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arxiv: 2604.17851 · v1 · submitted 2026-04-20 · ⚛️ physics.flu-dyn

Coherent structures in axis-switching elliptical jets

Naia Suzuki , Andr\'e V. G. Cavalieri , Daniel M. Edgington-Mitchell , Petr\^onio A. S. Nogueira This is my paper

Pith reviewed 2026-05-10 04:22 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords axis switchingelliptical jetscoherent structuresSPODflapping modewagging modejet dynamics
0
0 comments X

The pith

Axis switching transforms flapping modes into slower-growing wagging modes in elliptical jets

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

The paper examines coherent structures in elliptical jets that axis-switch, meaning their cross-section rotates downstream. Direct numerical simulations with varying forcing are used to generate the flows, followed by spectral proper orthogonal decomposition to isolate energetic modes tied to the flow symmetries. The central finding is that axis switching reorients the flapping mode into a wagging mode with respect to the new axis, which then grows more slowly. This shift also allows a new flapping mode to emerge and dominate after the switch, particularly at lower frequencies. Sympathetic readers would care because these structures govern how jets mix with surrounding air and produce noise, so controlling them via geometry or forcing could improve engineering designs.

Core claim

The axis-switching phenomenon causes the flapping mode to become a wagging mode relative to the new axis, lowering the growth rate of the structure. Two different coherent structures were found in the SA symmetry for the axis-switching cases: the wagging mode which was dominant in the pre-axis-switch region and a new flapping mode which is dominant in the post-axis-switch region. The new flapping mode was dominant in the low-frequency region of the full-field SPOD spectrum which was overtaken by the wagging mode at St≈0.2 for the medium-forcing case and at St≈0.4 for the high-forcing case. This new flapping mode is likely a flapping mode relative to the axis-switched mean flow, which arises

What carries the argument

Spectral proper orthogonal decomposition of DNS velocity fields, used to extract modes classified by the dihedral group D2 symmetry, showing how axis switching alters which mode is most energetic and its spatial growth.

If this is right

  • Higher forcing levels cause the jet to axis-switch earlier in the streamwise direction.
  • The flapping mode decays faster when axis switching occurs due to the reorientation effect.
  • A new flapping mode appears and dominates the post-axis-switch region because of slower shear-layer growth along the original major axis.
  • The frequency at which the wagging mode overtakes the new flapping mode increases with forcing level.

Where Pith is reading between the lines

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

  • If axis switching reliably slows coherent structure growth, it could be engineered to reduce jet noise or enhance mixing in propulsion systems.
  • The mode transformation might generalize to other jet shapes or forced flows where symmetry is broken downstream.
  • Varying the jet aspect ratio in follow-up studies could reveal how the switch location affects the dominant frequency range.

Load-bearing premise

The extracted SPOD modes correspond to physically meaningful, distinct coherent structures rather than being contaminated by numerical artifacts or overlapping unrelated dynamics.

What would settle it

If a follow-up simulation with finer grid or an experiment measuring velocity fluctuations shows that the flapping mode continues to grow at the same rate after the axis switch location, or if no distinct new flapping mode appears in the post-switch region, the claimed mechanism would be falsified.

Figures

Figures reproduced from arXiv: 2604.17851 by Andr\'e V. G. Cavalieri, Daniel M. Edgington-Mitchell, Naia Suzuki, Petr\^onio A. S. Nogueira.

