Hello, I want to solve a turbulent boundary layer over flat plate. I want to use zero equation turbulence model. In the equation for mixing length (l=ky(1-exp(-y+/A+)) how can I find y+ because there exists wall shear stress in the y+ relation. Is there any simpler way to calculate the mixing length?

thanks

y+ = y u_\tau / \nu

where u_\tau is the friction velocity. It comes from

\tau_wall = \rho u_\tau^2

where \tau_wall is the shear stress at the wall and found from

\tau_wall = \mu du/dy

(y is assumed to be wall normal direction)

i wanna solve turbulent boundary layer eq. by finite difference method. should I write difference form of du/dy in \tau_wall = \mu du/dy? du/dy is velocity gradient at the wall, isn't it? How can I write the difference form of du/dy at the wall?

Yes. Use a one-sided finite difference. Experiment with different finite difference formulae and see how the results change. You can compare your solution with experiments.

thanks alot