Linear Analysis of Turbulent Rayleigh Flow

Abstract

Turbulent Rayleigh flow is a test problem to investigate the effects of heating on turbulence. Last year, we implemented the direct numerical simulation of the turbulent Rayleigh flow and showed that counter-gradient diffusion of turbulent heat flux occurs in it, and the mechanism of the counter-gradient diffusion was discussed by analyzing the transport equation of the statistical quantities. In this study, we analyzed the transport equation of the statistical quantities focusing only on the linear terms, which plays crucial role in the mechanism of counter-gradient diffusion. As a result, analytical solution was obtained and was qualitatively consistent with the result of the direct numerical simulation. This result clearly explained the qualitative mechanism of the counter-gradient diffusion in turbulent Rayleigh flow.