  The Darrieus--Landau instability of premixed flames propagating in a narrow
Hele-Shaw channel in the presence of a strong shear flow is investigated,
incorporating also the Rayleigh--Taylor and diffusive-thermal instabilities.
The flow induces shear-enhanced diffusion (Taylor dispersion) in the streamwise
direction, but not in the spanwise direction and this leads to anisotropic
diffusion and flame propagation. To understand how such anisotropies affect
flame stability, two important cases are considered. These correspond to
initial unperturbed conditions pertaining to a planar flame propagating in the
streamwise or spanwise directions. The analysis is based on a two-dimensional
model derived by asymptotic methods and solved numerically. These address the
influence of the shear-flow strength (or Peclet number $Pe$), preferential
diffusion (or Lewis number $Le$) and gravity (or Rayleigh number $Ra$).
Dispersion curves characterizing the perturbation growth rate are computed for
selected values of $Pe$, $Le$ and $Ra$. Taylor dispersion induced by strong
shear flows is found to suppress the Darrieus--Landau instability and to weaken
the flame wrinkling when the flame propagates in the streamwise direction. In
contrast, when the flame propagates in the spanwise direction, the flame is
stabilized in $Le<1$ mixtures, but destabilized in $Le>1$ mixtures. In the
latter case, Taylor dispersion coupled with gas expansion facilitates flame
wrinkling in an unusual manner. Specifically, stagnation points and
counter-rotating vortices are encountered in the flame close to the unburnt gas
side. More generally, an original finding is the demonstration that vorticity
can be produced by a curved flame in a Hele-Shaw channel even in the absence of
gravity, whenever $Pe \neq 0$, and that the vorticity remains confined to the
flame preheat and reaction zones.
