Shell model intermittency is the hidden self-similarity

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.

25 pages, 7 figures

References in corpus (6)

• Hidden scale invariance in Navier-Stokes intermittency
• Hidden spatiotemporal symmetries and intermittency in turbulence
• Fibonacci turbulence
• Solvable intermittent shell model of turbulence
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Cited by in corpus (6)

• Hidden spatiotemporal symmetries and intermittency in turbulence
• Hidden scale invariance of turbulence in a shell model: from forcing to dissipation scales
• Dyadic models for fluid equations: a survey
• Shell Models on Recurrent Sequences: Fibonacci, Padovan and Other Series
• Nonlinear phase synchronization and the role of spacing in shell models
• Perturbative anomalous exponents from Kolmogorov multipliers