In this article, we wish to investigate the behavior of a two-layer $k-\epsilon$ 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 $\theta$ 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...

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...