  Direct Numerical Simulation data obtained earlier from two statistically 1D,
planar, fully-developed, weakly turbulent, single-step-chemistry, premixed
flames characterized by two significantly different (7.53 and 2.50) density
ratios {\sigma} are analyzed to explore the influence of combustion-induced
thermal expansion on the turbulence and the backward influence of such flow
perturbations on the reaction-zone surface. For this purpose, the simulated
velocity fields are decomposed into solenoidal and potential velocity
subfields. The approach is justified by the fact that results obtained adopting
(i) a widely used orthogonal Helmholtz-Hodge decomposition and (ii) a recently
introduced natural decomposition are close in the largest part of the
computational domain (including the entire mean flame brushes) except for
narrow zones near the inlet and outlet boundaries. The results show that
combustion-induced thermal expansion can significantly change turbulent flow of
unburned mixture upstream of a premixed flame by generating potential velocity
fluctuations. Within the flame brush, the potential and solenoidal velocity
fields are negatively (positively) correlated in unburned reactants (burned
products, respectively) provided that {\sigma}=7.53. Moreover, correlation
between strain rates generated by the solenoidal and potential velocity fields
and conditioned to the reaction zone is positive (negative) in the leading
(trailing, respectively) halves of the mean flame brushes. Furthermore, the
potential strain rate correlates negatively with the curvature of the reaction
zone, whereas the solenoidal strain rate and the curvature are negatively
(positively) correlated in the leading (trailing, respectively) halves of the
mean flame brushes.
