Perturbative anomalous exponents from Kolmogorov multipliers
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911717872631808 |
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| author | Mailybaev, Alexei A. Thalabard, Simon |
| author_facet | Mailybaev, Alexei A. Thalabard, Simon |
| contents | We introduce a perturbative framework for anomalous scaling in turbulent transport based on multiplier statistics, rather than zero-mode calculations. We illustrate the approach using a shell model combining deterministic and Kraichnan-like stochastic components. The problem is reduced 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 non-integer moments. More broadly, the results suggest that multiplier statistics provide a viable route for computing anomalous exponents in turbulent transport, complementing recent hidden-symmetry approaches while circumventing the limitations of zero-mode methods based on a closed Hopf hierarchy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_26359 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Perturbative anomalous exponents from Kolmogorov multipliers Mailybaev, Alexei A. Thalabard, Simon Fluid Dynamics We introduce a perturbative framework for anomalous scaling in turbulent transport based on multiplier statistics, rather than zero-mode calculations. We illustrate the approach using a shell model combining deterministic and Kraichnan-like stochastic components. The problem is reduced 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 non-integer moments. More broadly, the results suggest that multiplier statistics provide a viable route for computing anomalous exponents in turbulent transport, complementing recent hidden-symmetry approaches while circumventing the limitations of zero-mode methods based on a closed Hopf hierarchy. |
| title | Perturbative anomalous exponents from Kolmogorov multipliers |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2605.26359 |