In this article, we wish to investigate the behavior of a two-layer k - ε
turbulence model from the mathematical point of view, as this model is useful for the near-wall treatment in numerical simulations.
First, we explain the difficulties inherent in the
model. Then, we present a new variable θ that enables the mathematical study. Due to a problem of definition of the turbulent
viscosity on the wall boundary, we consider an alternative version of the original equation. We show that some physical aspects
of the model are preserved by the new formulation, and in particular, we show how the physicists can help us to prove
the existence of a solution of our problem. Finally, we are interested in the Navier-Stokes equations coupled with the modified turbulence
model and we show that the alternative model may be preferred to the original one, because of its good properties
(existence of a solution of the coupled problems).