Figure 1
Figure 1. Figure 1: FIG. 1: Instantaneous snapshot of the streamwise velocity fluctuations for the high-forcing case: ( [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Axial slices of mean-streamwise-velocity profiles [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Major and minor-axis slices of the mean-streamwise-velocity profiles for different forcing levels [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Jet half-width in the major and minor axis for different forcing levels: ( [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Vorticity thickness for different forcing levels: ( [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Isosurfaces of 10% pressure fluctuations of the first SPOD mode for low-forcing case at [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: SPOD mode-energy spectra of first 15 modes with AS symmetry for different forcing levels (top row) and [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Comparison of cross-plane integrated mode amplitude scaled by [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Mode-energy spectra for the leading SPOD mode for different forcing levels: ( [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Comparison of cross-plane integrated mode amplitude scaled by [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Minor-axis slices of the real component of leading SPOD mode shapes with AS symmetry. The red line [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: Minor-axis slices of the real component of the suboptimal SPOD mode shapes with AS symmetry. The red [PITH_FULL_IMAGE:figures/full_fig_p011_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: Frequency-axial distance diagram of mode amplitude for the leading SPOD mode with AS symmetry for [PITH_FULL_IMAGE:figures/full_fig_p012_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14: Frequency-axial distance diagram of mode amplitude for the first suboptimal SPOD mode with AS [PITH_FULL_IMAGE:figures/full_fig_p012_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15: Major-axis slices of the real component of the leading SPOD mode shapes with SA symmetry. The red line [PITH_FULL_IMAGE:figures/full_fig_p013_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16: Major-axis slices of the real component of the suboptimal SPOD mode shapes with SA symmetry. The red [PITH_FULL_IMAGE:figures/full_fig_p013_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17: Schematic for the weighted regions of the SPOD [PITH_FULL_IMAGE:figures/full_fig_p014_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18: Mode-energy spectra for full-domain, pre-axis-switch and post-axis-switch SPOD for the SA mode for each [PITH_FULL_IMAGE:figures/full_fig_p014_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19: Comparison of the real component of the SPOD mode shapes for full field SPOD from the low forcing case [PITH_FULL_IMAGE:figures/full_fig_p015_19.png] view at source ↗
Figure 2
Figure 2. Figure 2: fig. 2. The mean-flow profile for the high-forcing case not only switches its major and minor axes, but in fact appears [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗
Figure 21
Figure 21. Figure 21: fig. 21. Considering the full-domain SPOD, there appears to be a discontinuity in the mode amplitude [PITH_FULL_IMAGE:figures/full_fig_p015_21.png] view at source ↗
Figure 20
Figure 20. Figure 20: FIG. 20: Comparison of the real component of the SPOD mode shapes for post-axis-switch SPOD of medium- and [PITH_FULL_IMAGE:figures/full_fig_p016_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: FIG. 21: Frequency-axial distance diagram of mode amplitude for the leading SPOD mode with SA symmetry for [PITH_FULL_IMAGE:figures/full_fig_p016_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: FIG. 22: Cross-plane integrated turbulent kinetic energy budget for the medium-forcing case. [PITH_FULL_IMAGE:figures/full_fig_p018_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: FIG. 23: Turbulent kinetic energy spectra as a function of cross-plane wavenumber for the medium-forcing case at [PITH_FULL_IMAGE:figures/full_fig_p018_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: FIG. 24: Convergence of the leading and suboptimal SPOD modes with SA symmetry at [PITH_FULL_IMAGE:figures/full_fig_p018_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: FIG. 25: Mode-energy spectra for the leading SPOD mode with SS symmetry: ( [PITH_FULL_IMAGE:figures/full_fig_p019_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: FIG. 26: Major-axis slices of the real component of the suboptimal SPOD mode shapes with SS symmetry. The red [PITH_FULL_IMAGE:figures/full_fig_p019_26.png] view at source ↗
Figure 24
Figure 24. Figure 24: fig. 24. The leading SPOD mode is well converged, with [PITH_FULL_IMAGE:figures/full_fig_p019_24.png] view at source ↗
Figure 27
Figure 27. Figure 27: FIG. 27: Minor-axis slices of the real component of the suboptimal SPOD mode shapes with SS symmetry. The red [PITH_FULL_IMAGE:figures/full_fig_p020_27.png] view at source ↗
read the original abstract

