold (e.g., a critical value of a surface-response parameter) rather than left qualitative.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which identify important gaps in quantitative support for the central claims. We respond to each major comment below and will revise the manuscript accordingly to strengthen the presentation of the simulation results and the ocean-data comparison.

read point-by-point responses

  1. Referee: [Simulations section] Simulations section (and associated figures): the claim that 'fully resolved and nonlinear simulations do not inhibit the onset of wave turbulence' yet exhibit 'strong agreement with theoretical predictions' is load-bearing for the decision to drop nonlinear wave-wave terms. No quantitative diagnostics are provided for wave steepness, nonlinear interaction time scales relative to simulation duration, or spectral signatures of an energy cascade; without these it is impossible to determine whether the observed agreement reflects genuine linear dominance or simply that the nonlinear regime was not reached.

    Authors: We agree that the absence of these diagnostics limits the strength of the argument that nonlinear wave-wave interactions remain negligible. In the revised manuscript we will add explicit calculations of wave steepness, estimates of nonlinear interaction timescales relative to the simulation duration, and spectral analysis for signatures of an energy cascade. These additions will be placed in the Simulations section and associated figures to allow direct assessment of whether the nonlinear regime was reached. revision: yes

  2. Referee: [Ocean-data comparison] Ocean-data comparison paragraph: the reported 'notable agreement' with aerial surveys is presented as supporting evidence for the two-regime picture, yet no error bars, quantitative metrics (e.g., spectral slopes, regime classification criteria), or discussion of how the data distinguish turbulence-induced waves from wave turbulence are supplied. This weakens the external-validation component of the central claim.

    Authors: We acknowledge that the ocean-data comparison is presented qualitatively and lacks error bars or quantitative metrics. The available aerial survey data do not contain the detailed spectral information or error estimates needed for a rigorous quantitative comparison or clear regime classification. In the revision we will expand the paragraph to state these limitations explicitly, include any quantitative aspects that can be extracted from the published surveys (such as reported spectral slopes), and clarify that the comparison serves as supplementary rather than definitive external validation. revision: partial

Circularity Check

0 steps flagged

No circularity: linear theory derived independently from pressure statistics

full rationale

The paper constructs a linear response framework for surface deformation driven by turbulent pressure fluctuations, explicitly excluding nonlinear wave-wave interactions by assumption. This derivation stands on its own from the governing equations and pressure input statistics, predicting regimes of intrinsic surface dynamics versus enslaved interface without reducing to fitted outputs or self-referential definitions. Validation against fully nonlinear simulations and ocean data is presented as external support rather than a forced consequence of the theory itself. No load-bearing self-citations, ansatz smuggling, or renaming of known results appear in the derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper adds a linear response model; core assumptions are standard in fluid dynamics with no new free parameters or entities introduced in the abstract.

axioms (1)
  • domain assumption Surface response is linear in pressure fluctuations from turbulence
    Theory excludes nonlinear wave-wave interactions by construction.

pith-pipeline@v0.9.0 · 8899 in / 980 out tokens · 188347 ms · 2026-05-25T03:40:36.646363+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

300 extracted references · 300 canonical work pages · 4 internal anchors

  1. [1]

    Earth Syst

    Global Carbon Budget 2024 , author =. Earth Syst. Sci. Data , year =

    work page 2024

  2. [2]

    A comprehensive analysis of air--sea CO2 flux uncertainties constructed from surface ocean data products , author =. Glob. Biogeochem. Cycles , year =

    work page

  3. [3]

    Relationship between wind speed and gas exchange over the ocean revisited , author =. Limnol. Oceanogr.: Methods , year =

    work page

  4. [4]

    An eddy cell model of mass transfer into the surface of a turbulent liquid , author =. AIChE J. , year =

    work page

  5. [5]

    Environmental turbulent mixing controls on air--water gas exchange in marine and aquatic systems , author =. Geophys. Res. Lett. , year =

    work page

  6. [6]

