Beyond Mixing-length Theory: a step toward 321D

Casey Meakin; John Lattanzio; Maxime Viallet; Miroslav Moc\'ak; Simon W. Campbell; W. David Arnett

RECORD

Beyond Mixing-length Theory: a step toward 321D

W. David Arnett, Casey Meakin, Maxime Viallet, Simon W. Campbell, John Lattanzio, Miroslav Mocák

Solar and Stellar Astrophysics · Submitted 1 Mar 2015

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We find that (1) braking regions (boundary layers in which mixing occurs) automatically appear {\it beyond} the edges of convection as defined by the Schwarzschild criterion, (2) dynamic (non-local) terms imply a non-zero turbulent kinetic energy flux (unlike MLT), (3) the effects of composition gradients on flow can be comparable to thermal effects, and (4) convective boundaries in neutrino-cooled stages differ in nature from those in photon-cooled stages (different P\'eclet numbers).

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

arXiv ID1503.00342 (version 2)

Pith IDJWDADECV, Pith's permanent record of this paper and its review

CitationCasey Meakin, John Lattanzio, Maxime Viallet, Miroslav Moc\'ak, Simon W. Campbell, W. David Arnett. "Beyond Mixing-length Theory: a step toward 321D." arXiv:1503.00342 (2015). https://pith.science/paper/JWDADECV

Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 7,810 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.18 · human participants 0.01 · controlled comparison 0.33 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.91 · mentions code or data availability 0.03.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We examine the physical basis for algorithms to replace mixing-length theory (MLT) in stellar evolutionary computations. Our 321D procedure is based on numerical solutions of the Navier-Stokes equations. These implicit large eddy simulations (ILES) are three-dimensional (3D), time-dependent, and turbulent, including the Kolmogorov cascade. We use the Reynolds-averaged Navier-Stokes (RANS) formulation to make concise the 3D simulation data, and use the 3D simulations to give closure for the RANS equations. We further analyze this data set with a simple analytical model, which is non-local and time-dependent, and which contains both MLT and the Lorenz convective roll as particular subsets of solutions. A characteristic length (the damping length) again emerges in the simulations; it is determined by an observed balance between (1) the large-scale driving, and (2) small-scale damping. The nature of mixing and convective boundaries is analyzed, including dynamic, thermal and compositional effects, and compared to a simple model. We find that (1) braking regions (boundary layers in which mixing occurs) automatically appear {\it beyond} the edges of convection as defined by the Schwarzschild criterion, (2) dynamic (non-local) terms imply a non-zero turbulent kinetic energy flux (unlike MLT), (3) the effects of composition gradients on flow can be comparable to thermal effects, and (4) convective boundaries in neutrino-cooled stages differ in nature from those in photon-cooled stages (different P\'eclet numbers). The algorithms are based upon ILES solutions to the Navier-Stokes equations, so that, unlike MLT, they do not require any calibration to astronomical systems in order to predict stellar properties. Implications for solar abundances, helioseismology, asteroseismology, nucleosynthesis yields, supernova progenitors and core collapse are indicated.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We examine the physical basis for algorithms to replace mixing-length theory (MLT) in stellar evolutionary computations.	contribution 0.68	0.86	0.04	unclear 0.56
s1	Our 321D procedure is based on numerical solutions of the Navier-Stokes equations.	method 0.95	0.85	0.06	asserted 1.00
s2	These implicit large eddy simulations (ILES) are three-dimensional (3D), time-dependent, and turbulent, including the Kolmogorov cascade.	method 0.98	0.77	0.05	asserted 1.00
s3	We use the Reynolds-averaged Navier-Stokes (RANS) formulation to make concise the 3D simulation data, and use the 3D simulations to give closure for the RANS equations.	method 0.99	0.91	0.06	asserted 1.00
s4	We further analyze this data set with a simple analytical model, which is non-local and time-dependent, and which contains both MLT and the Lorenz convective roll as particular subsets of solutions.	method 0.92	0.93	0.07	asserted 1.00
s5	A characteristic length (the damping length) again emerges in the simulations; it is determined by an observed balance between (1) the large-scale driving, and (2) small-scale damping.	result 0.97	0.88	0.08	asserted 1.00
s6	The nature of mixing and convective boundaries is analyzed, including dynamic, thermal and compositional effects, and compared to a simple model.	contribution 0.70	0.85	0.05	asserted 0.78
s7	We find that (1) braking regions (boundary layers in which mixing occurs) automatically appear {\it beyond} the edges of convection as defined by the Schwarzschild criterion, (2) dynamic (non-local) terms imply a non-zero turbulent kinetic energy flux (unlike MLT), (3) the effects of composition gradients on flow can be comparable to thermal effects, and (4) convective boundaries in neutrino-cooled stages differ in nature from those in photon-cooled stages (different P\'eclet numbers).	result 1.00	0.95	0.65	asserted 1.00
s8	The algorithms are based upon ILES solutions to the Navier-Stokes equations, so that, unlike MLT, they do not require any calibration to astronomical systems in order to predict stellar properties.	interpretation 0.33	0.71	0.26	asserted 1.00
s9	Implications for solar abundances, helioseismology, asteroseismology, nucleosynthesis yields, supernova progenitors and core collapse are indicated.	interpretation 0.97	0.39	0.07	hedged possibility 0.97

