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arxiv: 1907.05421 · v1 · pith:PN2C54O2new · submitted 2019-07-11 · ⚛️ physics.flu-dyn

A DNS Study of entrainment in an axisymmetric turbulent jet as an episodic process

Prasanth Prabhakaran , Sachin Shinde , Roddam Narasimha This is my paper

Pith reviewed 2026-05-24 23:00 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords entrainmentturbulent jetDNST/NT interfacenibblingepisodic processburstiness
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0 comments X

The pith

Entrainment in an axisymmetric turbulent jet occurs as an episodic process of inrush into interface gulfs followed by nibbling.

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

The paper performs DNS of a steady self-preserving incompressible axisymmetric turbulent jet at Reynolds number 2400 to produce accurate maps of the outer irrotational flow and the vorticity field inside the core. It establishes that entrainment proceeds through distinct periods of large inrush of ambient fluid that distorts the turbulent/nonturbulent interface into deep, twisted gulfs or wells; part of the inrushing fluid then crosses the interface by nibbling. The duration of each inrush reaches up to 20 flow units and produces an entrainment burstiness of order 0.75, comparable to momentum-flux burstiness in a boundary layer. A sympathetic reader would care because the finding reframes mixing rates in jets as intermittent rather than continuous.

Core claim

The DNS data require two separate jet boundaries: an inner turbulent/nonturbulent (T/NT) boundary where vorticity rises steeply toward the core, and an outer rotational/irrotational boundary beyond which the flow is irrotational. Axial and diametral sections show intervals when ambient fluid rushes inward, accelerating even as it is forced into a narrowing gulf that distorts the T/NT interface; fluid then penetrates the interface inside the gulf by nibbling. These inrush episodes last up to 20 flow units and produce an entrainment burstiness of order 0.75.

What carries the argument

The distinction between the inner T/NT boundary (where vorticity rises steeply) and the outer rotational/irrotational boundary, together with identification of inrush events from the DNS velocity and vorticity fields that form gulfs or wells.

If this is right

  • Entrainment proceeds by inrush of ambient fluid into the T/NT interface followed by nibbling inside the resulting gulf.
  • Individual inrush episodes last up to 20 flow units.
  • The entrainment burstiness reaches order 0.75 and matches the momentum-flux burstiness reported for turbulent boundary layers.
  • Ordered, nearly irrotational circulatory motions outside the outer boundary are induced by vorticity elements inside coherent structures of the turbulent core.

Where Pith is reading between the lines

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

  • Average entrainment-rate models for jets may need explicit intermittency corrections to match observed burstiness.
  • The same inrush-and-nibbling sequence could be examined in other free shear flows such as plane mixing layers.
  • Lagrangian particle tracking in the same DNS fields could directly measure the fraction of inrushing fluid that crosses the interface by nibbling.

Load-bearing premise

The DNS vorticity and velocity fields permit unbiased identification of inrush events and the two boundaries that capture the actual entrainment mechanism.

What would settle it

A similar DNS at higher Reynolds number or finer resolution in which inrush events are absent and entrainment proceeds at a steady rate would falsify the episodic characterization.

Figures

Figures reproduced from arXiv: 1907.05421 by Prasanth Prabhakaran, Roddam Narasimha, Sachin Shinde.

Figure 1
Figure 1. Figure 1: FIG. 1. Diagram of an axial section to illustrate main termin [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Axial section in the [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Axial section in the [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Temporal evolution of a part of the jet from Fig. 2. Thr [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Temporal variation of the total vorticity modulus at [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a & b) Instantaneous velocity in the ambient fluid and [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Ambient velocity and core azimuthal vorticity ( [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Four instantaneous diametral sections of images at [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Four instantaneous diametral sections at same [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Conventions followed for overlap analysis; see tex [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. See Fig. 10 for conventions. (a) Instantaneous imag [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Schematic for the mass flux budget (see text for detai [PITH_FULL_IMAGE:figures/full_fig_p018_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Streamwise variation of radial mass flux into the 8 [PITH_FULL_IMAGE:figures/full_fig_p019_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Streamwise variation of the mass flux within the T/NT [PITH_FULL_IMAGE:figures/full_fig_p020_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Azimuthal variation of mass flux at the R/IR interfac [PITH_FULL_IMAGE:figures/full_fig_p020_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. Variation of fractional contribution to mass flux at [PITH_FULL_IMAGE:figures/full_fig_p021_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17. Variation of cumulative mass flux as a function of cum [PITH_FULL_IMAGE:figures/full_fig_p021_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18. Burstiness curve: Variation of cumulative mass flux [PITH_FULL_IMAGE:figures/full_fig_p022_18.png] view at source ↗
Figure 2
Figure 2. Figure 2: The azimuthal variation of mass flux near the T/NT interface [PITH_FULL_IMAGE:figures/full_fig_p023_2.png] view at source ↗
read the original abstract

