arxiv: 2604.26291 · v1 · submitted 2026-04-29 · ⚛️ physics.flu-dyn

Recognition: unknown

Coherent structures in Newtonian and viscoelastic turbulent planar jets

Christian Amor , Adri\'an Corrochano , Giovanni Soligo , Soledad Le Clainche , Marco Edoardo Rosti

Authors on Pith no claims yet

Pith reviewed 2026-05-07 12:39 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn

keywords viscoelastic jetselastic turbulencecoherent structuresKoopman decompositionplanar jetspolymer filamentsnear-field dynamics

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The pith

Elasticity-driven streaks in the near field sustain elastic turbulence in viscoelastic planar jets.

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

The paper compares coherent structures in high-Reynolds-number Newtonian planar jets with those in viscoelastic planar jets using a spatio-temporal decomposition of the simulated velocity and polymer fields. It establishes that low-frequency streaks and high-frequency wave packets dominate the global dynamics in both cases, yet the near-field region of the viscoelastic jet contains distinct elasticity-driven streaks that modify the potential core and interact with the base flow instability. Polymer-field analysis further identifies stretched filaments and centre-mode structures that tie these near-field streaks to the maintenance of elastic turbulence. A sympathetic reader would care because the result isolates a specific mechanism by which small polymer additions can trigger and sustain turbulence at low Reynolds numbers where inertial turbulence would otherwise be absent.

Core claim

Global flow structures are similar between Newtonian and viscoelastic turbulent planar jets, with low-frequency streaks and high-frequency wave packets dominating the turbulent dynamics. However, structures are strikingly different in the near field, where elasticity-driven streaks affect the dynamics in the potential core of the viscoelastic planar jet, modifying the bulk flow and interacting with the flow instability. The analysis of the polymer field reveals stretched polymer filaments and centre-mode structures, which support the implication of the near-field streaks on sustaining elastic turbulence in three-dimensional viscoelastic planar jets.

What carries the argument

Spatio-temporal Koopman decomposition applied to the velocity and polymer fields, which extracts dominant spatial patterns ordered by frequency and growth rate to isolate the coherent structures.

If this is right

Elasticity modifies the near-field dynamics of planar jets, producing streaks that alter the potential core and interact with the flow instability.
Stretched polymer filaments and centre-mode structures appear in the viscoelastic case and correlate with the near-field streaks.
These near-field features provide a route to sustain elastic turbulence in three-dimensional jets even when inertial effects are weak.
The global low-frequency streaks and high-frequency wave packets remain comparable to those in Newtonian jets, indicating that elasticity mainly perturbs the near-field region.

Where Pith is reading between the lines

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

The same decomposition could be applied to other viscoelastic configurations such as round jets or wakes to test whether near-field streaks play a comparable sustaining role.
Varying polymer relaxation time or concentration while tracking the strength of near-field streaks would provide a direct test of their causal importance.
If near-field streaks prove generic, targeted polymer injection near the nozzle exit might offer a practical way to control the onset of elastic turbulence in industrial jets.

Load-bearing premise

That the Koopman decomposition applied to the velocity and polymer fields fully captures the dominant mechanisms without significant truncation error or missing modes that could alter the interpretation of near-field streaks.

What would settle it

A simulation or experiment in which the near-field streaks are selectively suppressed while the polymer field remains unchanged, yet the overall elastic turbulence levels and mixing rates stay the same.

Figures

Figures reproduced from arXiv: 2604.26291 by Adri\'an Corrochano, Christian Amor, Giovanni Soligo, Marco Edoardo Rosti, Soledad Le Clainche.

**Figure 1.** Figure 1: Sketch of the delay embedding. A window of length view at source ↗

**Figure 2.** Figure 2: Instantaneous fields of the streamwise fluctuating velocity view at source ↗

**Figure 3.** Figure 3: HODMD spectra overlapped for multiple calibrations for the Newtonian (upper view at source ↗

**Figure 4.** Figure 4: Spatial structure of robust DMD modes in the Newtonian and viscoelastic jets. view at source ↗

**Figure 5.** Figure 5: Spatio-temporal spectra. Normalised spanwise wavenumber, 𝜅ℎ, compared to their normalised spatio-temporal amplitude, ˆ𝑎/𝑎ˆ11, with ˆ𝑎11 the largest amplitude in each series. Panels a and c correspond to low-frequency modes, while high-frequency modes are shown in b and d. A power-law decay of the normalized amplitude is suggested in each subpanel for high wavenumbers. with the wavenumber, with the lowest n… view at source ↗

**Figure 6.** Figure 6: Spatial structure of two low-frequency spatio-temporal modes. The upper panel view at source ↗

**Figure 7.** Figure 7: Reconstruction of the near-field streaks in the viscoelastic jet. Real (panels view at source ↗

**Figure 8.** Figure 8: Spatial structure of four high-frequency spatio-temporal modes. For each jet, the left column shows 𝑥𝑦-planes at 𝑧 = 0 for 𝜅 = 0, and the right column the three-dimensional iso-surfaces for 𝜅1. Both cases show the normalised streamwise velocity, with iso-surfaces indicating regions of magnitude +0.5 (red) and −0.5 (blue). Insets provide a closer view at the near-field up to 𝑥 ≈ 30ℎ. The yellow lines and tr… view at source ↗

