  The theory of inertial manifolds (IM) is used to develop reduced-order models
of turbulent combustion. In this approach, the dynamics of the system are
tracked in a low-dimensional manifold determined in-situ without invoking
laminar flame structures or statistical assumptions about the underlying
turbulent flow. The primary concept in approximate IM (AIM) is that slow
dominant dynamical behavior of the system is confined to a low-dimension
manifold, and fast dynamics respond to the dynamics on the IM instantaneously.
Decomposition of slow/fast dynamics and formulation of an AIM is accomplished
by only exploiting the governing equations. Direct numerical simulations (DNS)
of initially non-premixed fuel-air mixtures developing in forced isotropic
turbulence have been carried out to investigate the proposed model. Reaction
rate parameters are varied to allow for varying levels of extinction and
reignition. The AIM performance in capturing different flame behaviors is
assessed both a priori and a posteriori. It is shown that AIM captures the
dynamics of the flames including extinction and reignition. Moreover, AIM
provides scalar dissipation rate, mixing time for reactive scalars, and
closures for nonlinear terms without any additional modeling. The AIM
formulation is found promising, and provides a new approach to modeling
turbulent combustion.
