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Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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Partial Universal Critical Point in Turbulent Flows: Spectral Gap Universality Without Blow-Up Scaling

Authors: Williams, Keenan;

Partial Universal Critical Point in Turbulent Flows: Spectral Gap Universality Without Blow-Up Scaling

Abstract

We report evidence for partial universality in turbulent flows through systematic analysis of the Johns Hopkins Turbulence Database and cross-model theoretical validation. While temporal blow-up scaling remains model-dependent, we find spectral gap consistency in idealized models following the Möbius transformation γ = (3c_l − 1)/(2c_l − 1). Phenomenological derivation from self-similar dynamics predicts the value γ = 8/5, with signature detection in isotropic turbulence at Re_λ ≈ 1250 showing evidence consistent with this spectral gap value (8.8% deviation) while the full Möbius structure remains model-specific. This suggests selective universality as a paradigm in turbulence physics: some mathematical structures may show consistency between idealized models and realistic flows while temporal dynamics remain system-specific. Our findings provide evidence consistent with universal critical point mathematics under our estimator in three-dimensional turbulent flows.

Keywords

computational methods, Isotropic turbulence, intermittency, scaling laws, Navier-Stokes, spectral, Turbulence theory, Vortex dynamics, homogenous turbulence, self-similar, singular, blow-up

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
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