Critical theory of turbulence in incompressible fluids

TL;DR

This paper develops a critical theoretical framework for understanding turbulence in incompressible fluids by analyzing the Navier-Stokes equation with random initial conditions and identifying a stable fixed point in a dimensional expansion.

Contribution

It introduces a critical theory approach to turbulence, identifying an infrared stable fixed point in the Navier-Stokes equation using epsilon expansion near four dimensions.

Findings

Existence of an infrared stable fixed point at d=4

Viscous fluid behavior as a perturbation around the fixed point

Application of epsilon expansion to turbulence theory

Abstract

The Navier-Stokes equation describes the deterministic evolution of incompressible fluids. The effects of random initial conditions on solutions of this equation are studied. It is shown that there is an infrared stable fixed point accessible within the epsilon expansion, about $d_c=4,$ with a particular choice of viscosity. The behaviour of the usual viscous fluid is obtained as a relevant perturbation about this fixed point, with the usual viscosity serving as $T-T_c.$