The computation of compressible coaxial jets has moved into the field of interest not only in fundamental research but also in industrial applications, especially in chemical engineering. Numerical simulations of such flows are performed here, using a code specifically developed for gaseous turbulent flows which can also take into account chemical reactions. The coaxial jet can be regarded as a model of injection device in industrial applications; one can cite combustion and aeroacoustics technology. Three-dimensional numerical simulations in this configuration, already published by various authors in open literature are limited to incompressible isothermal flow. In our work, we have explicitly taken into account the temperature gradient effects on the dynamics and mixing mechanisms. Indeed, we have investigated a spatially developing compressible (isothermal and non-isothermal coaxial jet). The numerical model is based on time and space resolutions of compressible Navier-Stokes equations. The piecewise parabolic method (PPM) is combined with a linearized Riemann solver. This scheme adds non-linear dissipation intermittently just where and when needed in order to avoid spurious oscillations and guarantee monotonicity for the advection equation. The simulation can, therefore, be regarded as large-Eddy simulations: large scales are accurately solved with minimal viscosity and nonlinear dissipation extracts energy out of the small scales in order to avoid non-physical oscillations. In order to study the mixing between Air-Air flows, we consider the mixture fraction f to track the mixing between two species seeded in the coaxial jets. A great attention is paid to the spatial-temporal evolution of the mixture fraction f, with a particular interest to probability density function. The comparison between the numerical results and experimental data is fairly good, with respect to the mean and turbulent fields. We found that the inner potential core length in the non-isothermal configuration reduced with respect to the isothermal coaxial jet due to the gradient of temperature. It was shown that in the non-isothermal coaxial jet, the temperature gradient leads to the rapid development of the inner Kelvin-Helmholtz vortices implying an efficient mixing of the species close to the exit of the computational domain. (C) 2020 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.