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arxiv: 2606.24630 · v1 · pith:SAIPL7YFnew · submitted 2026-06-23 · ⚛️ physics.flu-dyn

How is the free surface influence transported in turbulent open channel flows?

Yoshiyuki Sakai , Christian Bauer This is my paper

Pith reviewed 2026-06-25 22:56 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords open channel flowfree surfaceturbulent kinetic energy budgetdirect numerical simulationvery-large-scale motionspressure transportviscous diffusionpressure-strain
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The pith

The free-surface influence in open-channel turbulence is transported mainly through pressure transport and viscous diffusion across multiple scales.

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

The paper compares direct numerical simulations of open and closed channel flows at matching Reynolds numbers to isolate free-surface effects on turbulence. It shows that the surface influence spreads primarily via the transport terms of the turbulent kinetic energy budget rather than through local production or dissipation alone. Pressure transport brings energy toward the interface while turbulent transport and dissipation drop, and viscous diffusion carries the excess energy outward. These budget contributions follow distinct scalings tied to different near-surface lengths, and pressure-strain events are modulated by outer-layer motions. The result frames the surface effect as a coupled process linking local constraints, Reynolds-dependent layers, and large-scale structures.

Core claim

The free-surface influence is communicated primarily through transport terms. Near the free surface, pressure transport supplies energy towards the interface, whereas turbulent transport and dissipation are reduced; the resulting energy surplus is exported away from the surface predominantly by viscous diffusion. The near-surface budget terms do not exhibit a single universal similarity scaling: viscous diffusion is organised over the near-surface viscous scale, dissipation over the Kolmogorov sublayer scale, and pressure-related terms require the mixed velocity scale. The pressure-strain redistribution further reveals outer-inner coupling organised by low-velocity streaks.

What carries the argument

The turbulent kinetic energy budget terms obtained from matched open- and closed-channel direct numerical simulations, which isolate surface-induced differences in transport, production, and redistribution.

If this is right

  • Surface effects extend into the outer layer through viscous diffusion rather than remaining confined near the interface.
  • No single similarity scaling applies to the near-surface region; separate scales govern different budget terms.
  • Outer-layer very-large-scale motions organize the magnitude and direction of pressure-strain events at the surface.
  • The overall process combines local kinematic constraints at the surface, Reynolds-number-dependent layers, and outer coherent motions.

Where Pith is reading between the lines

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

  • If the multi-scale transport persists at higher Reynolds numbers, engineering models for open-channel mixing would need to incorporate outer-layer modulation of surface layers.
  • The same transport pathways may operate in related free-surface flows such as wind-driven water bodies or shallow rivers.
  • Direct comparison of the reported budget terms against field measurements at natural Reynolds numbers could test whether the DNS scale separation survives in real flows.

Load-bearing premise

That the TKE budget differences between the open- and closed-channel runs at Re_tau up to 900 cleanly isolate free-surface transport without contamination from domain-size effects or unaccounted statistics.

What would settle it

A simulation at Re_tau well above 900 in which all near-surface TKE budget terms collapse to a single scaling law instead of showing the reported separation into viscous, Kolmogorov, and mixed scales would falsify the multi-scale transport description.

Figures

Figures reproduced from arXiv: 2606.24630 by Christian Bauer, Yoshiyuki Sakai.

