The k-epsilon model in the theory of turbulence

by Scott-Pomerantz, Colleen Dawn

We consider the $k-varepsilon$ model in the theory of turbulence, where $k$ is the turbulent kinetic energy, $varepsilon$ is the dissipation rate of the turbulent energy, and $alpha,$ $eta,$ and $gamma$ are positive constants. In particular we examine the Barenblatt self-similar $k-varepsilon$ model, along with boundary conditions taken to ensure the symmetry and compactness of the support of solutions. Under the assumptions: $eta>alpha,$ $3alpha>2eta,$ and $gamma$>3/2, we show the existence of $mu$ for which there is a positive solution to the system and corresponding boundary conditions by proving a series of lemmas. We also include graphs of solutions obtained by using XPPAUT 5.85.