Highlights • Direct numerical and large eddy simulations of very anisothermal flows • Spectral analysis of turbulence • Study of the thermal gradient effect by comparison with isothermal simulations • Study of two turbulent Reynolds numbers 180 and 395 Abstract In very anisothermal turbulent flows, the temperature gradient and turbulence are strongly coupled. The impact of the temperature gradient on turbulent kinetic energy (TKE) balance terms is of particular importance. It is investigated using direct numerical simulations and large eddy simulations of a fully developed anisothermal channel flow. A low Mach flow at two turbulent Reynolds number (180 and 395) is considered. The temperatures of the two channel walls are 293 K and 586 K. Comparison with isothermal channel flows are carried out.The turbulent kinetic energy spectral evolution equation is established and is decomposed into the three distinctive mechanisms: production, nonlinear transfer and viscous effects. The decomposition isolates the terms that vanish in the isothermal case, namely purely anisothermal effects. The behavior of each term is first discussed in the isothermal case. The alteration of the TKE balance terms with the temperature gradient is then analysed relatively to the Reynolds number variation. The thermal gradient effect is characterized by the combined effect of local Reynolds number variation and the complex interaction between temperature and turbulence. The purely anisothermal contribution moves the energy from the hot side to the cold side and accounts for near 10% of the total $ This work is dedicated to Dr. Chuck Leith in respectful acknowledgement of his exemplary scientific career.

This paper investigates the energy exchanges associated with the half-trace of the velocity fluctuation correlation tensor in a strongly anisothermal low Mach fully developed turbulent channel flow. The study is based on direct numerical simulations of the channel within the low Mach number hypothesis and without gravity. The overall flow behaviour is governed by the variable fluid properties. The temperature of the two channel walls are imposed at 293 K and 586 K to generate the temperature gradient. The mean friction Reynolds number of the simulation is 180. The analysis is carried out in the spatial and spectral domains. The spatial and spectral studies use the same decomposition of the terms of the evolution equation of the half-trace of the velocity fluctuation correlation tensor. The importance of each term of the decomposition in the energy exchanges is assessed. This lets us identify the terms associated with variations or fluctuations of the fluid properties that are not negligible. Then, the behaviour of the terms is investigated. The spectral energy exchanges are first discussed in the incompressible case since the analysis is not present in the literature with the decomposition used in this study. The modification of the energy exchanges by the temperature gradient is then investigated in the spatial and spectral domains. The temperature gradient generates an asymmetry between the two sides of the channel. The asymmetry can in a large part be explained by the combined effect of the mean local variations of the fluid properties, combined with a Reynolds number effect.