    Bhunia and J.H

    S.K. Bhunia and J.H. Lienhard V , title =. J. Fluids Eng. , year =

    work page

  7. [7]

    Zonta and A

    F. Zonta and A. Soldati and M. Onorato , title =. J. Fluid Mech. , year =. doi:10.1017/jfm.2015.356 , publisher =

    work page doi:10.1017/jfm.2015.356 2015

  8. [8]

    Galtier , title =

    S. Galtier , title =. Geoph. Astroph. Fluid Dyn. , year =. doi:10.1080/03091929.2021.1909980 , publisher =

    work page doi:10.1080/03091929.2021.1909980 2021

  9. [9]

    Deike and D

    L. Deike and D. Fuster and M. Berhanu and E. Falcon , title =. Phys. Rev. Lett. , year =. doi:10.1103/PhysRevLett.112.234501 , publisher =

    work page doi:10.1103/physrevlett.112.234501

  10. [10]

    1994 , journal =

    Numerical Investigation of the Flow Properties of He Ii , author =. 1994 , journal =

    work page 1994

  11. [11]

    TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems

    Abadi, M. and Agarwal, A. and Barham, P. and Brevdo, E. and Chen, Z. and Citro, C. and Corrado, Greg S. and Davis, A. and Dean, J. and Devin, M. and Ghemawat, S. and Goodfellow, I. and Harp, A. and Irving, G. and Isard, M. and Jia, Y. and Jozefowicz, R. and Kaiser, L. and Kudlur, M. and Levenberg, J. and Mane, D. and Monga, R. and Moore, S. and Murray, D....

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1603.04467

  12. [12]

    2013 , journal =

    Aerodynamic Technologies to Improve Aircraft Performance , author =. 2013 , journal =. doi:10.1016/j.ast.2012.10.008 , urldate =

    work page doi:10.1016/j.ast.2012.10.008 2013

  13. [13]

    2017 , month = sep, journal =

    Drag Reduction via Turbulent Boundary Layer Flow Control , author =. 2017 , month = sep, journal =. doi:10.1007/s11431-016-9013-6 , urldate =

    work page doi:10.1007/s11431-016-9013-6 2017

  14. [14]

    and von Doenhoff, A.E

    Abbott, I.H. and von Doenhoff, A.E. , year =. Theory of

    work page

  15. [15]

    2023 , month = jul, journal =

    Scaling and Intermittency in Turbulent Flows of Elastoviscoplastic Fluids , author =. 2023 , month = jul, journal =. doi:10.1038/s41567-023-02018-2 , urldate =

    work page doi:10.1038/s41567-023-02018-2 2023

  16. [16]

    2019 , month = apr, journal =

    Modulation of Near-Wall Turbulence in the Transitionally Rough Regime , author =. 2019 , month = apr, journal =. doi:10.1017/jfm.2019.41 , urldate =

    work page doi:10.1017/jfm.2019.41 2019

  17. [17]

    2017 , month = nov, journal =

    Analysis of Anisotropically Permeable Surfaces for Turbulent Drag Reduction , author =. 2017 , month = nov, journal =. doi:10.1103/PhysRevFluids.2.114609 , urldate =

    work page doi:10.1103/physrevfluids.2.114609 2017

  18. [18]

    2017 , month = dec, journal =

    Reynolds-Number Dependence of Wall-Pressure Fluctuations in a Pressure-Induced Turbulent Separation Bubble , author =. 2017 , month = dec, journal =. doi:10.1017/jfm.2017.694 , urldate =

    work page doi:10.1017/jfm.2017.694 2017

  19. [19]

    2016 , journal =

    Relationship between the Energy Dissipation Function and the Skin Friction Law in a Turbulent Channel Flow , author =. 2016 , journal =

    work page 2016

  20. [20]

    2009 , journal =

    Correlation between Small-Scale Velocity and Scalar Fluctuations in a Turbulent Channel Flow , author =. 2009 , journal =

    work page 2009

  21. [21]

