The thermal expansion induced by the chemical reactions taking place in a turbulent reactive flow affects the velocity field so strongly that velocity fluctuations and velocity gradients can be governed by chemistry rather than by turbulence. Moreover, thermal expansion is well known to be responsible for counter-gradient turbulent diffusion and flame-generated turbulence phenomena. In the present paper, a specific description of the velocity field is used, which allows to separate the influence of thermal expansion from the effects related only to the turbulent motion. Using this description, all the usual turbulent quantities are expressed in terms of two contributions: one due to thermal expansion and one due to turbulence. The theoretical analysis shows that only the contributions due to turbulence should be resolved by transport equations in which unclosed terms do not depend on thermal expansion. Deduced from this analysis, a relatively simple closure model is proposed and successfully validated through comparison with Direct Numerical Simulation data. Results show the ability of this model to represent the counter-gradient diffusion region of the flame as well as the region controlled by gradient transport, crucial to the propagation mechanism of the flame brush.