This investigation is based on a DNS of a steady self-preserving incompressible axisymmetric turbulent jet at a Reynolds number of 2400. The DNS data enable accurate maps of the outer irrotational flow field, and also the vorticity field in the turbulent core of the jet. It is found necessary to define two separate boundaries of the jet. The first is an inner boundary (turbulent/nonturbulent, T/NT), from where vorticity rises steeply towards to the core. The second is an outer rotational/irrotational boundary, beyond which the flow may be considered irrotational. The velocity field beyond the outer boundary often has ordered, nearly irrotational circulatory motions. These can be shown, in simpler cases, to be the velocity field induced by one or more vorticity elements in a coherent structure in the turbulent core. A detailed examination of axial and diametral sections indicates that there are periods when there is a large inrush of ambient fluid into parts of the T/NT interface, which gets distorted into a gulf or well that can be both twisted and deep. Sections of these wells often appear as what may be called as lakes of irrotational fluid in diametral sections of the jet flow. Part of the inrushing fluid crosses the T/NT interface within the well and is entrained into the turbulent core, by a process that can legitimately be called nibbling. The duration of such an inrush process can be of the order up to 20 flow units and suggests that entrainment can be an episodic process in which an inrush event accelerates ambient fluid even as it is pushed into a narrowing gulf, where it penetrates the T/NT interface of the gulf by nibbling. In the turbulent round jet, the entrainment burstiness is found to be of order 0.75, comparable to the momentum flux burstiness found in a turbulent boundary layer.

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 DNS results for a steady self-preserving incompressible axisymmetric turbulent jet at Re=2400. It defines an inner T/NT boundary (where vorticity rises steeply) and an outer rotational/irrotational boundary. From examination of axial and diametral sections, it concludes that entrainment occurs as an episodic process: inrush events accelerate ambient fluid into narrowing gulfs or wells at the interface, followed by nibbling across the inner T/NT boundary. The entrainment burstiness is reported as order 0.75, comparable to momentum-flux burstiness in boundary layers.

Significance. If the episodic characterization and burstiness value can be placed on an objective, statistically representative footing, the work would supply a mechanistic distinction between continuous and intermittent entrainment models in free shear flows, with direct implications for entrainment-rate closures. The DNS access to simultaneous vorticity and velocity fields is a clear strength supporting the two-boundary description.

major comments (2)
  1. [Abstract] Abstract: the entrainment burstiness is stated as 'of order 0.75' with no explicit definition of the metric, no formula for its extraction from the DNS velocity or vorticity fields, and no uncertainty or convergence information. Because this scalar is the sole quantitative support for the central claim that entrainment is episodic, the absence of its definition is load-bearing.
  2. [Abstract] Abstract: the identification of inrush events and gulfs rests on 'detailed examination of axial and diametral sections' without any statement of sampling protocol (random, exhaustive, or threshold-based), number of sections examined, or a priori criteria (e.g., radial-velocity threshold or duration). This directly engages the concern that the reported phenomena and burstiness value may reflect post-hoc selection rather than unconditional statistics of the Re=2400 fields.
minor comments (1)
  1. [Abstract] The normalization used for 'flow units' (mentioned for the ~20-unit duration of inrush events) is not stated in the abstract; a brief definition would aid readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and for recognizing the value of the simultaneous vorticity and velocity fields from the DNS. We address each major comment below. The requested clarifications will be incorporated into the revised manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the entrainment burstiness is stated as 'of order 0.75' with no explicit definition of the metric, no formula for its extraction from the DNS velocity or vorticity fields, and no uncertainty or convergence information. Because this scalar is the sole quantitative support for the central claim that entrainment is episodic, the absence of its definition is load-bearing.

    Authors: We agree that the abstract lacks an explicit definition of the burstiness metric. The revised manuscript will add a clear definition, the formula used to compute it from the DNS fields, and available information on uncertainty or convergence. This will provide the necessary quantitative grounding for the episodic characterization. revision: yes

  2. Referee: [Abstract] Abstract: the identification of inrush events and gulfs rests on 'detailed examination of axial and diametral sections' without any statement of sampling protocol (random, exhaustive, or threshold-based), number of sections examined, or a priori criteria (e.g., radial-velocity threshold or duration). This directly engages the concern that the reported phenomena and burstiness value may reflect post-hoc selection rather than unconditional statistics of the Re=2400 fields.

    Authors: We agree that the description of the examination process is insufficiently detailed. The revised manuscript will specify the sampling protocol, the number of axial and diametral sections inspected, and the criteria applied to identify inrush events and interface distortions. This will clarify that the reported features are drawn from systematic inspection of the available fields. revision: yes

Circularity Check

0 steps flagged

No circularity: claims rest on direct DNS field observations without fitted inputs or self-referential derivations

full rationale

The paper reports observations from a Re=2400 DNS of an axisymmetric jet, defining inner T/NT and outer irrotational boundaries from vorticity and velocity fields, then describing inrush events and nibbling from examination of axial/diametral sections. The burstiness value of order 0.75 is stated as extracted from the data and compared to an external boundary-layer result; no equations, parameters, or uniqueness theorems are invoked that reduce the central claims to inputs by construction. The analysis is self-contained against the simulation fields as external benchmark, with no self-citation load-bearing steps or ansatz smuggling.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the accuracy of the DNS vorticity field and the chosen definitions of the two boundaries; no free parameters, axioms, or invented entities are introduced beyond standard incompressible Navier-Stokes assumptions.

axioms (2)
  • standard math The flow is incompressible and governed by the Navier-Stokes equations at the stated Reynolds number.
    Invoked implicitly as the basis for the DNS.
  • domain assumption The jet reaches a steady self-preserving state.
    Stated in the abstract as the condition of the simulated flow.

pith-pipeline@v0.9.0 · 5891 in / 1286 out tokens · 29940 ms · 2026-05-24T23:00:01.806857+00:00 · methodology

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Reference graph

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