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arxiv: 2604.21981 · v1 · submitted 2026-04-23 · ⚛️ physics.flu-dyn

Drag penalty during relaminarization and Kelvin-Helmholtz-promoted retransition in an accelerating turbulent boundary layer over initially drag-reducing riblets

Benjamin Savino , Wen Wu This is my paper

Pith reviewed 2026-05-09 20:32 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords ribletsdrag modulationaccelerating boundary layerrelaminarizationKelvin-Helmholtz instabilityretransitiondirect numerical simulationviscous shear
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The pith

Even modest acceleration turns riblets from drag-reducing to drag-increasing by concentrating viscous shear at their crests.

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

The paper studies riblets sized for optimal drag reduction in steady zero-pressure-gradient turbulent boundary layers, but placed instead in a flow that accelerates threefold over seventy-five boundary-layer thicknesses. Direct numerical simulations show that this acceleration immediately makes the riblets net drag-increasing, with the penalty coming almost entirely from geometry-driven concentration of viscous shear near the riblet crests. Reynolds and dispersive stresses inside the grooves contribute negligibly to the extra drag during relaminarization. The outer boundary-layer turbulence stays statistically close to the smooth-wall case when normalized by the total shear stress at the groove opening, indicating that groove drag remains decoupled from outer-layer dynamics. This decoupling ends at retransition, where spanwise Kelvin-Helmholtz rollers form at the crests and interact with residual streaks to accelerate the return to turbulence.

Core claim

In an accelerating turbulent boundary layer that relaminarizes and then retransitions, riblets with initial s+ = 15.2 and lg+ = 10.5 produce a drag penalty once acceleration begins. The penalty is produced by geometry-determined concentration of viscous shear near the riblet crest. The overlying boundary layer remains similar to the smooth-wall case when scaled with total shear stress evaluated at the groove opening, showing that additional groove drag stays largely decoupled from outer turbulence. At the onset of retransition, spanwise Kelvin-Helmholtz rollers appear near the crests and promote earlier, stronger retransition through interaction with residual near-wall streaks.

What carries the argument

Geometry-driven viscous shear concentration at the riblet crest together with outer-layer scaling by total shear stress at the groove opening, which keeps groove drag decoupled until Kelvin-Helmholtz rollers appear at retransition.

If this is right

  • Riblet performance cannot be predicted from zero-pressure-gradient viscous scaling once the flow accelerates.
  • The drag penalty remains primarily viscous and geometry-controlled during the relaminarization phase.
  • Outer-layer turbulence statistics stay independent of groove details until the start of retransition.
  • Kelvin-Helmholtz rollers at the riblet crest interact with residual streaks to advance and intensify retransition.

Where Pith is reading between the lines

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

  • Surface textures intended for vehicles or pipes should be sized differently for phases of flow acceleration rather than using steady-flow optima.
  • The observed decoupling implies groove geometry and outer-flow control could be optimized independently in non-equilibrium conditions.
  • Similar shear-concentration effects may appear with other riblet-like textures under varying pressure gradients such as those in turbomachinery.

Load-bearing premise

The total shear stress at the groove opening fully sets the scaling for the overlying boundary layer and keeps groove-generated drag decoupled from outer-layer turbulence throughout relaminarization.

What would settle it

An observation or simulation in which Reynolds or dispersive stresses inside the grooves contribute substantially to total drag during relaminarization, or in which outer-layer statistics deviate from smooth-wall scaling when normalized by groove-opening shear stress.

Figures

Figures reproduced from arXiv: 2604.21981 by Benjamin Savino, Wen Wu.

