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Mean Strain rateHi,
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: http://www.cfd-online.com/Forums/vbL...66aad1f8-1.gif and the mean strain rate defined as: Sij=0.5*(dUi/dxj+dUj/dxi) Some times I can read: S=sqrt((dUi/dxj)^2+(dUj/dxi)^2) I would be very grateful for a short explanation. Thank you very much! Michael |

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 http://www.cfd-online.com/Forums/vbL...66aad1f8-1.gif from the other expression, S=sqrt((dUi/dxj)^2+(dUj/dxi)^2) you get S^2=Ui,jUi,j+ Uj,iUj,i = 4SijSij - 2Ui,jUj,i so it is different due to the last term. |

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