Gradients...

Question..

The below message was posted some months ago:

"i know that the local rate of strain (a) effects the flame characteristics, i.e. extinction etc.

but which direction of strain (e.g. S11, S22, S33, S12, S13, S23) in an LES or DNS simualation actually has the effect. is it the magnitude of all strain directions or one in particular?!?!?

basically i think i want to know the relationship between 'a' and 'Sij'. "

I am aware the answer to this is the strain the direction normal to the flame. Now, how would I calculate this is I new the Sij components and the Scalar normal components....? Can someone write it down in tensor or vector notation for me..?

thank you.