    2018 , journal =

    Large-Scale Structures in a Turbulent Channel Flow with a Minimal Streamwise Flow Unit , author =. 2018 , journal =

    work page 2018

  22. [22]

    and Kawamura, H

    Abe, H. and Kawamura, H. and Choi, H. , year =. Very. J. Fluids Engineering , volume =

    work page

  23. [23]

    and Kawamura, H

    Abe, H. and Kawamura, H. and Matsuo, Y. , year =. International Journal of Heat and Fluid Flow , series =. doi:10.1016/j.ijheatfluidflow.2004.02.010 , urldate =

    work page doi:10.1016/j.ijheatfluidflow.2004.02.010 2004

  24. [24]

    2017 , month = nov, journal =

    Relationship between the Heat Transfer Law and the Scalar Dissipation Function in a Turbulent Channel Flow , author =. 2017 , month = nov, journal =. doi:10.1017/jfm.2017.564 , urldate =

    work page doi:10.1017/jfm.2017.564 2017

  25. [25]

    2017 , month = jun, journal =

    Identification of Flow Regimes around Two Staggered Square Cylinders by a Numerical Study , author =. 2017 , month = jun, journal =. doi:10.1007/s00162-017-0424-2 , urldate =

    work page doi:10.1007/s00162-017-0424-2 2017

  26. [26]

    2005 , journal =

    Friction Drag Resulting from the Simultaneous Imposed Motions of a Freestream and Its Bounding Surface , author =. 2005 , journal =

    work page 2005

  27. [27]

    1975 , month = nov, journal =

    Collision Rates of Small Particles in a Vigorously Turbulent Fluid , author =. 1975 , month = nov, journal =. doi:10.1016/0009-2509(75)85067-6 , urldate =

    work page doi:10.1016/0009-2509(75)85067-6 1975

  28. [28]

    and Stegun, I.A

    Abramowitz, M. and Stegun, I.A. , year =. Handbook of

    work page

  29. [29]

    2020 , month = oct, journal =

    Resolvent Modelling of Near-Wall Coherent Structures in Turbulent Channel Flow , author =. 2020 , month = oct, journal =. doi:10.1016/j.ijheatfluidflow.2020.108662 , urldate =

    work page doi:10.1016/j.ijheatfluidflow.2020.108662 2020

  30. [30]

    and Smith, C.R

    Acarlar, M.S. and Smith, C.R. , year =. A. J. Fluid Mech. , volume =

    work page

  31. [31]

    and Chang, M

    Acharya, N. and Chang, M. S. H.-C. , year =. Heat. Int. J. Heat Mass Transfer , volume =

    work page

  32. [32]

    Experiments on the Flow Past Spheres at Very High

    Achenbach, Elmar , year =. Experiments on the Flow Past Spheres at Very High. Journal of Fluid Mechanics , volume =. doi:10.1017/S0022112072000874 , urldate =

    work page doi:10.1017/s0022112072000874

  33. [33]

    1974 , month = jan, journal =

    Vortex Shedding from Spheres , author =. 1974 , month = jan, journal =. doi:10.1017/S0022112074000644 , urldate =

    work page doi:10.1017/s0022112074000644 1974

  34. [34]

    Ackerman, J. D. and Okubo, A. , year =. Reduced. Funct. Ecol. , volume =. doi:10.2307/2390209 , urldate =. 2390209 , eprinttype =

    work page doi:10.2307/2390209

  35. [35]

    2007 , month = apr, journal =

    Hairpin Vortex Organization in Wall Turbulence , author =. 2007 , month = apr, journal =. doi:10.1063/1.2717527 , urldate =

    work page doi:10.1063/1.2717527 2007

  36. [36]

    2000 , journal =

    Vortex Organization in the Outer Region of the Turbulent Boundary Layer , author =. 2000 , journal =

    work page 2000

  37. [37]

