Turbulence closure in the light of phase transition

TL;DR

This paper introduces new turbulence closure equations based on the concept of turbulence as a continuous phase transition, solved numerically for jet flow, showing promising agreement with existing literature.

Contribution

It derives novel turbulence closure equations considering turbulence as a phase transition, treating turbulent viscosity as a tensor for improved modeling.

Findings

Results agree with existing literature for jet flow

Turbulent stresses exhibit symmetry patterns linked to phase transition theory

New closure equations effectively model turbulence phenomena

Abstract

In this study, new turbulence closure equations are derived in the light of turbulence as a continuous phase transition phenomenon. Closed-form Reynolds averaged Navier-Stokes equations due to those closure equations are solved numerically by treating turbulent viscosity as a tensor, unlike the eddy viscosity, for a plane turbulent jet. Overall agreement between the obtained results and the existing literature for the jet flow demonstrates the effectiveness of the new closure equations. Besides, turbulent stresses as a function of the normalized mean velocity exhibit their odd and even symmetries in the flow, which are manifestations of the free energy symmetry of continuous phase transition.