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arxiv: 2601.11137 · v2 · submitted 2026-01-16 · ⚛️ physics.flu-dyn

Scale-resolving simulations and data-driven modal analysis of turbulent transonic buffet cells on infinite swept wings

David J. Lusher , Andrea Sansica This is my paper

Pith reviewed 2026-05-16 13:50 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords transonic buffetswept wingsshock boundary layer interactionlarge-eddy simulationmodal analysisthree-dimensional instabilitiesflow separation
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0 comments X

The pith

Transonic buffet on swept wings arises from coexisting 2D shock oscillations and 3D separation instabilities.

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

This paper runs scale-resolving simulations of transonic buffet on infinite swept wings with spanwise periodic domains up to aspect ratio three. It establishes that the unsteady flow combines two independent mechanisms: low-frequency two-dimensional shock motion that stays largely uniform across the span, and higher-frequency three-dimensional cells of separation and reattachment whose strength grows when the mean flow is more separated at the shock. The work tracks how increasing sweep leaves the two-dimensional mode almost unchanged while turning the three-dimensional mode into a traveling wave whose frequency rises. A reader cares because these cells produce the unsteady loads that limit the safe operating envelope of transonic aircraft.

Core claim

Transonic buffet on infinite wings arises from the superposition of distinct but coexisting 2D shock motion and separation-driven 3D instabilities, with mean flow separation at the shock identified as a necessary condition for dominant 3D buffet dynamics to emerge. In the minimally separated case the shock motion remains spanwise uniform with only weak intermittent cells near the trailing edge. When mean separation increases, pronounced three-dimensional cells appear with a spanwise wavelength of one to 1.5 chord lengths; the quasi-stationary low-frequency separation mode identified on unswept wings becomes a traveling wave whose frequency shifts upward with sweep.

What carries the argument

Implicit large-eddy simulations combined with spectral proper orthogonal decomposition on span-periodic domains up to aspect ratio three.

If this is right

  • The frequency and structure of the two-dimensional shock mode remain essentially unchanged when sweep is added.
  • The three-dimensional separation mode increases in both frequency and energy content with sweep while its spanwise wavelength stays constant.
  • Dominant three-dimensional buffet cells emerge only after the mean flow reaches significant separation at the shock foot.
  • The low-frequency separation mode that is quasi-stationary on unswept wings becomes a spanwise-traveling wave once sweep is present.

Where Pith is reading between the lines

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

  • Control strategies aimed at transonic buffet could target reduction of shock-foot separation rather than direct suppression of shock motion.
  • The same modal picture applied to finite-span wings would show how the infinite-wing cells couple to tip vortices and root effects.
  • Reduced-order models used for aircraft load prediction must retain both the two-dimensional and three-dimensional mechanisms rather than treating buffet as a purely two-dimensional phenomenon.

Load-bearing premise

Periodic simulations on domains of aspect ratio three or less are assumed to let three-dimensional buffet cells develop freely without artificial spanwise confinement.

What would settle it

If three-dimensional buffet cells of the reported wavelength and strength fail to appear in simulations with much larger aspect ratios or in experiments on swept wings with artificially suppressed mean separation at the shock, the necessity of that separation would be refuted.

Figures

Figures reproduced from arXiv: 2601.11137 by Andrea Sansica, David J. Lusher.

Figure 1
Figure 1. Figure 1: FIG. 1. (left) Example spanwise separation ‘buffet cells’ in a low-fidelity steady RANS-based transonic airfoil simulation and [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Span- and time-averaged mean ( [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: reports sectional evaluation of the (a) lift coefficient history and (b) Power Spectral Density (PSD) of lift fluctuations at a single spanwise grid location (z = Lz/2) for the α = 5◦ case. Sweep angles of λ = [0◦ , 5 ◦ , 25◦ ] are shown. Sectional evaluation is necessary here to assess macroscopic spanwise inhomogeneity which would be lost when performing a spanwise average (as in [PITH_FULL_IMAGE:figure… view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Instantaneous flow visualisations over the suction side of the airfoil surface at [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Sectional evaluation of ( [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Instantaneous flow visualisations over the suction side of the airfoil surface at a sweep angle of [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. SPOD spectra for pressure (blue, solid), [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Instantaneous streamwise velocity contours for the [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. SPOD modes for the [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. SPOD spectra for pressure (blue, solid), [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. SPOD modes at [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. SPOD modes of the [PITH_FULL_IMAGE:figures/full_fig_p016_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. ( [PITH_FULL_IMAGE:figures/full_fig_p017_13.png] view at source ↗
read the original abstract

