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arxiv: 2605.31380 · v1 · pith:DDDSZPMEnew · submitted 2026-05-29 · ⚛️ physics.flu-dyn · nlin.CD

Subcritical transition to turbulence in buoyancy-driven flows with multiple hysteresis loops under quasi-one-dimensional confinement

Lu Zhang , Ke-Qing Xia This is my paper

Pith reviewed 2026-06-28 20:47 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn nlin.CD
keywords Rayleigh-Bénard convectionsubcritical transitionbuoyancy-driven turbulencehysteresis loopsdirect numerical simulationfinite-amplitude instabilityquasi-one-dimensional confinement
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The pith

Buoyancy-driven convection transitions to turbulence subcritically through finite disturbances and multiple hysteresis loops.

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

The paper establishes that in a quasi-one-dimensional Rayleigh-Bénard setup, the flow can pass from steady convection to intermittent turbulence without the gradual growth of small disturbances that defines a supercritical transition. Instead, the steady state remains linearly stable yet yields abruptly to turbulence once a finite-amplitude kick is applied, producing three coexisting states and three distinct hysteresis loops in the global transport quantities. A sympathetic reader would care because this route mirrors the well-known subcritical paths in shear-driven flows and therefore supplies the first concrete bridge toward a single description of how ordered convection gives way to turbulence in buoyancy-driven systems.

Core claim

Static and quasi-static direct numerical simulations identify a narrow Rayleigh-number interval containing three coexisting states—steady convection, oscillatory chaos, and intermittent turbulence—linked by abrupt jumps and pronounced hysteresis in both Nusselt and Reynolds numbers. The steady convection state resists infinitesimal perturbations yet becomes unstable to finite-amplitude disturbances, furnishing the defining signature of a subcritical transition. This observation directly contradicts the longstanding supposition that buoyancy-driven turbulence always onsets supercritically.

What carries the argument

The quasi-one-dimensional confinement that isolates a narrow band of Rayleigh numbers where steady convection, oscillatory chaos, and intermittent turbulence coexist and exhibit normal, reverse, and anomalous hysteresis loops.

If this is right

  • The Nusselt and Reynolds numbers exhibit discontinuous jumps accompanied by three separate hysteresis loops when the Rayleigh number is varied.
  • Steady convection persists under infinitesimal noise but collapses to intermittent turbulence once a sufficient finite disturbance is introduced.
  • The subcritical route supplies a common instability mechanism that can be compared directly with those already established for shear-driven flows.
  • The narrow parameter window of multistability can be used to study switching between ordered and turbulent states under controlled forcing.

Where Pith is reading between the lines

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

  • The same subcritical mechanism may appear in other geometries once the confinement aspect ratio is reduced sufficiently to suppress secondary instabilities.
  • Engineering models of natural convection could incorporate finite-amplitude thresholds rather than relying solely on linear stability criteria.
  • Varying the Prandtl number across the identified window would test whether the three hysteresis loops persist or merge.

Load-bearing premise

The linear stability of the steady state and its response to finite-amplitude disturbances are physical properties of the buoyancy-driven flow rather than artifacts introduced by the confinement geometry or the chosen numerical methods.

What would settle it

An experiment or simulation in the same quasi-one-dimensional domain that finds only supercritical onset, no hysteresis, and no stable coexistence of the three states would falsify the subcritical claim.

Figures

Figures reproduced from arXiv: 2605.31380 by Ke-Qing Xia, Lu Zhang.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: presents the time series of Nut and Nub dur￾ing different transitions. It is noteworthy that the for￾ward and reverse processes between each pair of states occur at different Ra values, indicating strong hystere￾sis. First, the convection-to-chaos transition at Ra0 = 8.18 × 107 and Ra1 = 8.20 × 107 takes O(104 ) time units [ [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: presents the quasi-static simulations that un￾cover the hysteretic transitions between convection and turbulence. In the forward quasi-static process with c = +50, start￾ing from a steady convective state at Ra0 = 7.6 × 107 [ [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: (a) presents the forward process, starting from the convective state at Ra0 = 7.9 × 107 . The system re￾mains in steady convection, with a linearly increasing Nu, for about 166, 000 free-fall units, before abruptly jumping to the high-Nu chaotic state (see the red ar￾row). The reverse process [ [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗
read the original abstract

We present both static and quasi-static direct numerical simulations of Rayleigh-B\'enard convection in a quasi-one-dimensional domain, revealing for the first time a clear subcritical transition to turbulence in a buoyancy-driven flow. Within a narrow range of Rayleigh number (Ra), three coexisting flow states are identified: steady convection, oscillatory chaos, and intermittent turbulence. The transitions between these states are accompanied by abrupt jumps in both the Nusselt number (Nu) and Reynolds number (Re), the key global transport quantities in buoyancy-driven flows. Additionally, they exhibit pronounced hysteresis, forming three distinct hysteresis loops in the Nu-Ra plane: normal, reverse, and anomalous loops. More importantly, we show that the steady convection state is linearly stable against infinitesimal perturbations but can transition to intermittent turbulence when subjected to finite-amplitude disturbances, which is a defining hallmark of subcriticality. Thus, contrary to the prevailing view that the transition from convection to turbulence is supercritical, our results demonstrate that buoyancy-driven turbulence can emerge via a subcritical route, paving the way for a unified framework that describes instability mechanisms in both buoyancy-driven and shear-driven 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

