On the Steady State Distributions for Turbulence

TL;DR

This paper proposes explicit steady state distributions for turbulence in 2D and 3D, emphasizing the role of area and volume preserving transformations, potentially explaining key turbulence scaling laws.

Contribution

It introduces explicit forms for turbulence distributions based on diffeomorphisms, linking mathematical structures to turbulence scaling behaviors.

Findings

Distributions can reproduce Kolmogorov and Kraichnan scaling laws.

Highlights the importance of diffeomorphisms in turbulence modeling.

Provides a theoretical framework for steady state turbulence distributions.

Abstract

We propose explicit forms for the steady state distributions governing fully developed turbulence in two and three spatial dimensions. We base our proposals on the crucial importance of the area and volume preserving diffeomorphisms in the space of velocities. We argue that these distributions can lead to the relevant (Kolmogorov and Kraichnan) scaling laws.