  Influence of statistically stationary, homogeneous, and isotropic turbulence
on the mean area of a passive self-propagating front and, hence, on the rate of
fluid consumption by the front is analysed in the case of asymptotically high
turbulent Reynolds number $Re_L$ and asymptotically high ratio of the
Kolmogorov velocity to a constant speed $u_0$ of the front. By considering an
early stage of the front evolution, the mean (over the studied early stage)
front area and consumption velocity $\bar{u}_T$ are analytically determined.
The analysis shows that the mean $\bar{u}_T$ is proportional to the rms
turbulent velocity, which characterizes large-scale turbulent eddies, even if
the instantaneous rate of an increase in the front area is mainly controlled by
the smallest Kolmogorov eddies. A straightforward dependence of the mean area
or $\bar{u}_T$ on the Kolmogorov velocity, length, and time scales vanishes due
to the following physical mechanism. At high $Re_L$, turbulent stretching
created by small-scale eddies increases the front area exponentially with time,
whereas a volume bounded by the leading and trailing edges of the front grows
significantly slower. Therefore, after a short time, the volume is tightly
filled by the front and the mean distance between opposed front elements
becomes small with respect to Kolmogorov length scale. Subsequently, such front
elements collide, thus, reducing the front area and limiting the mean
$\bar{u}_T$.
