Published February 4, 2026 | Version v1
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Partial Universal Critical Point in Turbulent Flows: Spectral Gap Universality Without Blow-Up Scaling

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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.

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Submitted
2026-02-04