    Adrian, R. J. and Moin, P. , year =. Stochastic Estimation of Organized Turbulent Structure: Homogeneous Shear Flow , shorttitle =. Journal of Fluid Mechanics , volume =. doi:10.1017/S0022112088001442 , urldate =

    work page doi:10.1017/s0022112088001442

  38. [38]

    2017 , month = sep, journal =

    On the Role of Initial Velocities in Pair Dispersion in a Microfluidic Chaotic Flow , author =. 2017 , month = sep, journal =. doi:10.1038/s41467-017-00389-8 , urldate =

    work page doi:10.1038/s41467-017-00389-8 2017

  39. [39]

    Millikan's Argument at Moderately Large

    Afzal, Noor , year =. Millikan's Argument at Moderately Large. The Physics of Fluids , volume =

    work page

  40. [40]

    and Kim, K.-Y

    Afzal, A. and Kim, K.-Y. , year =. Optimization of. Chem. Eng. J. , volume =

    work page

  41. [41]

    and Kim, K.-Y

    Afzal, A. and Kim, K.-Y. , year =. Passive. Chem. Eng. J. , volume =

    work page

  42. [42]

    2016 , month = mar, journal =

    Laminar and Turbulent Flows over Hydrophobic Surfaces with Shear-Dependent Slip Length , author =. 2016 , month = mar, journal =. doi:10.1063/1.4943671 , urldate =

    work page doi:10.1063/1.4943671 2016

  43. [43]

    2016 , month = jan, journal =

    Skewness-Induced Asymmetric Modulation of Small-Scale Turbulence by Large-Scale Structures , author =. 2016 , month = jan, journal =. doi:10.1063/1.4939718 , urldate =

    work page doi:10.1063/1.4939718 2016

  44. [44]

    2014 , journal =

    On the Influence of Outer Large-Scale Structures on near-Wall Turbulence in Channel Flow , author =. 2014 , journal =. doi:10.1063/1.4890745 , urldate =

    work page doi:10.1063/1.4890745 2014

  45. [45]

    and Leschziner, M

    Agostini, L. and Leschziner, M. , year =. Spectral Analysis of Near-Wall Turbulence in Channel Flow at. Phys. Rev. Fluids , volume =

    work page

  46. [46]

    Agostini, Lionel and Leschziner, Michael , year =. The. Flow Turbulence Combust , volume =. doi:10.1007/s10494-018-9917-3 , urldate =

    work page doi:10.1007/s10494-018-9917-3

  47. [47]

    2019 , month = jul, journal =

    The Connection between the Spectrum of Turbulent Scales and the Skin-Friction Statistics in Channel Flow At , author =. 2019 , month = jul, journal =. doi:10.1017/jfm.2019.297 , urldate =

    work page doi:10.1017/jfm.2019.297 2019

  48. [48]

    2019 , month = jul, journal =

    On the Departure of Near-Wall Turbulence from the Quasi-Steady State , author =. 2019 , month = jul, journal =. doi:10.1017/jfm.2019.395 , urldate =

    work page doi:10.1017/jfm.2019.395 2019

  49. [49]

    and Touber, E

    Agostini, L. and Touber, E. and Leschziner, M.A. , year =. Spanwise Oscillatory Wall Motion in Channel Flow: Drag-Reduction Mechanisms Inferred from. J. Fluid Mech. , volume =

    work page

  50. [50]

    2015 , journal =

    The Turbulence Vorticity as a Window to the Physics of Friction-Drag Reduction by Oscillatory Wall Motion , author =. 2015 , journal =

    work page 2015

  51. [51]

    2021 , month = sep, journal =

    Statistical Analysis of Outer Large-Scale/Inner-Layer Interactions in Channel Flow Subjected to Oscillatory Drag-Reducing Wall Motion Using a Multiple-Variable Joint-Probability-Density Function Methodology , author =. 2021 , month = sep, journal =. doi:10.1017/jfm.2021.585 , urldate =

    work page doi:10.1017/jfm.2021.585 2021

  52. [52]