**Figure 9.** Figure 9: Local HODMD spectrum for robust frequencies. Non-dimensional frequency, view at source ↗

**Figure 10.** Figure 10: Local spatio-temporal spectra. Normalised spanwise wavenumber, 𝜅ℎ, compared to their normalised amplitude, ˆ𝑎/𝑎ˆ11, from robust modes computed in all three boxes. Similar frequencies have same colours among plots. to spot smaller amplitude modes. In the following, we show the results for 𝑑 = 70 in the smallest box and 𝑑 = 80 in the remaining two, while 𝜀1 and 𝜀2 are set to 6 · 10−4 in all cases. The small… view at source ↗

**Figure 11.** Figure 11: Reconstruction of the bulk flow at the near-field. Two-dimensional view at source ↗

**Figure 12.** Figure 12: Reconstruction of the wave packet modes at the near-field. Three-dimensional view at source ↗

**Figure 13.** Figure 13: Temporal (a) and spatio-temporal (b) spectra of the trace of conformation tensor. Panel a shows the non-dimensional temporal frequency, 𝑆𝑡, compared to the normalised amplitude, 𝑎/𝑎1, with 𝑎1 the largest amplitude in each series of robust modes from the polymer field (light purple), that are compared to those from the velocity field (purple) reported in fig. 3. Red outlines indicate modes of the polymer t… view at source ↗

**Figure 14.** Figure 14: Spatial structures of two low frequency spatio-temporal modes from the view at source ↗

**Figure 15.** Figure 15: Spatial structures of three high frequency spatio-temporal modes from the view at source ↗

read the original abstract

The addition of a small amount of long-chain polymers confers viscoelastic properties to Newtonian flows. The resulting non-Newtonian solution now exhibits different dynamics, such as enhanced mixing at low Reynolds, where elastic instabilities can trigger elastic turbulence even though inertial turbulence is absent. Here, we study this phenomenon in viscoelastic planar jets and, in particular, we do it from the perspective of coherent structures to understand how elastic turbulence is triggered and sustained, which remain barely explored in this setup. We introduce the spatio-temporal Koopman decomposition for extracting the dominant flow patterns, and we compare them with those from Newtonian planar jets at high Reynolds number. Global flow structures are similar between jets, with low-frequency streaks and high-frequency wave packets dominating the turbulent dynamics. However, structures are strikingly different in the near field, where elasticity-driven streaks affect the dynamics in the potential core of the viscoelastic planar jet, modifying the bulk flow and interacting with the flow instability. The analysis of the polymer field reveals stretched polymer filaments and centre-mode structures, which support the implication of the near-field streaks on sustaining elastic turbulence in three-dimensional viscoelastic planar jets.

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.

Desk Editor's Note private letter to a colleague

The paper uses spatio-temporal Koopman decomposition on DNS of planar jets to show global structural similarity between Newtonian and viscoelastic cases but clear near-field differences where elasticity-driven streaks modify the potential core and tie into polymer filaments sustaining elastic turbulence.

read the letter

The main point is that viscoelastic planar jets develop distinct near-field streaks driven by elasticity that alter the potential core and interact with instabilities, unlike the Newtonian reference, and the polymer field shows stretched filaments plus centre-mode structures that support those streaks helping sustain the turbulence. The authors extract this by applying their spatio-temporal Koopman approach to both velocity and polymer data and contrasting the two jet types at comparable conditions. Global features like low-frequency streaks and high-frequency wave packets line up, which is not surprising, but the local contrast is the actual addition. They do a clean job of the comparison and of extending the decomposition to the polymer field to make the mechanistic link. That gives a concrete handle on how elastic turbulence gets maintained in this three-dimensional setup. The soft spot sits with the method. The interpretation that near-field streaks are the key sustainer depends on the retained Koopman modes capturing the dominant dynamics without meaningful truncation or omitted interactions. If the finite-mode approximation misses contributions from the polymer stress or other near-field effects, the causal weight assigned to those streaks weakens. The abstract does not spell out convergence metrics or reconstruction errors, so the full paper needs to show those checks are solid; otherwise the claim stays more observational than definitive. This work is for people already working on coherent structures in non-Newtonian flows or on elastic turbulence in jets. A reader focused on drag reduction or low-Re mixing would pick up useful qualitative differences. It has enough new application of the tool and direct simulation evidence to deserve peer review, even if referees will press on the mode validation and any quantitative support for the sustaining role.

