Euler equations and turbulence: analytical approach to intermittency

TL;DR

This paper provides a rigorous mathematical framework for intermittency in turbulence using Littlewood-Paley analysis, deriving corrected scaling laws for energy spectrum and structure functions.

Contribution

It introduces precise mathematical definitions for phenomenological concepts in turbulence and derives corrected scaling laws using these definitions.

Findings

Recovered scaling laws for energy spectrum with intermittency correction

Derived second order structure function scaling with intermittency effects

Established a rigorous mathematical foundation for turbulence intermittency

Abstract

Physical models of intermittency in fully developed turbulence employ many phenomenological concepts such as active volume, region, eddy, energy accumulation set, etc, used to describe non-uniformity 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.