Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 84 / 4 / a

The K-epsilon turbulence model evolves turbulent kinetic energy $k$ and its turbulent kinetic energy dissipation rate $ϵ$, rather than resolving turbulent fluctuations. It closes the Reynolds stress with an isotropic eddy viscosity, ${\nu }_T=C_{\mu }{k}^2/ϵ$, and models transport of $k$ and $ϵ$ by gradient diffusion with coefficients ${\nu }_T/{\sigma }_k$ and ${\nu }_T/{\sigma }_{ϵ}$. Production is tied to mean strain; dissipation-equation production and destruction are modeled terms with empirical constants. The characteristic velocity and length are $\sqrt{k}$ and $k^{3/2}/ϵ$. These assumptions are primarily for high Reynolds number, and strongly anisotropic flow, sharp interfaces and molecular-viscosity-dominated regions need additional treatment. The dissipation equation is a closure, not a second exact energy-conservation law.