i know that the convention for repeated indicies is summation.

but if i have (where bracketed terms are the indicies) -

Ans1 = [ M(ij) * M(ij) ] / [ F(kl) * F(kl) ]

is this the same as -

Ans2 = [ M(ij) * M(ij) ] / [ F(ij) * F(ij) ]

is Ans1 = Ans2 ???

ans2 is just rubbish. The rule is very simple, no index can be repeated more than twice in the same term

hi ahmed, thanks for your reply.

i have regularly seen the following expression for the dynamic smagorinsky coefficient ...

C = -0.5 * [L(ij)M(ij)] / [M(ij)M(ij)]

are you saying that this is incorrect?

Yes(in what refers to the indices). Once again the rule "No index may appear more than twice in any term" and the expression as written by you breaks the rule. Remember all these are dummy indices and meant to indicate summation so any letter can do but for clarity they are not repeated more than twice, books on turbulence in general have an appendix that list all these rules so stretch your legs to the library or pay ten dollars to amazon and they will send you the book by Aris.