$k-\omega$ Model

Since there is no really mathematical definition for the specific dissipation ratio, we have to use some physical process to make up the equation for $\omega$. We know that the most common processes in a fluid are unsteadiness, advection, dissipation and production. Kolmogorov postulated the following equation for $\omega$,

$$\frac{\partial\omega}{\partial t}+U_j\frac{\partial\omega}{\parti... ...l}{\partial\omega_j}\left(\sigma\nu_t\frac{\partial\omega}{\partial x_j}\right)$$ (2.23)

Dissipation ratio $\omega$ can be described as a frequency characteristic of the turbulence decay process under its self-interaction. In this model turbulent eddy viscosity is obtained from scale analysis as

$$\nu_t=k/\omega$$ (2.24)