Referee Report

1 major / 2 minor

Summary. The manuscript uses direct numerical simulations of Newtonian (high-Re) and viscoelastic planar jets to extract coherent structures via a newly introduced spatio-temporal Koopman decomposition applied to velocity and polymer fields. It reports that global structures are similar across both flows, dominated by low-frequency streaks and high-frequency wave packets, but that near-field structures differ markedly in the viscoelastic case: elasticity-driven streaks modify the potential core, interact with the primary instability, and—supported by stretched polymer filaments and centre-mode polymer structures—sustain elastic turbulence in three dimensions.

Significance. If the central interpretation holds, the work offers a concrete mechanistic picture of how elastic turbulence is triggered and maintained in 3-D viscoelastic jets, distinguishing near-field elasticity effects from the inertial mechanisms that dominate farther downstream. The side-by-side comparison with Newtonian jets and the polymer-field analysis provide useful benchmarks for future modeling. The spatio-temporal Koopman approach itself is a methodological contribution whose utility will depend on demonstrated robustness.

major comments (1)

[Spatio-temporal Koopman decomposition] The claim that near-field elasticity-driven streaks sustain elastic turbulence (abstract and concluding discussion) rests on the retained Koopman modes faithfully representing the dominant dynamics. The skeptic note correctly identifies that finite-mode truncation or choice of observables could omit near-field interactions or polymer-stress contributions that would weaken or reassign this causal role. Without reported residual-energy spectra, mode-convergence tests, or sensitivity to additional observables in the section describing the spatio-temporal Koopman decomposition, the load-bearing interpretation remains vulnerable.

minor comments (2)

The abstract would be strengthened by stating the specific Reynolds and Weissenberg numbers (or ranges) employed, allowing readers to gauge the inertial versus elastic regime immediately.
Figure captions and legends should explicitly distinguish Newtonian versus viscoelastic cases and indicate the frequency bands corresponding to the reported streaks and wave packets.

Simulated Author's Rebuttal

1 responses · 0 unresolved

Thank you for the constructive feedback on our manuscript. We address the referee's major comment on the spatio-temporal Koopman decomposition below, providing additional evidence and revisions to strengthen the claims regarding the role of near-field structures in sustaining elastic turbulence.

read point-by-point responses

Referee: The claim that near-field elasticity-driven streaks sustain elastic turbulence (abstract and concluding discussion) rests on the retained Koopman modes faithfully representing the dominant dynamics. The skeptic note correctly identifies that finite-mode truncation or choice of observables could omit near-field interactions or polymer-stress contributions that would weaken or reassign this causal role. Without reported residual-energy spectra, mode-convergence tests, or sensitivity to additional observables in the section describing the spatio-temporal Koopman decomposition, the load-bearing interpretation remains vulnerable.

Authors: We thank the referee for highlighting the importance of demonstrating the robustness of the Koopman decomposition. While the original manuscript selected modes based on their contribution to the overall energy and frequency content to capture the dominant coherent structures, we acknowledge that explicit residual-energy spectra and convergence tests were not presented. In the revised manuscript, we have added these analyses in the methods section describing the spatio-temporal Koopman decomposition. The residual energy spectra indicate that the retained modes account for the majority of the variance in both velocity and polymer fields, and convergence tests varying the number of modes and including additional polymer stress observables confirm that the near-field elasticity-driven streaks and their interaction with the potential core remain consistent. This supports our interpretation of their role in sustaining elastic turbulence, as further evidenced by the stretched polymer filaments and centre-mode structures identified in the polymer field. We have also clarified this in the abstract and discussion sections. revision: yes

Circularity Check

0 steps flagged

No significant circularity: claims are observational results from data-driven decomposition

full rationale

The paper performs direct numerical simulations of Newtonian and viscoelastic planar jets and applies a spatio-temporal Koopman decomposition to the resulting velocity and polymer fields to identify coherent structures. All reported findings (global similarity of low-frequency streaks and high-frequency wave packets, near-field differences due to elasticity-driven streaks, stretched polymer filaments, and centre-mode structures) are extracted as dominant modes from the simulated data. No load-bearing step in the abstract or described methodology reduces a prediction to a fitted parameter by construction, invokes a self-citation chain as the sole justification for a uniqueness theorem, or renames a known result under new coordinates. The derivation chain is therefore self-contained as an empirical analysis technique applied to external simulation output, with no self-definitional or fitted-input circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work rests on standard incompressible Navier-Stokes equations augmented by a viscoelastic constitutive model (likely FENE-P or Oldroyd-B) whose parameters are not detailed in the abstract; no new entities are postulated.

axioms (2)

domain assumption The flow is governed by the incompressible Navier-Stokes equations coupled to a viscoelastic stress tensor.
Invoked implicitly as the basis for the simulations described in the abstract.
domain assumption Koopman decomposition can be applied to the spatio-temporal velocity and polymer fields to extract dominant coherent structures.
Central methodological assumption stated in the abstract.

pith-pipeline@v0.9.0 · 5505 in / 1554 out tokens · 40159 ms · 2026-05-07T12:39:02.479254+00:00 · methodology

discussion (0)

Reference graph

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