What kind of paper the classifier reports this is: method or tool 0.54 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

We examine the physical basis for algorithms to replace mixing-length theory (MLT) in stellar evolutionary computations. Our 321D procedure is based on numerical solutions of the Navier-Stokes equations. These implicit large eddy simulations (ILES) are three-dimensional (3D), time-dependent, and turbulent, including the Kolmogorov cascade. We use the Reynolds-averaged Navier-Stokes (RANS) formulation to make concise the 3D simulation data, and use the 3D simulations to give closure for the RANS equations. We further analyze this data set with a simple analytical model, which is non-local and time-dependent, and which contains both MLT and the Lorenz convective roll as particular subsets of solutions. A characteristic length (the damping length) again emerges in the simulations; it is determined by an observed balance between (1) the large-scale driving, and (2) small-scale damping. The nature of mixing and convective boundaries is analyzed, including dynamic, thermal and compositional effects, and compared to a simple model. We find that (1) braking regions (boundary layers in which mixing occurs) automatically appear {\it beyond} the edges of convection as defined by the Schwarzschild criterion, (2) dynamic (non-local) terms imply a non-zero turbulent kinetic energy flux (unlike MLT), (3) the effects of composition gradients on flow can be comparable to thermal effects, and (4) convective boundaries in neutrino-cooled stages differ in nature from those in photon-cooled stages (different P\'eclet numbers). The algorithms are based upon ILES solutions to the Navier-Stokes equations, so that, unlike MLT, they do not require any calibration to astronomical systems in order to predict stellar properties. Implications for solar abundances, helioseismology, asteroseismology, nucleosynthesis yields, supernova progenitors and core collapse are indicated.

Human review

How Pith checks papers → · Full audit of this paper →

References

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

An asteroseismic age estimate for the Pleiades using a neural-network emulator of rotating $\delta$ Scuti pulsation models
astro-ph.SR 2026-10 conditional novelty 7.0 of 10

A probabilistic neural-network emulator of rotating delta Scuti pulsation models yields a combined Pleiades cluster age of 113.3 ± 4.5 Myr, consistent with lithium-depletion and isochrone methods.
The Mass Function of Neutron Stars from Core-Collapse Supernova Simulations
astro-ph.HE 2026-08 conditional novelty 5.0 of 10

Using a compactness-to-mass mapping from 3D supernova simulations, the authors construct a theoretical neutron star birth mass function that, after fitting black-hole and kick fractions, resembles the observed mass di...
Effects of Rotation on 3D Core-Collapse Supernova Models for Low-Mass Progenitors
astro-ph.HE 2026-07 conditional novelty 5.0 of 10

For a low-mass CCSN progenitor, rotation alone weakly and non-monotonically affects explosion energy and observables; only the fastest spin yields T/|W| spiral modes and spin-kick alignment, with core spin amplified by ~4000.

How the literature uses it

4 arXiv papers cite this in 5 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 3 sentences without a confident label

Cites it as background 2 papers

Despite extensive efforts to study stellar convection [ref] , the mixing length theory [ref] ,

On the possibility of chemically driven convection in red giants. Implications for the He-core flash and mixing above the Red Giant Branch Bump · Introduction · 0.90
For our work, the compositional changes induced by multi-dimensional effects in the progenitor evolution [ref] would be of particular interest and could be the subject of future work.

Pushing 1D CCSNe to explosions: model and SN 1987A · Summary and Conclusions · 0.80

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.