Exercise 8.II Grid turbulence and k-s modeling

Write the equations of the k-e model for this situation, retaining only non-zero terms. For the remainder of this exercise, diffusion terms in the Ox direction will be neglected (it will be easily verified, at the end of the exercise, that these terms are indeed negligible). 

The equations of the k-e model ate coupled and notrlinear, which ittakes their resolution non-trivial. Prove that the two equatiorrs of the k-s model can be combined to establish that  

This results in s x)lSo =(k x)lko f . Use this relation to integrate the evolution equation for k x) and prove that  

Adapt the resnlts obtained in Question 2 to determine the variations with x of the turbulent velocity u x), of the integral scale lt x), and of the turbulent Reynolds number Re )  

Comment upon the solution obtained when C2 = 2. Why is it necessary that C2 2 for the solution of the k-s model to be physically meaningful  

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