Absolute and convective instability of an oblique flame front in a combustible gas mixture flow

The influence of the velocity component $u_\tau$ of a combustible gas mixture, tangent to the flame front, on the character of instability (absolute or convective) of the front in the presence of the force of gravity is considered. For $u_\tau$ = 0, the velocity $v_*$ of expansion of the region occupied by flame-front perturbations increasing with time is numerically found, using Markstein's dispersion equation for different dimensionless parameters of the problem. Using the power expansions of $\omega(k)$, approximate analytical formulas for $v_*$ are derived. The instability is convective if $|u_\tau|>v_*$; otherwise, it is absolute.