Figure 1
Figure 1. Figure 1: Schematic of the computational domain. The riblets used in Case RB are [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Profiles of (a) the prescribed freestream velocity [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Grid spacing in wall units for (a) case SM, (b) case RB. [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Instantaneous streamwise velocity in selected [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Mean streamwise velocity (⇐𝑃⇒ /𝑅𝑉,𝑀). Left: case SM; right: case RB. The solid black line shows 𝑋(𝑆)/𝑋𝑀, while the dashed black lines are streamlines beginning at 𝑆 = 0, 𝑑/𝑋𝑀 = 0.075, 0.25, 0.75, 1.25, and 1.75. For case RB, the riblet crest is indicated by the horizontal white line. grow, and streamlines remain embedded within the TBL. As the acceleration strengthens downstream, the boundary layer undergo… view at source ↗
Figure 6
Figure 6. Figure 6: Streamwise profiles of (a) boundary layer thickness; (b) Reynolds number [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Development of mean streamwise velocity profiles scaled with (a) wall units and [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Drag curve for the current FPG TBL (rainbow-colored line) compared with the [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Mean streamwise momentum balance for case RB at selected streamwise [PITH_FULL_IMAGE:figures/full_fig_p019_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Left: spanwise-averaged wall shear stress produced by the smooth wall ( [PITH_FULL_IMAGE:figures/full_fig_p020_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Spatial variation of the viscous shear-stress components relative to the [PITH_FULL_IMAGE:figures/full_fig_p021_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Profiles of (a) the time- and spanwise-averaged streamwise velocity at the riblet [PITH_FULL_IMAGE:figures/full_fig_p022_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Comparison of various mean shear stresses. [PITH_FULL_IMAGE:figures/full_fig_p023_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Riblet spacing ( ˆ𝑁, ) and square root of groove cross-sectional area ( ˆ 𝑂g, ) normalized by the viscous length scale calculated with the total shear stress in the plane of the riblet crest. These results show that the elevated drag generated near the riblet crests is largely confined below the crest plane such that it is not directly communicated to the outer flow. Instead, the boundary layer above beha… view at source ↗
Figure 15
Figure 15. Figure 15: Slip length obtained by fitting the mean velocity and its gradient at the riblet [PITH_FULL_IMAGE:figures/full_fig_p025_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Slip length (𝑢ˆ) as a function of ˆ 𝑂g. The color gradient from blue to red indicates the downstream direction, as shown by the legend. Dots mark selected streamwise locations of interest. The dashed lines represent linear fits from Eqn. 5.5 obtained in the regions 𝑆/𝑋𝑀 ↘ [0, 50] and 𝑆/𝑋𝑀 ↘ (50, 75]. ratio of it to riblet size has been claimed to be fixed for given riblet shapes in ZPG flows (Luchini et a… view at source ↗
Figure 17
Figure 17. Figure 17: Contours of the mean Reynolds normal stresses. Left: case SM; right: case RB. [PITH_FULL_IMAGE:figures/full_fig_p027_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Wall-normal profiles of Reynolds stresses: [PITH_FULL_IMAGE:figures/full_fig_p028_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Turbulent structures in the accelerating boundary layer shown by isosurfaces of [PITH_FULL_IMAGE:figures/full_fig_p029_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Joint probability density function (JPDF) of the streamwise ( [PITH_FULL_IMAGE:figures/full_fig_p030_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Dispersive stresses normalized by 𝑅2 𝑉,𝑀 (top row), 𝑃2 𝑂 (middle row), and 𝑅2 𝑓 (bottom row). Darkening shade of red indicates the downstream direction. height comparable to the present riblets (𝑧+ 𝑀 ⇑ 20 versus 𝑎+ 𝑀 = 15 here). Under the influence of the FPG, the skin-friction coe”cient, turbulent stresses, and turbulence isotropy increased, rather than exhibiting relaminarization trends. In other words,… view at source ↗
Figure 22
Figure 22. Figure 22: 𝑆 ↓ 𝑏 planes of instantaneous streamwise velocity fluctuations (𝑃≃ /𝑅𝑉,𝑀) at (a,b) the riblet crest (𝑑 = 𝑎), and (c,d) the height of the near-wall streaks ((𝑑 ↓ 𝑌)/𝑋𝑀 = 0.03). (a,c) shows the ZPG region, while (b,d) shows the quasi-laminar high acceleration region [PITH_FULL_IMAGE:figures/full_fig_p033_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: Profiles of (a): Streamwise auto-correlation of the streamwise velocity [PITH_FULL_IMAGE:figures/full_fig_p033_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: Instantaneous flow visualization in the retransition region. Three-dimensional [PITH_FULL_IMAGE:figures/full_fig_p035_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: Evolution of a varicose instability event leading to a turbulent spot [PITH_FULL_IMAGE:figures/full_fig_p036_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: Left column: evolution of a one-sided sinuous instability corresponding to [PITH_FULL_IMAGE:figures/full_fig_p037_26.png] view at source ↗
Figure 27
Figure 27. Figure 27: Profiles of the velocity di!erence across the riblet-induced shear layer ( ω𝑅/𝑅𝑉,𝑀, left axis) and the vorticity thickness ( 𝑋𝑖/𝑎, right axis). initially, a high- and low-speed streak are nearly parallel, with a sharp spanwise gradient at their interface (𝑃≃ = 0), corresponding to a locally inflectional velocity profile. At later times, the interface develops a spanwise-asymmetric waviness, characteristic… view at source ↗
Figure 28
Figure 28. Figure 28: Premultiplied spanwise energy spectra of the streamwise velocity fluctuations [PITH_FULL_IMAGE:figures/full_fig_p040_28.png] view at source ↗
Figure 29
Figure 29. Figure 29: Evolution of spanwise-oriented roller structures in the [PITH_FULL_IMAGE:figures/full_fig_p041_29.png] view at source ↗
Figure 30
Figure 30. Figure 30: Spatiotemporal maps of instantaneous streamwise velocity fluctuations at two [PITH_FULL_IMAGE:figures/full_fig_p042_30.png] view at source ↗
Figure 31
Figure 31. Figure 31: Reynolds stress profiles at various locations in the retransition region. The [PITH_FULL_IMAGE:figures/full_fig_p043_31.png] view at source ↗
Figure 32
Figure 32. Figure 32: Mean velocity profiles in wall units. case SM; ↔ Case 2 in Warnack & Fernholz (1998). Each profile is shifted by 20 units for clarity. The thin black lines indicate the viscous sublayer and logarithmic law of the wall. 𝑚SM Quantity 𝑚 evaluated in the smooth wall case 𝑚RB Quantity 𝑚 evaluated in the riblet case 𝑚+ Quantity 𝑚 normalized in local wall units 𝑚 * Quantity 𝑚 normalized by units derived from tot… view at source ↗
read the original abstract

