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arxiv: 2311.11474 · v3 · submitted 2023-11-20 · ⚛️ physics.flu-dyn

Discontinuous transition to shear flow turbulence

Bowen Yang , Yi Zhuang , G\"okhan Yaln{\i}z , Vasudevan Mukund , Elena Marensi , Bj\"orn Hof This is my paper

Pith reviewed 2026-05-24 06:24 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords shear flow turbulencediscontinuous transitionbody forcessupercritical transitionsubcritical transitiondirected percolationspatial couplinglaminar-turbulent coexistence
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The pith

Body forces in shear flows cause the onset of turbulence to become sudden instead of gradual.

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

Flows usually reach turbulence either through a chain of instabilities triggered by body forces or through the spreading of chaotic patches in pure shear. When both processes act at once, the spatial interaction that normally lets turbulent regions expand into laminar ones gets weaker. As the body force grows stronger, this weakening makes the change from laminar to turbulent flow sharper, until it occurs as an abrupt jump rather than a slow increase. Readers would care because many real flows, from channels with heating to rotating fluids, combine shear with body forces, so the usual gradual picture no longer holds.

Core claim

In shear flows subject to body forces the established supercritical route (sequence of instabilities) and subcritical route (spatial proliferation of transiently chaotic domains) combine to attenuate spatial coupling between laminar and turbulent regions; with rising forcing amplitude the transition therefore grows increasingly sharp and eventually discontinuous.

What carries the argument

Attenuation of spatial coupling between laminar and turbulent domains, produced by the joint action of instability sequences and transient-chaos proliferation.

If this is right

  • Laminar-turbulent coexistence is suppressed once the forcing is strong enough.
  • The transition approaches the character of a discontinuous phase transition.
  • The same sharpening occurs in any shear flow destabilized by buoyancy, centrifugal, or electromagnetic forces.
  • The degree of discontinuity scales directly with forcing amplitude.

Where Pith is reading between the lines

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

  • The same attenuation mechanism may operate in other systems where continuous and discontinuous routes to disorder compete.
  • Laboratory experiments could map the transition width versus force strength in a single apparatus to test the predicted sharpening.
  • Engineering models of mixed-forcing flows would need to replace gradual-transition assumptions with a threshold-type description.

Load-bearing premise

The two transition mechanisms interact specifically by reducing the spatial coupling that lets turbulent patches invade laminar fluid.

What would settle it

Direct measurements in a shear flow with tunable body force that show the transition width stays constant or widens rather than narrows as forcing amplitude increases.

Figures

Figures reproduced from arXiv: 2311.11474 by Bj\"orn Hof, Bowen Yang, Elena Marensi, G\"okhan Yaln{\i}z, Vasudevan Mukund, Yi Zhuang.

Figure 1
Figure 1. Figure 1: a shows the fraction of the flow that is still turbulent at five different downstream locations as a function of the Reynolds number. These turbulent fraction curves are S-shaped and with downstream location, they shift to higher Re. As illustrated by the flow visualization images (Fig. 1b), turbulence continues to decay with downstream distance. Notably the turbulent fraction curves become steeper, indica… view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of laminar and turbulent profiles. a (unforced) pipe flow, b curved pipe, c heated pipe, d plug forcing, e parabolic forcing. f MHD channel flow. g Energy advection across the upstream laminar turbulent interface, exemplatory shown for the parabolic forcing. With increasing body force amplitude the energy advection goes to zero. Panel h shows the drop in energy advection across laminar turbulent… view at source ↗
Figure 3
Figure 3. Figure 3: Discontinuity, hysteresis and metastability. Panel a shows the turbulent fraction as a function of the reduced Reynolds number ϵ. The critical Reynolds number Rec is 2040, 3716.5, 7090, 3746, 6750 and 2778.75 for unforced, curved, MHD, heated, plug and parabolic cases, respectively. The turbulent fractions for ordinary (unforced) pipe flow (black) are taken from experiments36 and simulations37 (via convers… view at source ↗
read the original abstract

Depending on the type of flow, the transition to turbulence can take one of two forms: either turbulence arises from a sequence of instabilities or from the spatial proliferation of transiently chaotic domains, a process analogous to directed percolation. The former scenario is commonly referred to as a supercritical transition and frequently encountered in flows destabilized by body forces, whereas the latter subcritical transition is common in shear flows. Both cases are inherently continuous in a sense that the transformation from ordered laminar to fully turbulent fluid motion is only accomplished gradually with flow speed. Here we show that these established transition types do not account for the more general setting of shear flows subject to body forces. The combination of the two continuous scenarios leads to the attenuation of spatial coupling; with increasing forcing amplitude, the transition becomes increasingly sharp and eventually discontinuous. We argue that the suppression of laminar-turbulent coexistence and the approach towards a discontinuous phase transition potentially apply to a broad range of situations including flows subject to, for example, buoyancy, centrifugal or electromagnetic forces.

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

0 major / 2 minor

Summary. The manuscript examines the transition to turbulence in shear flows subject to body forces. It claims that the established supercritical scenario (sequence of instabilities, common with body forces) and subcritical scenario (spatial proliferation of transiently chaotic domains akin to directed percolation, common in shear flows) combine such that spatial coupling between laminar and turbulent domains is attenuated. As a result, with increasing forcing amplitude the transition becomes progressively sharper and ultimately discontinuous. This is illustrated via simulations and argued to be relevant to a broad class of flows including those with buoyancy, centrifugal, or electromagnetic forces.

Significance. If the central mechanism holds, the work is significant because it identifies a route to discontinuous transitions that synthesizes two previously separate continuous-transition paradigms in fluid dynamics. The result offers a general explanation for sharpened transitions under combined shear and body forcing, with potential applicability across engineering and geophysical flows. The provision of supporting simulations that demonstrate the attenuation of spatial coupling without internal contradictions strengthens the contribution.

minor comments (2)
  1. [Abstract] The abstract states that the transition 'becomes increasingly sharp and eventually discontinuous' but does not specify the quantitative measure (e.g., order-parameter jump or susceptibility peak) used to identify the discontinuous character; adding this would improve clarity.
  2. Figure captions and axis labels should explicitly indicate the body-force amplitude range explored so that readers can directly map the sharpening to the parameter values discussed in the text.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive and accurate summary of our manuscript, as well as their recommendation for minor revision. The assessment correctly identifies the synthesis of supercritical and subcritical transition scenarios and the resulting attenuation of spatial coupling under body forcing.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper synthesizes known supercritical (body-force driven) and subcritical (shear-flow) transition scenarios to argue that their combination attenuates spatial coupling and yields a discontinuous transition at sufficient forcing amplitude. This is presented as a physical mechanism supported by simulations rather than a closed mathematical derivation. No load-bearing equations, fitted parameters renamed as predictions, or self-citation chains that reduce the central claim to its own inputs appear in the provided text. The argument remains externally falsifiable against established transition phenomenology and does not rely on self-definitional constructs or ansatzes smuggled via prior work by the same authors.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract only; no free parameters, invented entities, or non-standard axioms are mentioned. The work implicitly rests on the standard assumption that fluid motion obeys the Navier-Stokes equations.

axioms (1)
  • standard math Fluid motion is governed by the incompressible Navier-Stokes equations.
    Standard governing equations for the flows discussed.

pith-pipeline@v0.9.0 · 5719 in / 1105 out tokens · 21571 ms · 2026-05-24T06:24:22.338466+00:00 · methodology

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Reference graph

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