Transonic buffet is a class of shock-wave/boundary-layer interaction known to exhibit self-sustained two-dimensional (2D) chordwise shock wave oscillations (Strouhal number St=0.05-0.1), and three-dimensional (3D) spanwise-modulated flow separation/reattachment (St=0.2-0.4). Due to computational cost, scale-resolving simulations of span-periodic configurations to date have been limited to narrow airfoils, insufficient to accommodate the 3D buffet cell instability reported in low-fidelity simulations and experiments. In this work, implicit large-eddy simulations (ILES) and modal analysis are performed on infinite swept wings up to AR=3. The sensitivity of the 2D and 3D modes to crossflow is detailed. Two flow conditions are examined, corresponding to minimally and largely separated mean flow at the shock location. For the minimally separated case, the shock dynamics remain essentially spanwise-uniform (quasi-2D), with only weak and intermittent separation cells confined to the trailing-edge region and exhibiting negligible interaction with the shock. In contrast, increased mean separation leads to the emergence of pronounced 3D buffet cells with a characteristic spanwise wavelength: 1-1.5c. SPOD reveals that a quasi-stationary low-frequency 3D separation mode previously identified on unswept wings (St=0.02) becomes a spanwise travelling mode as sweep is imposed, shifting monotonically to intermediate frequencies (St=0.06-0.35). The 2D shock mode is largely insensitive to sweep, whereas the frequency and energy content of the 3D mode increase with sweep while its wavelength remains unchanged. The results demonstrate that transonic buffet on infinite wings arises from the superposition of distinct but coexisting 2D shock motion and separation-driven 3D instabilities, with mean flow separation at the shock identified as a necessary condition for dominant 3D buffet dynamics to emerge.

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 paper performs implicit large-eddy simulations (ILES) and spectral proper orthogonal decomposition (SPOD) modal analysis on spanwise-periodic infinite swept wings up to aspect ratio AR=3 to study transonic buffet. It contrasts two regimes: minimally separated mean flow at the shock, where shock motion remains quasi-2D with only weak trailing-edge 3D cells, versus largely separated flow, where pronounced 3D buffet cells of spanwise wavelength 1-1.5c emerge. The analysis shows the 2D shock mode is largely insensitive to sweep while the 3D separation mode shifts from quasi-stationary to traveling with increasing frequency and energy content; the central claim is that buffet arises from superposition of distinct 2D shock and 3D separation instabilities, with mean separation at the shock a necessary condition for dominant 3D dynamics.

Significance. If the results hold, the work advances understanding of 3D transonic buffet mechanisms on swept wings by demonstrating the coexistence of 2D shock oscillation and separation-driven 3D instabilities via scale-resolving simulations on domains larger than prior narrow-airfoil studies, together with data-driven modal analysis that tracks sweep-induced changes in mode frequency and wavelength. The identification of mean-flow separation as a necessary condition for 3D cell dominance provides a concrete criterion that could inform reduced-order modeling and control strategies.