    Large scale dynamics in turbulent Rayleigh-Benard convection

    Ahlers, Guenter and Grossmann, Siegfried and Lohse, Detlef , year =. Large Scale Dynamics in Turbulent. Rev. Mod. Phys. , volume =. doi:10.1103/RevModPhys.81.503 , urldate =. arXiv , keywords =:0811.0471 , primaryclass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/revmodphys.81.503

  53. [53]

    2015 , month = jan, journal =

    Numerical Investigation of Turbulent-Drag Reduction Induced by Active Control of Streamwise Travelling Waves of Wall-Normal Velocity , author =. 2015 , month = jan, journal =. doi:10.1016/j.euromechflu.2014.09.004 , urldate =

    work page doi:10.1016/j.euromechflu.2014.09.004 2015

  54. [54]

    2000 , month = nov, journal =

    On the Mechanisms of Modifying the Structure of Turbulent Homogeneous Shear Flows by Dispersed Particles , author =. 2000 , month = nov, journal =. doi:10.1063/1.1308509 , urldate =

    work page doi:10.1063/1.1308509 2000

  55. [55]

    2003 , journal =

    Film Cooling from Two Rows of Holes with Opposite Orientation Angles: Injectant Behavior and Adiabatic Film Cooling Effectiveness , author =. 2003 , journal =

    work page 2003

  56. [56]

    Direct Numerical Simulation of a

    Ahn, Junsun and Lee, Jae Hwa and Lee, Jin and Kang, Ji-hoon and Sung, Hyung Jin , year =. Direct Numerical Simulation of a. Physics of Fluids , volume =. doi:10.1063/1.4922612 , urldate =

    work page doi:10.1063/1.4922612

  57. [57]

    1993 , month = jun, journal =

    Turbulence Control in Wall-Bounded Flows by Spanwise Oscillations , author =. 1993 , month = jun, journal =. doi:10.1007/BF01082552 , urldate =

    work page doi:10.1007/bf01082552 1993

  58. [58]

    1993 , journal =

    Control of Wall Turbulence by High Frequency Wall Oscillations , author =. 1993 , journal =

    work page 1993

  59. [59]

    and Kamm, R

    Akhavan, R. and Kamm, R. D. and Shapiro, A. H. , year =. An Investigation of Transition to Turbulence in Bounded Oscillatory. Journal of Fluid Mechanics , volume =

    work page

  60. [60]

    2024 , month = dec, journal =

    Envelope Boundary Conditions for the Upper Surface of Two-Dimensional Canopy Interacting with Fluid Flow , author =. 2024 , month = dec, journal =. doi:10.1007/s10404-024-02779-z , urldate =

    work page doi:10.1007/s10404-024-02779-z 2024

  61. [61]

    2018 , month = nov, journal =

    Turbulence Structure and Similarity in the Separated Flow above a Low Building in the Atmospheric Boundary Layer , author =. 2018 , month = nov, journal =. doi:10.1016/j.jweia.2018.09.016 , urldate =

    work page doi:10.1016/j.jweia.2018.09.016 2018

  62. [62]

    and Moin, P

    Akselvoll, K. and Moin, P. , year =. Large. Engineering

    work page

  63. [63]

    1996 , journal =

    Large-Eddy Simulation of Turbulent Confined Coannular Jets , author =. 1996 , journal =

    work page 1996

  64. [64]

    2000 , month = jan, journal =

    Direct Numerical Simulation of `Short' Laminar Separation Bubbles with Turbulent Reattachment , author =. 2000 , month = jan, journal =. doi:10.1017/S0022112099007119 , urldate =

    work page doi:10.1017/s0022112099007119 2000

  65. [65]

    2012 , journal =

    Analysis of Mixing in a Curved Microchannel with Rectangular Grooves , author =. 2012 , journal =

    work page 2012

  66. [66]

    2014 , journal =

    Mixing Performance of a Planar Micromixer with Circular Obstructions in a Curved Microchannel , author =. 2014 , journal =

    work page 2014

  67. [67]

