On the relation between the conditional moment closure and unsteady flamelets

We consider the relation between the conditional moment closure (CMC) and t he unsteady flamelet model (FM). The CMC equations were originally construc ted as global equations, while FM was derived asymptotically for a thin rea ction zone. The recent tendency is to use FM-type equations as global equat ions. We investigate the possible consequences and suggest a new version of FM: coordinate-invariant FM (CIFM). Unlike FM, CIFM complies with conditio nal properties of the exact transport equations which are used effectively in CMC. We analyse the assumptions needed to obtain another global version of FM: representative interactive flamelets (RIF), from original FM and dem onstrate that, in homogeneous turbulence, one of these assumptions is equiv alent to the main CMC hypothesis.