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arxiv: 2604.16495 · v1 · submitted 2026-04-14 · ⚛️ physics.flu-dyn · astro-ph.GA· cond-mat.stat-mech· nlin.PS· physics.ao-ph

Recognition: unknown

Effect of gap width on turbulent transition in Taylor-Couette flow

Chang-Quan Zhou, Hua-Shu Dou, Lin Niu, Wen-Qian Xu

Authors on Pith no claims yet

Pith reviewed 2026-05-10 16:18 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn astro-ph.GAcond-mat.stat-mechnlin.PSphysics.ao-ph
keywords Taylor-Couette flowturbulent transitiongap widthenergy gradient theoryflow stabilitynumerical simulationradius ratiovelocity distribution
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0 comments X

The pith

Increasing the gap width in Taylor-Couette flow reduces the maximum energy gradient and delays the transition to turbulence.

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

The paper performs numerical simulations of flow between two concentric cylinders where the inner one rotates and the outer is stationary. It examines how changing the radial gap width affects the onset of turbulence while holding the inner radius and rotation rate constant. The results indicate that wider gaps stabilize the flow because the velocity distribution shifts toward that of a free vortex, lowering the peak of the energy gradient function used to predict transition. This matters because it reveals that transition cannot be characterized by gap-based Reynolds number alone and requires including the radius ratio.

Core claim

Under the same inner cylinder radius and rotating speed, as the gap width increases the flow in the Taylor-Couette configuration becomes more stable. The average velocity distribution approaches free vortex flow, which enhances stability. The maximum value of the energy gradient function in the gap decreases with increasing gap width, thereby delaying the turbulent transition. Consequently the larger the gap width the later the transition occurs, and the radius ratio must be taken into account rather than using gap-width Reynolds number alone.

What carries the argument

The energy gradient function from energy gradient theory, whose maximum value in the gap determines the likelihood and location of transition to turbulence.

If this is right

  • As gap width increases the transition occurs at higher effective Reynolds numbers.
  • The radius ratio becomes an essential parameter for characterizing stability in Taylor-Couette flows.
  • Velocity profiles closer to free vortex flow correlate with greater resistance to turbulence.
  • Designs with larger gaps between rotating cylinders can achieve stable flow at higher speeds.

Where Pith is reading between the lines

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

  • This suggests that experimental studies varying the radius ratio independently could confirm the predicted delay in transition.
  • Similar effects might appear in other rotating annular flows such as in turbomachinery.
  • The approach could be extended to predict transition in non-Newtonian fluids or with axial flow components.

Load-bearing premise

That the energy gradient theory correctly identifies the transition threshold for Taylor-Couette flow and that the simulations faithfully represent the transitional regime.

What would settle it

Direct experimental measurement showing that the critical Reynolds number for transition does not increase with gap width, or that the location of transition does not correlate with the computed maximum of the energy gradient function.

read the original abstract

Simulations of the transitional flow in Taylor-Couette configuration are carried out to study the effect of the gap width on turbulent transition. The research results show that, under the same radius and the rotating speed of the inner cylinder, as the gap width increases, the flow becomes more stable. It is discovered that the average velocity distribution in the gap approaches the free vortex flow as the width increase and the stability of the flow is enhanced. It is found that, as the gap width increases, the maximum of the energy gradient function (from the energy gradient theory) in the gap decreases, which delays the turbulent transition. As such, the larger the gap width, the later the transition occurs. As the gap width increases, the Reynolds number based on the gap width alone is not able to characterize the flow behavior in Taylor-Couette flows, and the effect of the radius ratio should be taken into account.

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 paper reports numerical simulations of transitional Taylor-Couette flow with fixed inner-cylinder radius and rotation rate while varying the gap width d. It claims that larger d stabilizes the flow: the mean velocity profile approaches free-vortex form, the maximum value of the energy-gradient function K decreases, and turbulent transition is thereby delayed. The work concludes that a Reynolds number based only on gap width is insufficient and that the radius ratio must be retained to characterize the flow.

Significance. If the numerical results and the attribution to energy-gradient theory are substantiated, the manuscript would supply a concrete geometric mechanism for delayed transition in annular rotating flows and would furnish an additional test case for the energy-gradient criterion. The absence of grid-convergence data, validation benchmarks, and a direct check that the critical K remains invariant with d currently limits the strength of this contribution.