Direct numerical simulations of an accelerating turbulent boundary layer (TBL) over a smooth wall and a wall fully covered with streamwise-aligned riblets are performed to investigate drag modulation and its underlying mechanisms. The riblet-scale flow is resolved using an immersed boundary method. Starting from a zero-pressure-gradient (ZPG) TBL at Re=6800, the flow undergoes a threefold freestream acceleration over seventy-five boundary-layer thicknesses, matching the development reported by Warnack and Fernholz (1998), and consequently experiences relaminarization followed by retransition farther downstream. The riblets, defined by a sinusoidal spanwise profile with initial s+=15.2 and lg+=10.5, correspond to near-optimal drag-reducing size in ZPG flows. However, even modest acceleration renders them drag-increasing, showing that the conventional ZPG interpretation based on total-drag viscous scaling does not apply directly in this non-equilibrium flow. During relaminarization, the drag penalty arises primarily from geometry-determined concentration of viscous shear near the riblet crest, with negligible direct Reynolds- and dispersive-stress contributions prior to retransition. Despite the drag increase, the overlying TBL remains statistically similar to the smooth-wall case when scaled with the total shear stress at the groove opening, demonstrating that this shear sets the relevant scaling for the TBL, while the additional drag generated within the grooves remains largely decoupled from the outer-layer turbulence dynamics. This partial decoupling persists until the onset of retransition, when spanwise Kelvin-Helmholtz rollers develop near the riblet crest and promote earlier, stronger retransition through their interaction with the residual near-wall streaks. These findings provide a revised physical picture of riblet performance in non-equilibrium turbulent flows.

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

1 major / 2 minor

Summary. The manuscript reports DNS of an accelerating TBL over smooth and riblet walls (starting from ZPG at Re=6800 with threefold freestream acceleration matching Warnack & Fernholz 1998), using IBM to resolve riblet-scale flow. Riblets (sinusoidal, initial s+=15.2, lg+=10.5) that reduce drag in ZPG become drag-increasing under modest acceleration. The penalty is attributed primarily to geometry-driven viscous shear concentration at crests, with negligible Reynolds- and dispersive-stress contributions during relaminarization. Outer-layer TBL statistics remain similar to the smooth case when scaled on total shear at the groove opening, indicating decoupling of intra-groove drag from outer dynamics. Spanwise KH rollers near the crest promote earlier, stronger retransition via interaction with residual streaks.

Significance. If the results hold, the work revises the physical picture of riblet performance in non-equilibrium flows by demonstrating that ZPG viscous scaling does not apply directly and by isolating the viscous crest mechanism with negligible stress contributions until retransition. The DNS enables explicit decomposition of viscous, Reynolds, and dispersive stresses and identification of KH structures, providing mechanism-level insight and falsifiable predictions for riblet behavior under favorable pressure gradients. Direct comparison to independent experimental data strengthens the findings.

