Euler Equations and Turbulence: Analytical Approach to Intermittency

Physical models of intermittency in fully developed turbulence employ many phenomenological concepts, including active volumes, regions, eddies, and energy accumulation sets, used to describe nonuniformity of the energy cascade. In this paper we give those notions a precise mathematical meaning in the language of the Littlewood--Paley analysis. We further use our definitions to recover scaling laws for the energy spectrum and second order structure function with proper intermittency correction.