  The performance of the dynamically bi-orthogonal (DBO) decomposition for the
reduced order modeling of turbulence-chemistry interactions is assessed. DBO is
an on-the-fly low-rank approximation technique, in which the instantaneous
composition matrix of the reactive flow field is decomposed into a set of
orthonormal spatial modes, a set of orthonormal vectors in the composition
space, and a factorization of the low-rank correlation matrix. Two factors
which distinguish between DBO and the reduced order models (ROMs) based on the
principal component analysis (PCA) are: (i) DBO does not require any offline
data generation; and (ii) in DBO the low-rank composition subspace is
time-dependent as opposed to static subspaces in PCA. Because of these
features, DBO can adapt on-the-fly to intrinsic and externally excited
transient changes in state of the transport variables. For demonstration,
simulations are conducted of a non-premixed CO/H2 flame in a temporally
evolving jet. The GRI-Mech 3.0 model with 53 species is used for chemical
kinetics modeling. The results are appraised via a posteriori comparisons
against data generated via full-rank direct numerical simulation (DNS) of the
same flame, and the PCA reduction of the DNS data. The DBO also yields
excellent predictions of various statistics of the thermo-chemical variables.