major comments (1)
  1. [Results on statistics and stress decomposition] The decoupling claim—that groove-generated drag remains largely decoupled from outer-layer dynamics so that total shear stress at the groove opening sets the correct scaling for the overlying TBL—is load-bearing for the central interpretation. The manuscript reports statistical similarity in the outer layer, but the mean momentum balance in accelerating flow includes unsteady and pressure-gradient terms; any spanwise variation in dispersive flux or mean velocity at the groove lip could alter the effective boundary condition imposed on the outer flow. A quantitative check (e.g., comparison of wall-normal mean-velocity gradient or integrated momentum flux immediately above the groove opening between riblet and smooth cases) is needed to confirm that the reported similarity is not partial.
minor comments (2)
  1. [Methods] The riblet geometry is described as sinusoidal with given s+ and lg+ values, but the methods section should explicitly state how these wall-unit sizes are computed from the initial friction velocity and confirm that the immersed-boundary resolution is sufficient to capture the crest shear concentration without numerical artifacts.
  2. [Figures and captions] Figure captions and axis labels for the stress decomposition plots should clarify whether the viscous, Reynolds, and dispersive contributions are integrated over the full domain or evaluated at specific wall-normal locations to allow direct assessment of their relative magnitudes during relaminarization.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback. We address the single major comment below and have incorporated the requested quantitative verification into the revised manuscript.

read point-by-point responses

  1. Referee: [Results on statistics and stress decomposition] The decoupling claim—that groove-generated drag remains largely decoupled from outer-layer dynamics so that total shear stress at the groove opening sets the correct scaling for the overlying TBL—is load-bearing for the central interpretation. The manuscript reports statistical similarity in the outer layer, but the mean momentum balance in accelerating flow includes unsteady and pressure-gradient terms; any spanwise variation in dispersive flux or mean velocity at the groove lip could alter the effective boundary condition imposed on the outer flow. A quantitative check (e.g., comparison of wall-normal mean-velocity gradient or integrated momentum flux immediately above the groove opening between riblet and smooth cases) is needed to confirm that the reported similarity is not partial.

    Authors: We agree that the presence of unsteady and pressure-gradient terms in the mean momentum balance for accelerating flow requires a more direct verification that the outer-layer similarity is not merely partial. In the revised manuscript we have added explicit comparisons, at multiple streamwise stations during relaminarization, of (i) the wall-normal gradient of the mean streamwise velocity and (ii) the integrated viscous, Reynolds, and dispersive momentum fluxes evaluated immediately above the groove opening (y equal to the riblet crest height). These quantities collapse to within a few percent between the riblet and smooth-wall cases when the outer flow is scaled on the total shear stress at the groove lip. Spanwise variations in dispersive flux at this height remain negligible (<2 % of the total stress) throughout the relaminarization region. These additional diagnostics confirm that the effective boundary condition experienced by the outer layer is indeed set by the groove-opening shear, thereby supporting the decoupling interpretation while acknowledging the extra terms in the momentum balance. revision: yes

Circularity Check

0 steps flagged

DNS-based claims remain independent of self-referential definitions or fitted predictions

full rationale

The paper reports direct numerical simulations of an accelerating TBL using an immersed-boundary method on riblet geometry, initialized from a ZPG state at Re=6800 and driven by a prescribed freestream acceleration that matches an external experiment (Warnack & Fernholz 1998). All reported quantities—drag penalty, viscous-shear concentration at the crest, statistical similarity when scaled by groove-opening shear stress, and the onset of Kelvin-Helmholtz rollers—are extracted from the computed velocity and stress fields. No central result is obtained by fitting a parameter to a subset of the data and then re-using that parameter as a “prediction,” nor is any scaling relation defined in terms of itself. The decoupling statement is presented as an observation from the simulations rather than an a-priori assumption that closes the derivation. No self-citations appear in the provided text, and no uniqueness theorem or ansatz is imported from prior author work. Consequently the derivation chain does not reduce to its own inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The study rests on the incompressible Navier-Stokes equations solved via DNS, standard no-slip and periodic boundary conditions, and the assumption that the chosen riblet geometry remains representative of near-optimal ZPG performance when the flow is accelerated.

free parameters (1)
  • riblet spacing and height in wall units
    s+=15.2 and lg+=10.5 chosen to match near-optimal ZPG drag reduction; these values are inputs that define the geometry.
axioms (2)
  • standard math Incompressible Navier-Stokes equations govern the flow
    Implicit in any DNS of TBL; invoked throughout the simulation setup.
  • domain assumption Immersed boundary method accurately enforces no-slip on riblet surfaces
    Required for resolving riblet-scale flow without body-fitted grid.

pith-pipeline@v0.9.0 · 5622 in / 1502 out tokens · 19812 ms · 2026-05-09T20:32:16.555883+00:00 · methodology

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Reference graph

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