Hidden spatiotemporal symmetries and intermittency in turbulence

Abstract We consider general infinite-dimensional dynamical systems with the Galilean and spatiotemporal scaling symmetry groups. Introducing equivalence relation respect to temporal scalings transformations, we define a representative set containing single element within each class. Temporal transformations do not commute evolution operator (flow) and, hence, is invariant. Despite of that, prove that normalized flow an invariant probability measure can be introduced on set, such symmetries are preserved in statistical sense. focus hidden symmetries, which broken original system but restored system. The central motivation application this construction intermittency phenomenon turbulence. show yield power law for structure functions, derive formulas their exponents terms measures. use transformation leads quasi-Lagrangian description, making developed theory applicable Euler Navier–Stokes systems.