2 major / 1 minor

Summary. The manuscript presents static and quasi-static direct numerical simulations of Rayleigh-Bénard convection in a quasi-one-dimensional domain. It reports the coexistence of steady convection, oscillatory chaos, and intermittent turbulence within a narrow Ra range, with abrupt jumps in Nu and Re, three distinct hysteresis loops (normal, reverse, anomalous), and a linearly stable steady state that transitions to turbulence under finite-amplitude perturbations, establishing a subcritical route contrary to the prevailing supercritical view.

Significance. If the subcritical transition and hysteresis are shown to be intrinsic rather than confinement-induced, the result would be significant for fluid dynamics, providing the first clear demonstration of subcriticality in buoyancy-driven turbulence and supporting a unified framework with shear-driven flows. The use of both static and quasi-static DNS to track the states is a methodological strength.

major comments (2)
  1. [Abstract] Abstract: the claim of a general 'subcritical route' for buoyancy-driven turbulence is load-bearing on the assertion that the observed linear stability and finite-amplitude transition are not artifacts of quasi-1D mode suppression. The abstract explicitly links the result to the narrow domain and the DNS protocols, yet no tests varying the transverse aspect ratio are referenced to rule out elimination of linearly unstable transverse modes that would destroy the steady state in wider geometries.
  2. [Abstract] The central evidence for subcriticality (linear stability to infinitesimal perturbations combined with transition under finite-amplitude disturbances) requires explicit verification that the steady convective base state remains linearly stable only because of the confinement; without such checks or comparisons to wider domains, the distinction from standard supercritical primary bifurcation in Rayleigh-Bénard convection cannot be established as intrinsic.
minor comments (1)
  1. [Abstract] The abstract mentions 'static and quasi-static DNS' but provides no details on grid resolution, time-stepping, or perturbation protocols; these should be added to allow reproducibility assessment.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments. We respond point-by-point to the major comments, emphasizing that our study is confined to the quasi-one-dimensional setup as stated in the title, abstract, and manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim of a general 'subcritical route' for buoyancy-driven turbulence is load-bearing on the assertion that the observed linear stability and finite-amplitude transition are not artifacts of quasi-1D mode suppression. The abstract explicitly links the result to the narrow domain and the DNS protocols, yet no tests varying the transverse aspect ratio are referenced to rule out elimination of linearly unstable transverse modes that would destroy the steady state in wider geometries.

    Authors: Our work is explicitly limited to a quasi-one-dimensional domain, as indicated throughout the manuscript including the abstract, which links the findings to the narrow domain and the static/quasi-static DNS protocols. We demonstrate that, within this confined geometry, the steady convective state is linearly stable to infinitesimal perturbations yet transitions to intermittent turbulence under finite-amplitude disturbances, establishing subcriticality in this setting. We make no claim that the behavior is independent of confinement or occurs in wider domains; the result shows that a subcritical route is possible under quasi-1D confinement. Tests varying the transverse aspect ratio are not included, as they lie outside the scope of the present study. revision: no

  2. Referee: [Abstract] The central evidence for subcriticality (linear stability to infinitesimal perturbations combined with transition under finite-amplitude disturbances) requires explicit verification that the steady convective base state remains linearly stable only because of the confinement; without such checks or comparisons to wider domains, the distinction from standard supercritical primary bifurcation in Rayleigh-Bénard convection cannot be established as intrinsic.

    Authors: The evidence for subcriticality consists of the verified linear stability of the steady state to infinitesimal perturbations together with its transition under finite-amplitude disturbances, as obtained from the DNS in the quasi-1D domain. We do not claim this linear stability holds only because of confinement in a manner that makes subcriticality intrinsic to all buoyancy-driven flows, nor do we assert a distinction from the standard supercritical bifurcation outside the confined geometry. The abstract and text present the subcritical route as occurring under the specified quasi-1D confinement, contrary to the prevailing view for standard cases. Direct comparisons to wider domains are not performed in this work. revision: no

Circularity Check

0 steps flagged

No circularity: results are direct numerical observations with no derivation chain

full rationale

The manuscript consists entirely of static and quasi-static DNS in a quasi-1D domain. No analytical derivation, fitted parameters renamed as predictions, or self-citation load-bearing steps are present. The reported linear stability, finite-amplitude transitions, and hysteresis loops are outputs of the simulations themselves rather than reductions of prior equations or citations. The central claim (subcritical route) is therefore an empirical finding from the numerics and does not reduce to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated in the provided text.

pith-pipeline@v0.9.1-grok · 5733 in / 1182 out tokens · 32098 ms · 2026-06-28T20:47:57.868720+00:00 · methodology

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