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A Refined Similarity Hypothesis for Transverse Structure Functions

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Shiyi Chen, Katepalli R. Sreenivasan, Mark Nelkin, Nianzheng Cao

chao-dyn · Submitted 6 Apr 1997

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

The authors' main claim We argue on the basis of empirical data that Kolmogorov's refined similarity hypothesis (RSH) needs to be modified for transverse velocity increments, and propose an alternative.

how it is stated · asserted 0.88 read the record →

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arXiv IDchao-dyn/9704009 (version 1)
Pith IDEEIUJGU5, Pith's permanent record of this paper and its review
CitationKatepalli R. Sreenivasan, Mark Nelkin, Nianzheng Cao, Shiyi Chen. "A Refined Similarity Hypothesis for Transverse Structure Functions." arXiv:chao-dyn/9704009 (1997). https://pith.science/paper/EEIUJGU5
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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.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,582 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.18 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.88 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We argue on the basis of empirical data that Kolmogorov's refined similarity hypothesis (RSH) needs to be modified for transverse velocity increments, and propose an alternative. In this new form, transverse velocity increments bear the same relation to locally averaged enstrophy (squared vorticity) as longitudinal velocity increments bear in RSH to locally averaged dissipation. We support this hypothesis by analyzing high-resolution numerical simulation data for isotropic turbulence. RSH and its proposed modification for transverse velocity increments (RSHT) appear to represent two independent scaling groups.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We argue on the basis of empirical data that Kolmogorov's refined similarity hypothesis (RSH) needs to be modified for transverse velocity increments, and propose an alternative. contribution 0.97 0.83 0.79 asserted 0.88
s1 In this new form, transverse velocity increments bear the same relation to locally averaged enstrophy (squared vorticity) as longitudinal velocity increments bear in RSH to locally averaged dissipation. contribution 0.93 0.44 0.59 asserted 1.00
s2 We support this hypothesis by analyzing high-resolution numerical simulation data for isotropic turbulence. method 0.93 0.95 0.06 asserted 0.99
s3 RSH and its proposed modification for transverse velocity increments (RSHT) appear to represent two independent scaling groups. interpretation 0.54 0.70 0.21 hedged possibility 0.96

What kind of paper the classifier reports this is: position or commentary 0.61 · evidence from simulation or computation 0.97.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • 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 argue on the basis of empirical data that Kolmogorov's refined similarity hypothesis (RSH) needs to be modified for transverse velocity increments, and propose an alternative. In this new form, transverse velocity increments bear the same relation to locally averaged enstrophy (squared vorticity) as longitudinal velocity increments bear in RSH to locally averaged dissipation. We support this hypothesis by analyzing high-resolution numerical simulation data for isotropic turbulence. RSH and its proposed modification for transverse velocity increments (RSHT) appear to represent two independent scaling groups.

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