Multi-time scale-invariance of turbulence in a shell model
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917981089431552 |
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| author | Mailybaev, Alexei A. |
| author_facet | Mailybaev, Alexei A. |
| contents | When time and velocities are dynamically rescaled relative to the instantaneous turnover time, the Sabra shell model acquires another (hidden) form of scaling symmetry. It has been previously shown that this symmetry is statistically restored in the inertial interval of developed turbulence, thereby establishing a self-similarity property derived from first principles and replacing the broken $1/3$-scaling of the K41 theory. Multifractal intermittency follows from the restored hidden symmetry, in which the anomalous scaling exponents $ζ_p$ are identified as Perron-Frobenius eigenvalues. In this paper, we use the hypothesis of restored hidden symmetry to address the multi-time statistics of turbulent fluctuations. The central result is the self-similarity rule stating that any observable that is time-scale homogeneous of degree $p$ is self-similar with the Hölder exponent $h = ζ_p/p$. As a particular case, it yields the scaling laws for decorrelation times of fluctuations obtained previously within the phenomenological multifractal approach. As further applications, we formulate self-similarity rules for multi-time structure functions and multi-time Kolmogorov multipliers and verify them numerically. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_06321 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multi-time scale-invariance of turbulence in a shell model Mailybaev, Alexei A. Fluid Dynamics When time and velocities are dynamically rescaled relative to the instantaneous turnover time, the Sabra shell model acquires another (hidden) form of scaling symmetry. It has been previously shown that this symmetry is statistically restored in the inertial interval of developed turbulence, thereby establishing a self-similarity property derived from first principles and replacing the broken $1/3$-scaling of the K41 theory. Multifractal intermittency follows from the restored hidden symmetry, in which the anomalous scaling exponents $ζ_p$ are identified as Perron-Frobenius eigenvalues. In this paper, we use the hypothesis of restored hidden symmetry to address the multi-time statistics of turbulent fluctuations. The central result is the self-similarity rule stating that any observable that is time-scale homogeneous of degree $p$ is self-similar with the Hölder exponent $h = ζ_p/p$. As a particular case, it yields the scaling laws for decorrelation times of fluctuations obtained previously within the phenomenological multifractal approach. As further applications, we formulate self-similarity rules for multi-time structure functions and multi-time Kolmogorov multipliers and verify them numerically. |
| title | Multi-time scale-invariance of turbulence in a shell model |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2501.06321 |