Perturbative Anomalous Exponents from Kolmogorov Multipliers.

Authors

Alexei A Mailybaev, Simon Thalabard

Published in

Physical review letters. Volume 137. Issue 9. Pages 094002. Aug 28, 2026.

Abstract

Intermittency, manifested through anomalous scaling, remains one of the central unresolved problems in turbulence theory, with few analytical approaches extending beyond idealized linear transport models. We introduce a perturbative framework for anomalous scaling in turbulent transport based on multiplier statistics, rather than zero-mode calculations. We demonstrate the approach using a shell model combining deterministic and Kraichnan-like stochastic components. We reduce the problem to the analysis of a stationary Fokker-Planck equation for Kolmogorov multipliers, defined as ratios of successive scalar amplitudes. Its solution yields the invariant measure through a perturbative expansion around a Gaussian distribution. Using the resulting multiplier statistics, we compute explicit anomalous scaling exponents for structure functions of arbitrary order, including odd, even, and noninteger moments. Although demonstrated here for a shell model, the framework suggests a systematic perturbative route toward analytical theories of intermittency in turbulence.

PMID:
42726986
Bibliographic data and abstract were imported from PubMed on 12 Sep 2026.

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