major comments (2)
  1. [Numerical setup] Numerical setup (domain and boundary conditions): The spanwise-periodic domains limited to AR=3 for reported 3D cell wavelengths of 1-1.5c admit at most two to three cells; periodicity then enforces discrete integer-mode selection that may artificially confine or stabilize wavelengths, directly undermining the claim that the observed modal superposition faithfully represents an unbounded infinite swept wing.
  2. [Results] Results section (quantitative support): No grid-convergence studies, experimental validation, or error bars are reported for the Strouhal numbers (St=0.05-0.1 for 2D shock, St=0.2-0.4 for 3D cells) or cell wavelengths that underpin the distinction between minimally and largely separated regimes and the necessity of mean separation; this weakens quantitative support for the central claim.
minor comments (2)
  1. [Abstract] Abstract: The two flow conditions are described only qualitatively as 'minimally' and 'largely' separated; explicit values of Mach number, Reynolds number, angle of attack, and sweep angles would improve reproducibility and context.
  2. [Throughout] Throughout: Notation for Strouhal number (St) and aspect ratio (AR) is used consistently but would benefit from a single definitions table or early section to aid readers unfamiliar with buffet literature.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the positive assessment of our work and the constructive comments. We have carefully considered each point and provide our responses below, along with planned revisions to the manuscript.

read point-by-point responses

  1. Referee: [Numerical setup] Numerical setup (domain and boundary conditions): The spanwise-periodic domains limited to AR=3 for reported 3D cell wavelengths of 1-1.5c admit at most two to three cells; periodicity then enforces discrete integer-mode selection that may artificially confine or stabilize wavelengths, directly undermining the claim that the observed modal superposition faithfully represents an unbounded infinite swept wing.

    Authors: We acknowledge the referee's valid concern about the finite domain size potentially influencing the modal selection. However, the AR=3 domain was selected to allow for at least two full wavelengths of the observed 1-1.5c cells, which is consistent with the minimal domain sizes used in previous studies of 3D buffet cells on infinite wings. The fact that the 3D cells emerge only under largely separated conditions and their wavelengths remain consistent across sweep angles suggests that the dynamics are driven by the flow physics rather than domain constraints. The 2D shock mode being insensitive further supports the robustness. We disagree that this undermines the claim for the infinite wing, as the periodic boundary conditions are the standard approach to model infinite span. In the revised manuscript, we will add a discussion on the domain-size choice and its justification based on literature. revision: partial

  2. Referee: [Results] Results section (quantitative support): No grid-convergence studies, experimental validation, or error bars are reported for the Strouhal numbers (St=0.05-0.1 for 2D shock, St=0.2-0.4 for 3D cells) or cell wavelengths that underpin the distinction between minimally and largely separated regimes and the necessity of mean separation; this weakens quantitative support for the central claim.

    Authors: We agree that additional quantitative support would strengthen the manuscript. In the revised version, we will include a grid-convergence study comparing the key Strouhal numbers and wavelengths between the baseline grid and a refined grid (approximately 1.5 times more points in each direction), demonstrating that the reported values are converged within 5%. Error bars will be added to the reported St values based on variations over multiple shedding cycles. Regarding experimental validation, while we compare our 2D shock frequencies to established experimental data for unswept cases, direct validation for the 3D cell dynamics on swept wings at these conditions is not available in the open literature. We will expand the discussion to include more comparisons with existing low-fidelity and experimental results on 3D buffet cells. revision: yes

standing simulated objections not resolved
  • Direct experimental validation for the specific 3D buffet cell dynamics on swept wings would require new experiments, which is beyond the scope of this numerical study.

Circularity Check

0 steps flagged

No circularity: results are direct outputs of ILES and SPOD on the simulated domains

full rationale

The paper contains no derivation chain. Its central claim—that transonic buffet on infinite wings arises from superposition of 2D shock motion and separation-driven 3D instabilities, with mean separation as a necessary condition—is presented as an empirical observation extracted from the ILES flow fields and SPOD modes at the two chosen conditions. No parameter is fitted to a subset of data and then relabeled as a prediction; no ansatz is smuggled via self-citation; no uniqueness theorem is invoked; and no quantity is defined in terms of itself. The domain-size concern (periodic AR=3) is an assumption about representativeness, not a circular reduction of the reported modal content to the input mesh or boundary conditions. The analysis is therefore self-contained against external benchmarks and receives the default non-circularity finding.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The work rests on standard assumptions of the Navier-Stokes equations, the validity of implicit large-eddy simulation for the resolved scales, and the adequacy of periodic spanwise boundaries for an infinite wing; no new free parameters, axioms, or invented entities are introduced beyond these conventional modeling choices.

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Reference graph

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