Energy cascades and flux locality in physical scales of the 3D Navier-Stokes equations

TL;DR

This paper provides rigorous estimates for energy flux in 3D Navier-Stokes equations, establishing conditions for the inertial range and energy cascade in decaying turbulence without assuming regularity or homogeneity.

Contribution

It introduces new bounds on energy flux in physical scales, linking them to physical parameters and proving flux locality without regularity assumptions.

Findings

Established sufficient conditions for inertial range existence

Derived bounds on energy flux in physical scales

Demonstrated flux locality in 3D turbulence

Abstract

Rigorous estimates for the total - (kinetic) energy plus pressure - flux in R^3 are obtained from the three dimensional Navier-Stokes equations. The bounds are used to establish a condition - involving Taylor length scale and the size of the domain - sufficient for existence of the inertial range and the energy cascade in decaying turbulence (zero driving force, non-increasing global energy). Several manifestations of the locality of the flux under this condition are obtained. All the scales involved are actual physical scales in R^3 and no regularity or homogeneity/scaling assumptions are made.