  We consider planar traveling fronts between stable steady states in
two-component singularly perturbed reaction-diffusion-advection equations,
where a small quantity $\delta^2$ represents the ratio of diffusion
coefficients. The fronts under consideration are large amplitude and contain a
sharp interface, induced by traversing a fast heteroclinic orbit in a suitable
slow fast framework. We explore the effect of advection on the spectral
stability of the fronts to long wavelength perturbations in two spatial
dimensions. We find that for suitably large advection coefficient $\nu$, the
fronts are stable to such perturbations, while they can be unstable for smaller
values of $\nu$. In this case, a critical asymptotic scaling $\nu\sim
\delta^{-4/3}$ is obtained at which the onset of instability occurs. The
results are applied to a family of traveling fronts in a dryland ecosystem
model.

Analysis of PDEs;Dynamical Systems;Pattern Formation and Solitons