Shell model intermittency is the hidden self-similarity

We show that the intermittent dynamics observed in the inertial interval of the 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 Kolmogorov 1941 (K41) theory] are replaced by the hidden scaling symmetry, which is an exact symmetry of in viscid dynamics represented in special rescaled coordinates and times. We derive formulas expressing the 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.