Figure 1
Figure 1. Figure 1: TKE budget for OCF in the near-wall region. [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: TKE budget for OCF in the near-surface region as a function of free surface [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Near-surface production–dissipation ratio [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: TKE budget for open channel flow as a function of distance from the wall [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: TKE budget for open channel flow as a function of free surface distance. The [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: TKE budget for open channel flow as a function of free surface distance. Here [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: TKE budget for open channel flow as a function of free surface distance. Here [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Diagonal components of the pressure-strain term, here normalised by [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Instantaneous: (a) streamwise velocity fluctuation [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Conditional average of the diagonal components of the pressure-strain term [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Conceptual sketch of super-streamwise vortex preferentially inducing [PITH_FULL_IMAGE:figures/full_fig_p016_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Diagonal components of the pressure-strain term, here normalised by [PITH_FULL_IMAGE:figures/full_fig_p017_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: OCF 𝑝rms normalised by 𝑢 2 𝜏 . , O200; , O400; , O600; , O900. transport and dissipation respond to the free-surface constraint on distinct Reynolds-number￾dependent length scales. The conditional pressure–strain statistics further indicate that the redistribution process cannot be regarded as a purely local near-surface adjustment. Although the instantaneous pressure–strain events remain small-scale, the… view at source ↗
Figure 14
Figure 14. Figure 14: TKE budget for open channel flow as a function of free surface distance. Here [PITH_FULL_IMAGE:figures/full_fig_p020_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: ⟨𝑢 ′𝑢 ′ ⟩ budget for OCF in the near-surface region as a function of free surface distance. , production; , pseudo-dissipation; , viscous diffusion; , turbulent transport; , pressure-strain. The magnitudes of the terms are normalised by 𝑢 4 𝜏 /𝜈, whereas the vertical positions are normalised by the outer scale ℎ. (a) O200; (b) O400; (c) O600; (d) O900. Grey lines indicate the corresponding CCF data. Notic… view at source ↗
Figure 16
Figure 16. Figure 16: ⟨𝑣 ′ 𝑣 ′ ⟩ budget for OCF in the near-surface region as a function of free surface distance. , pseudo-dissipation; , viscous diffusion; , turbulent transport; , pressure transport; , pressure-strain. The magnitudes of the terms are normalised by 𝑢 4 𝜏 /𝜈, whereas the vertical positions are normalised by the outer scale ℎ. (a) O200; (b) O400; (c) O600; (d) O900. Grey lines indicate the corresponding CCF da… view at source ↗
Figure 17
Figure 17. Figure 17: ⟨𝑤 ′𝑤 ′ ⟩ budget for OCF in the near-surface region as a function of free surface distance. , pseudo-dissipation; , viscous diffusion; , turbulent transport; , pressure-strain. The magnitudes of the terms are normalised by 𝑢 4 𝜏 /𝜈, whereas the vertical positions are normalised by the outer scale ℎ. (a) O200; (b) O400; (c) O600; (d) O900. Grey lines indicate the corresponding CCF data. Notice a difference… view at source ↗
Figure 18
Figure 18. Figure 18: ⟨𝑢 ′ 𝑖 𝑢 ′ 𝑖 ⟩ budget for open channel flow as a function of free surface distance. (a,b) ⟨𝑢 ′𝑢 ′ ⟩; (c,d) ⟨𝑣 ′ 𝑣 ′ ⟩; (e,f) ⟨𝑤 ′𝑤 ′ ⟩. Here normalised by 𝑢 3 𝜏 /ℎ. Solid ( ) lines, O200; dashed ( ) lines, O400; dash-dotted ( ) lines, O600; dotted ( ) lines, O900. , production; , pseudo-dissipation; , viscous diffusion; , turbulent transport; , pressure transport; , pressure-strain. The distance from the … view at source ↗
Figure 19
Figure 19. Figure 19: ⟨𝑢 ′ 𝑖 𝑢 ′ 𝑖 ⟩ budget for open channel flow as a function of free surface distance. (a,b) ⟨𝑢 ′𝑢 ′ ⟩; (c,d) ⟨𝑣 ′ 𝑣 ′ ⟩; (e,f) ⟨𝑤 ′𝑤 ′ ⟩. Here normalised by 𝑢 3 b /ℎ. Solid ( ) lines, O200; dashed ( ) lines, O400; dash-dotted ( ) lines, O600; dotted ( ) lines, O900. , production; , pseudo-dissipation; , viscous diffusion; , turbulent transport; , pressure transport; , pressure-strain. The distance from the … view at source ↗
Figure 20
Figure 20. Figure 20: ⟨𝑢 ′ 𝑖 𝑢 ′ 𝑖 ⟩ budget for open channel flow as a function of free surface distance. (a,b) ⟨𝑢 ′𝑢 ′ ⟩; (c,d) ⟨𝑣 ′ 𝑣 ′ ⟩; (e,f) ⟨𝑤 ′𝑤 ′ ⟩. Here normalised by 𝑢b𝑢 2 𝜏 /ℎ. Solid ( ) lines, O200; dashed ( ) lines, O400; dash-dotted ( ) lines, O600; dotted ( ) lines, O900. , production; , pseudo-dissipation; , viscous diffusion; , turbulent transport; , pressure transport. , pressure-strain. The distance from th… view at source ↗
Figure 21
Figure 21. Figure 21: ⟨𝑢 ′ 𝑖 𝑢 ′ 𝑖 ⟩ budget for open channel flow as a function of free surface distance. (a,b) ⟨𝑢 ′𝑢 ′ ⟩; (c,d) ⟨𝑣 ′ 𝑣 ′ ⟩; (e,f) ⟨𝑤 ′𝑤 ′ ⟩. Here normalised by 𝑢 2 b 𝑢𝜏 /ℎ. Solid ( ) lines, O200; dashed ( ) lines, O400; dash-dotted ( ) lines, O600; dotted ( ) lines, O900. , production; , pseudo-dissipation; , viscous diffusion; , turbulent transport; , pressure transport. , pressure-strain. The distance from t… view at source ↗
Figure 22
Figure 22. Figure 22: Diagonal components of the pressure-strain term, here normalised by [PITH_FULL_IMAGE:figures/full_fig_p029_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: Diagonal components of the pressure-strain term, here normalised by [PITH_FULL_IMAGE:figures/full_fig_p029_23.png] view at source ↗
read the original abstract

