Turbulence closure in the light of phase transition

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.