Three questions regarding scalar gradient equations in flamelet theory

A self-consistent extension of flamelet theory for partially premixed combustion

“…It is interesting to note at this point, that once Eq. ( 30) is specialized either for Z or φ, a tangential derivative will remain, which differs from previous formulations for g Z and g c derived for the classical non-premixed and premixed asymptotic limits [24,4,14,22,29]. Also, this result is not compatible with the use of simple analytical expressions for the closure of the conditioning scalar gradients typically having a one-dimensional dependency in composition space.…”

“…This expression stems from the definition of strain usually employed in strong stretch theory [30,31]. According to the recent work by Olguin et al [29], but using the notation adopted in the present work, the relation between the both possible definitions of strain is…”