# Baldwin-Barth model

## Kinematic Eddy Viscosity

$\nu _t = C_\mu \nu \tilde R_T D_1 D_2$

## Turbulence Reynolds Number

${\partial \over {\partial t}}\left( {\nu \tilde R_T } \right) = U_j {\partial \over {\partial x_j }}\left( {\nu \tilde R_T } \right) = \left( {C_{\varepsilon 2} f_2 - C_{\varepsilon 1} } \right)\sqrt {\nu \tilde R_T P} + \left( {\nu + {{\nu _T } \over {\sigma _\varepsilon }}} \right){{\partial ^2 } \over {\partial x_k \partial x_k }} - {1 \over {\sigma _\varepsilon }}{{\partial \nu _T } \over {\partial x_k }}{{\partial \left( {\nu \tilde R_T } \right)} \over {\partial x_T }}$

## Closure Coefficients and Auxilary Relations

$C_{\varepsilon 1} = 1.2$
$C_{\varepsilon 2} = 2.0$
$C_\mu = 0.09$
$A_o^ + = 26$
$A_2^ + = 10$

${1 \over {\sigma _\varepsilon }} = \left( {C_{\varepsilon 2} - C_{\varepsilon 1} } \right){{\sqrt {C_\mu } } \over {\kappa ^2 }}$
$\kappa = 0.41$

$P = \nu _T \left[ {\left( {{{\partial U_i } \over {\partial x_j }} + {{\partial U_j } \over {\partial x_i }}} \right){{\partial U_i } \over {\partial x_j }} - {2 \over 3}{{\partial U_k } \over {\partial x_k }}{{\partial U_k } \over {\partial x_k }}} \right]$