We investigate how the influence of a free surface is transported in turbulent open channel flow by analysing matched open- and closed-channel direct numerical simulations up to $Re_\mathrm{\tau} \approx 900$ in a domain large enough to accommodate very-large-scale motions (VLSMs). The turbulent kinetic energy (TKE) budget shows that the surface influence is communicated primarily through transport terms. Near the free surface, pressure transport supplies energy towards the interface, whereas turbulent transport and dissipation are reduced; the resulting energy surplus is exported away from the surface predominantly by viscous diffusion. The near-surface budget terms do not exhibit a single universal similarity scaling: viscous diffusion is organised over the near-surface viscous scale $\ell_\mathrm{V}$, dissipation over the Kolmogorov sublayer scale $\ell_\mathrm{K}$, and pressure-related terms require the mixed velocity scale $u_\mathrm{b} u_\mathrm{\tau}^2 /h$. The pressure-strain redistribution further reveals outer-inner coupling: although intense pressure-strain events remain small-scale, their magnitude and directional bias are organised by low-velocity VLSM streaks. The free-surface influence is therefore best understood as a coupled multi-scale process involving local kinematic constraints, Reynolds-number-dependent surface layers, and outer-layer coherent motions.

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 / 1 minor

Summary. The manuscript claims that free-surface influence in turbulent open channel flow is transported primarily via TKE budget transport terms, based on differences between matched open- and closed-channel DNS up to Re_τ ≈ 900 in a domain sized for VLSMs. Near the surface, pressure transport supplies energy to the interface while turbulent transport and dissipation are reduced, with the surplus exported by viscous diffusion. Budget terms lack a single universal scaling (viscous diffusion on ℓ_V, dissipation on ℓ_K, pressure terms on u_b u_τ²/h). Pressure-strain redistribution shows outer-inner coupling, with small-scale events organized in magnitude and bias by low-velocity VLSM streaks. The influence is therefore a coupled multi-scale process of local kinematics, Re-dependent layers, and outer coherent motions.

