CFD Online Discussion Forums

CFD Online Discussion Forums (
-   Main CFD Forum (
-   -   Mean Strain rate (

rembe January 10, 2013 08:53

Mean Strain rate
I'm not an expert in fluid mechanics. In the SMAGORINSKY-model I need the square root of Sij*Sij. I'm a little confused about the different notations. What is the defference between the mean strain rate defined as:

and the mean strain rate defined as:


Some times I can read:


I would be very grateful for a short explanation.

Thank you very much!


Rami January 14, 2013 04:11

Hi Michael,

That's simply tensor algebra (using the sum convention).

If you use the definition Sij=0.5*(dUi/dxj+dUj/dxi) , substitute it in s^2 =Sij*Sij and sum over i and j, you'l get the result
from the other expression,
you get
S^2=Ui,jUi,j+ Uj,iUj,i = 4SijSij - 2Ui,jUj,i
so it is different due to the last term.

All times are GMT -4. The time now is 14:18.