An Application of the Modified 0-4th-Cumulant Approximation to Homogeneous Axisymmetric Temperature Fluctuations in an Isotropic Turbulence with a Mean Temperature Gradient

Dynamical equations for the power spectra of turbulence energy, heat flux and temperature variance are formulated by applying the modified 0-4th-cumulant approximation, and are numerically solved at moderate Reynolds number 32 and Prandtl number unity. Results are compared with the theoretical prediction and experiment by Sirivat & Warhaft (J. Fluid Mech. 128 (1983) 323). In particular the evolution of temperature variance <θ²> and heat flux <θ w> in the direction of a linear mean temperature gradient agree well with their theoretical predictions <θ²>{\propto}t^2-t and <θ w>{\propto}t^1-t. (n is the decay exponent of the turbulence energy < q²>/2{\propto}t^-t.) Moreover temperature and heat flux transfer spectra are shown; they are essential to understand these turbulent fields.