Significance. If the DNS budget differences robustly isolate surface-driven transport, the work clarifies that free-surface effects are not purely local but involve VLSM-mediated coupling across scales. The matched open/closed-channel setup and large domain (to accommodate VLSMs) are clear strengths, providing direct comparative evidence without ad-hoc parameters.

major comments (2)
  1. [TKE budget analysis] TKE budget analysis (abstract and results): the central claim that budget differences isolate free-surface transport rests on unshown numerical evidence; no quantitative error bars, grid-convergence studies, or explicit validation against established closed-channel benchmarks are reported, which is load-bearing because residual domain-size effects or higher-order contamination could produce similar imbalances without the claimed kinematic constraints.
  2. [Pressure-strain analysis] Pressure-strain and VLSM coupling (discussion): the interpretation that VLSM streaks organize the magnitude and directional bias of pressure-strain events assumes the chosen domain and Re_τ range fully eliminate box-size modulation of mean shear or unclosed correlations; without explicit checks this remains a correctness risk for the outer-inner coupling claim.
minor comments (1)
  1. [Abstract] The mixed velocity scale u_b u_τ²/h is introduced in the abstract without a preceding definition or reference, which reduces immediate clarity for readers.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive report. We respond point-by-point to the major comments below and indicate where revisions will be made to address the concerns.

read point-by-point responses

  1. Referee: [TKE budget analysis] TKE budget analysis (abstract and results): the central claim that budget differences isolate free-surface transport rests on unshown numerical evidence; no quantitative error bars, grid-convergence studies, or explicit validation against established closed-channel benchmarks are reported, which is load-bearing because residual domain-size effects or higher-order contamination could produce similar imbalances without the claimed kinematic constraints.

    Authors: We agree that explicit documentation of numerical validation strengthens the central claim. The DNS were performed with resolutions sufficient to resolve the Kolmogorov scale, and the closed-channel cases were validated against established benchmarks (mean profiles and Reynolds stresses) at comparable Re_τ. Residuals in the TKE budget are below 1% of production. To make this evidence visible, we will add a dedicated numerical-methods subsection with quantitative comparisons, grid-convergence metrics, and error estimates in the revised manuscript. revision: yes

  2. Referee: [Pressure-strain analysis] Pressure-strain and VLSM coupling (discussion): the interpretation that VLSM streaks organize the magnitude and directional bias of pressure-strain events assumes the chosen domain and Re_τ range fully eliminate box-size modulation of mean shear or unclosed correlations; without explicit checks this remains a correctness risk for the outer-inner coupling claim.

    Authors: The domain was sized according to literature criteria for VLSM capture, and the mean shear and low-order statistics match those from smaller-domain closed-channel simulations, indicating negligible box-size modulation. Pressure-strain terms are obtained directly from the resolved fields. Nevertheless, to remove any ambiguity we will insert explicit checks (streamwise spectra, two-point correlations, and mean-shear comparisons with literature) in the revised discussion section. revision: yes

Circularity Check

0 steps flagged

No circularity: claims are direct DNS observations

full rationale

The paper's central claims derive from comparative analysis of TKE budget terms extracted from matched open- and closed-channel DNS at Re_τ up to 900. Differences in pressure transport, turbulent transport, viscous diffusion, dissipation, and pressure-strain events are reported as empirical findings and interpreted as evidence of multi-scale transport. No equations define a quantity in terms of itself, no fitted parameters are relabeled as predictions, and no load-bearing steps rely on self-citations or imported uniqueness theorems. The derivation chain consists of simulation data processing and direct comparison, remaining self-contained against external benchmarks without reduction to author-defined inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work rests on the standard incompressible Navier-Stokes equations solved by DNS; no additional free parameters, ad-hoc axioms, or new entities are introduced in the abstract.

axioms (1)
  • standard math Incompressible Navier-Stokes equations govern the velocity field
    Implicit foundation of all DNS reported in the abstract

pith-pipeline@v0.9.1-grok · 5748 in / 1248 out tokens · 21989 ms · 2026-06-25T22:56:35.970345+00:00 · methodology

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Reference graph

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