major comments (3)
  1. [Abstract / Results] Abstract and results description: the central claim that max(K) decreases with gap width and thereby delays transition rests on simulations whose grid resolution, validation against known Taylor-Couette cases, and error bars are not reported. Without these, the quantitative trend cannot be assessed for numerical artifacts.
  2. [Energy gradient function discussion] Energy-gradient analysis: the transition threshold is identified solely by the maximum of the energy-gradient function K, a quantity introduced in prior work by co-author Dou. The reported 'delay' therefore reduces, within the paper's own framework, to a re-expression of that definition rather than an independent verification that the onset occurs at the same K_crit for all gap widths.
  3. [Results on transition onset] Transition criterion: the conclusion that increasing d delays transition assumes K_crit is independent of gap width. No section compares the actual value of K attained at the numerically observed transition point across the different gaps; without this check the causal link to energy-gradient theory remains unsecured even if the velocity fields are correct.
minor comments (2)
  1. [Abstract] The abstract would be clearer if it stated the specific range of gap widths and Reynolds numbers examined.
  2. [Introduction / Methods] Notation for the energy-gradient function K and its critical value should be defined explicitly on first use rather than assumed from prior literature.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the insightful comments on our manuscript. We address each of the major comments point by point below, providing clarifications and indicating revisions where necessary.

read point-by-point responses

  1. Referee: [Abstract / Results] Abstract and results description: the central claim that max(K) decreases with gap width and thereby delays transition rests on simulations whose grid resolution, validation against known Taylor-Couette cases, and error bars are not reported. Without these, the quantitative trend cannot be assessed for numerical artifacts.

    Authors: We agree that additional details on numerical accuracy are essential for substantiating the results. In the revised manuscript, we will include a dedicated section on grid-convergence studies, demonstrating that the reported velocity profiles and energy-gradient function values are insensitive to further grid refinement. We will also provide validation by comparing our simulations for standard radius ratios against established benchmarks in the Taylor-Couette literature, such as the onset of Taylor vortices and wavy vortices, and include error estimates for the key quantities. revision: yes

  2. Referee: [Energy gradient function discussion] Energy-gradient analysis: the transition threshold is identified solely by the maximum of the energy-gradient function K, a quantity introduced in prior work by co-author Dou. The reported 'delay' therefore reduces, within the paper's own framework, to a re-expression of that definition rather than an independent verification that the onset occurs at the same K_crit for all gap widths.

    Authors: While the transition criterion is based on the energy-gradient theory, our contribution lies in elucidating the physical mechanism by which gap width affects the flow stability. Specifically, we show through direct simulation that larger gaps drive the mean velocity profile closer to the free-vortex distribution, which reduces the peak value of K. This geometric effect provides an independent insight into why transition is delayed, beyond merely applying the existing criterion. The theory itself predicts that K_crit is a material property independent of geometry, and our results support this by demonstrating consistent behavior across different configurations. revision: no

  3. Referee: [Results on transition onset] Transition criterion: the conclusion that increasing d delays transition assumes K_crit is independent of gap width. No section compares the actual value of K attained at the numerically observed transition point across the different gaps; without this check the causal link to energy-gradient theory remains unsecured even if the velocity fields are correct.

    Authors: We acknowledge the value of explicitly verifying the invariance of K at the transition onset. In the revised version, we will add a comparison of the maximum K values at the points where transition is observed in our simulations for the various gap widths. This will confirm that the critical threshold remains approximately constant, thereby strengthening the connection to the energy-gradient theory. revision: yes

Circularity Check

1 steps flagged

Transition delay claim reduces to unverified invariance of K_crit from co-author's prior energy-gradient theory

specific steps
  1. self citation load bearing [Abstract]
    "It is found that, as the gap width increases, the maximum of the energy gradient function (from the energy gradient theory) in the gap decreases, which delays the turbulent transition. As such, the larger the gap width, the later the transition occurs."

    The statement equates a computed decrease in max(K) with delayed transition only by assuming K_crit is gap-width invariant. This invariance is not demonstrated by comparing K at the observed transition Reynolds numbers across the studied gaps; it is presupposed from the energy-gradient theory whose prior formulation is by co-author Hua-Shu Dou.

full rationale

The paper's central derivation observes that max(K) decreases with increasing gap width d (at fixed inner radius and rotation) and concludes this delays transition. This step is load-bearing only if the critical threshold K_crit remains constant across d, an assumption imported from the energy-gradient theory without explicit cross-gap verification that observed transition points attain the same K value. The abstract directly links the decrease to delay via the theory, but the provided text does not report a check of K at numerically detected onset for each gap, rendering the causal attribution circular within the paper's own framework. The velocity-profile approach to free-vortex form is independent, but the stability interpretation is not.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of energy gradient theory for identifying transition and on the fidelity of the numerical method; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption The maximum value of the energy gradient function determines the onset of turbulent transition in shear flows.
    Invoked to interpret the decrease in this maximum as the cause of delayed transition.

pith-pipeline@v0.9.0 · 5479 in / 1226 out tokens · 34650 ms · 2026-05-10T16:18:06.166307+00:00 · methodology

discussion (0)

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