    2019 , month = aug, journal =

    Wall-Bounded Flow over a Realistically Rough Superhydrophobic Surface , author =. 2019 , month = aug, journal =. doi:10.1017/jfm.2019.419 , urldate =

    work page doi:10.1017/jfm.2019.419 2019

  68. [68]

    2011 , month = feb, journal =

    The Wake of Two Side-by-Side Square Cylinders , author =. 2011 , month = feb, journal =. doi:10.1017/S0022112010005288 , urldate =

    work page doi:10.1017/s0022112010005288 2011

  69. [69]

    2016 , month = aug, journal =

    The Wake of Two Staggered Square Cylinders , author =. 2016 , month = aug, journal =. doi:10.1017/jfm.2016.303 , urldate =

    work page doi:10.1017/jfm.2016.303 2016

  70. [70]

    2001 , journal =

    Analysis of Fluid Flow and Heat Transfer Interfacial Conditions between a Porous Medium and a Fluid Layer , author =. 2001 , journal =

    work page 2001

  71. [71]

    2008 , month = nov, journal =

    Optimal Flexibility of a Flapping Appendage in an Inviscid Fluid , author =. 2008 , month = nov, journal =. doi:10.1017/S0022112008003297 , urldate =

    work page doi:10.1017/s0022112008003297 2008

  72. [72]

    2002 , month = dec, journal =

    Drag Reduction through Self-Similar Bending of a Flexible Body , author =. 2002 , month = dec, journal =. doi:10.1038/nature01232 , urldate =

    work page doi:10.1038/nature01232 2002

  73. [73]

    and Meysonnat, P

    Albers, M. and Meysonnat, P. S. and Schr. Actively. 2019 , month = apr, journal =. doi:10.1007/s10494-018-9998-z , urldate =

    work page doi:10.1007/s10494-018-9998-z 2019

  74. [74]

    2021 , month = apr, journal =

    Lower Drag and Higher Lift for Turbulent Airfoil Flow by Moving Surfaces , author =. 2021 , month = apr, journal =. doi:10.1016/j.ijheatfluidflow.2020.108770 , urldate =

    work page doi:10.1016/j.ijheatfluidflow.2020.108770 2021

  75. [75]

    and Fernex, Daniel and Semaan, Richard and Noack, Bernd R

    Albers, Marian and Meysonnat, Pascal S. and Fernex, Daniel and Semaan, Richard and Noack, Bernd R. and Schr. Drag. 2020 , month = jun, journal =. doi:10.1007/s10494-020-00110-8 , urldate =

    work page doi:10.1007/s10494-020-00110-8 2020

  76. [76]

    Alekseev, V. V. and Gachechiladze, I. A. and Kiknadze, G. I. and Oleinikov, V.G. , year =. Tornado-like Energy Transfer on Three-Dimensional Concavities of Reliefs-Structures of Self Organizing Flow, Their Visualisation, and Surface Streamlining Mechanism , booktitle =

    work page

  77. [77]

    2017 , month = feb, journal =

    Helically Decomposed Turbulence , author =. 2017 , month = feb, journal =. doi:10.1017/jfm.2016.831 , urldate =

    work page doi:10.1017/jfm.2016.831 2017

  78. [78]

    2021 , month = jun, journal =

    Long Non-Axisymmetric Fibres in Turbulent Channel Flow , author =. 2021 , month = jun, journal =. doi:10.1017/jfm.2021.185 , urldate =

    work page doi:10.1017/jfm.2021.185 2021

  79. [79]

    Influence of

    Alipour, Mobin and Paoli, Marco De and Soldati, Alfredo , year =. Influence of. Journal of Fluid Mechanics , volume =. doi:10.1017/jfm.2021.1145 , urldate =

    work page doi:10.1017/jfm.2021.1145 2021

  80. [80]

    2002 , journal =

    Fluid Mechanics of the Interface Region between Two Porous Layers , author =. 2002 , journal =

    work page 2002

Showing first 80 references.