Shell model intermittency is the hidden self-similarity
arXiv:2201.04005 · doi:10.1103/PhysRevFluids.7.034604
Abstract
We show that the intermittent dynamics observed in the inertial interval of Sabra shell model of turbulence can be rigorously related to the property of scaling self-similarity. In this connection, the space-time scaling symmetries (like in the K41 theory) are replaced by the new hidden scaling symmetry, which is an exact symmetry of inviscid dynamics represented in special rescaled coordinates and times. We derive the formulas expressing anomalous scaling exponents in terms of Perron-Frobenius eigenvalues of linear operators based on the self-similar statistics. Theoretical conclusions are verified by extensive numerical simulations.
arXiv comment25 pages, 7 figures
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- Nonlinear phase synchronization and the role of spacing in shell models
- Perturbative anomalous exponents from Kolmogorov multipliers