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Wilcox's k-omega model

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Kinematic Eddy Viscosity

\nu _T = {k \over \omega }

Turbulence Kinetic Energy

{{\partial k} \over {\partial t}} + U_j {{\partial k} \over {\partial x_j }} = \tau _{ij} {{\partial U_i } \over {\partial x_j }} - \beta ^* k\omega + {\partial \over {\partial x_j }}\left[ {\left( {\nu + \sigma ^* \nu _T } \right){{\partial k} \over {\partial x_j }}} \right]

Specific Dissipation Rate

{{\partial \omega } \over {\partial t}} + U_j {{\partial \omega } \over {\partial x_j }} = \alpha {\omega \over k}\tau _{ij} {{\partial U_i } \over {\partial x_j }} - \beta \omega ^2 + {\partial \over {\partial x_j }}\left[ {\left( {\nu + \sigma \nu _T } \right){{\partial \omega } \over {\partial x_j }}} \right]


f_{\beta ^* } = \left\{ \begin{matrix} {1,} & {\chi _k \le 0} \\ {{{1 + 680\chi _k^2 } \over {1 + 80\chi _k^2 }},} & {\chi _k > 0} \\ \end{matrix} \right.
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