Coherent structures in aspect ratio 2, axis-switching elliptical jets are studied using direct numerical simulation (DNS). Three different datasets are studied with varying near-nozzle forcing levels. Increasing the forcing level causes the jet to axis switch at an earlier streamwise location. Spectral proper orthogonal decomposition was applied to the dataset to extract the most-energetic coherent structures in the flow, and modes associated with the main symmetries of the flow were identified. The flapping mode was found to decay faster at the high forcing level, a feature that was linked to the axis-switching behavior. The axis-switching phenomenon causes the flapping mode to become a wagging mode relative to the new axis, lowering the growth rate of the structure. Two different coherent structures were found in the SA (dihedral group $D_2$) symmetry for the axis-switching cases: the wagging mode which was dominant in the pre-axis-switch region and a new flapping mode which is dominant in the post-axis-switch region. The new flapping mode was dominant in the low-frequency region of the full-field SPOD spectrum which was overtaken by the wagging mode at $St\approx 0.2$ for the medium-forcing case and at $St\approx 0.4$ for the high-forcing case. This new flapping mode is likely a flapping mode relative to the axis-switched mean flow, which develops due to the slower growth of the shear layer in the major axis.

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

3 major / 2 minor

Summary. The manuscript investigates coherent structures in aspect-ratio-2 elliptical jets undergoing axis-switching using direct numerical simulations at three different near-nozzle forcing levels. Spectral proper orthogonal decomposition (SPOD) is employed to extract energetic modes respecting the flow symmetries, particularly the SA (D2 dihedral) symmetry. The key finding is that increasing forcing advances the axis-switch location, leading to faster decay of the flapping mode, which is attributed to its transformation into a wagging mode relative to the switched axis; additionally, a new flapping mode emerges post-switch that dominates at low Strouhal numbers, with crossover frequencies depending on forcing level.

Significance. Should the causal link between axis-switching and the observed mode transitions and growth-rate reductions be confirmed, the work would advance understanding of symmetry-breaking effects on coherent structures in non-circular jets. This has relevance for applications in jet propulsion and mixing enhancement. The multi-dataset approach with symmetry classification is a positive aspect, providing a basis for further linear stability analyses.

major comments (3)
  1. [Abstract] The assertion that axis-switching causes the flapping mode to become a wagging mode and lowers its growth rate is not supported by an isolation of the geometric effect; since forcing level simultaneously shifts the switch location and modifies the initial shear-layer development, the observed changes in dominant SA-symmetric structures and St-dependent crossovers could stem from base-flow alterations rather than axis rotation itself. A comparison at fixed forcing with axis-switching suppressed (e.g., via different initial conditions) is absent.
  2. [SPOD analysis and results] The manuscript reports consistent trends in mode dominance across forcing levels but provides no quantitative error bars on SPOD eigenvalues, no grid-resolution convergence checks for the DNS, and no validation against experimental data on elliptical jets, leaving the central mode-transition claim only partially supported.
  3. [Symmetry identification] The claim that the new post-axis-switch flapping mode is 'likely a flapping mode relative to the axis-switched mean flow' relies on the assumption that SPOD modes accurately isolate physically distinct structures without significant numerical artifacts or mode mixing; no sensitivity tests to SPOD parameters or checks for orthogonality with other modes are described.
minor comments (2)
  1. [Notation] The use of 'SA symmetry' and 'D2' should be defined more explicitly early in the text, including how the symmetry groups are applied to the velocity fields.
  2. [Figures] The SPOD mode visualizations would benefit from clearer labeling of pre- and post-switch regions and quantitative growth-rate comparisons.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for the careful and constructive review of our manuscript. Below we respond point by point to the major comments, indicating planned revisions where appropriate.

read point-by-point responses

  1. Referee: [Abstract] The assertion that axis-switching causes the flapping mode to become a wagging mode and lowers its growth rate is not supported by an isolation of the geometric effect; since forcing level simultaneously shifts the switch location and modifies the initial shear-layer development, the observed changes in dominant SA-symmetric structures and St-dependent crossovers could stem from base-flow alterations rather than axis rotation itself. A comparison at fixed forcing with axis-switching suppressed (e.g., via different initial conditions) is absent.

    Authors: We agree that the forcing level simultaneously influences the axis-switch location and the initial shear-layer development, so the geometric effect of axis rotation cannot be fully isolated with the present datasets. The observed correlations between earlier switching, faster flapping-mode decay, and the emergence of the post-switch mode are consistent across the three forcing cases. We will revise the abstract and relevant discussion sections to replace causal phrasing with language of association (e.g., “linked to” rather than “causes”), while explicitly noting the potential confounding role of base-flow modifications. A controlled comparison at fixed forcing with axis-switching suppressed would require new simulations and is therefore not feasible at this stage. revision: partial

  2. Referee: [SPOD analysis and results] The manuscript reports consistent trends in mode dominance across forcing levels but provides no quantitative error bars on SPOD eigenvalues, no grid-resolution convergence checks for the DNS, and no validation against experimental data on elliptical jets, leaving the central mode-transition claim only partially supported.

    Authors: We will add a short subsection on numerical validation: (i) SPOD eigenvalue variability estimated from data-subset comparisons to supply quantitative uncertainty measures; (ii) explicit statements on grid resolution criteria and the adequacy of the near-nozzle shear-layer resolution; and (iii) a concise note that the axis-switching location and dominant coherent structures are qualitatively consistent with prior experimental literature on elliptical jets (already cited in the manuscript). These additions will strengthen support for the reported trends without altering the central findings. revision: partial

  3. Referee: [Symmetry identification] The claim that the new post-axis-switch flapping mode is 'likely a flapping mode relative to the axis-switched mean flow' relies on the assumption that SPOD modes accurately isolate physically distinct structures without significant numerical artifacts or mode mixing; no sensitivity tests to SPOD parameters or checks for orthogonality with other modes are described.

    Authors: SPOD is performed strictly within the SA-symmetric subspace, guaranteeing orthogonality among the retained modes by construction of the decomposition. The post-switch mode is identified by its spatial structure aligned with the switched axes and its dominance at low Strouhal numbers. We used standard SPOD parameters (block length, overlap) drawn from the literature; explicit sensitivity tests were not performed. We will insert a brief clarifying paragraph on these points and retain the qualifier “likely” to reflect the interpretive nature of the identification. revision: partial

standing simulated objections not resolved
  • A direct numerical comparison at fixed forcing with axis-switching deliberately suppressed (e.g., via altered initial conditions) to isolate the pure geometric effect of axis rotation.

Circularity Check

0 steps flagged

No significant circularity; claims extracted directly from DNS/SPOD data

full rationale

The paper reports observations from direct numerical simulations of elliptical jets at varying forcing levels, followed by standard SPOD decomposition to identify symmetric modes. The central statements—that the flapping mode decays faster with earlier axis-switching and transforms into a wagging mode—are interpretive links drawn from the extracted mode energies and frequencies in the simulation datasets. No derivation chain reduces a claimed result to a fitted parameter, self-citation, or ansatz by construction; the symmetry groups and St-dependent crossovers are read out from the computed spectra without intermediate equations that presuppose the conclusion. The analysis remains self-contained against the external benchmark of the DNS fields.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work rests on standard assumptions of computational fluid dynamics and modal analysis rather than new postulates.

axioms (2)
  • domain assumption Direct numerical simulation faithfully reproduces the coherent structures and axis-switching dynamics of the elliptical jet.
    Invoked by studying three DNS datasets with varying forcing to draw conclusions about mode behavior.
  • domain assumption Spectral proper orthogonal decomposition isolates the most energetic and dynamically relevant coherent structures.
    Used to identify flapping, wagging, and symmetry-specific modes.

pith-pipeline@v0.9.0 · 5581 in / 1353 out tokens · 48453 ms · 2026-05-10T04:22:00.415467+00:00 · methodology

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