  Premixed turbulent flames, encountered in power generation and propulsion
engines, are an archetype of a randomly advected, self-propagating surface.
While such a flame is known to exhibit large-scale intermittent flapping, the
possible intermittency of its small-scale fluctuations has been largely
disregarded. Here, we experimentally reveal the inner intermittency of a
premixed turbulent V-flame, while clearly distinguishing this small-scale
feature from large-scale outer intermittency. From temporal measurements of the
fluctuations of the flame, we find a frequency spectrum that has a power-law
subrange with an exponent close to $-2$, which is shown to follow from
Kolmogorov phenomenology. Crucially, however, the moments of the temporal
increment of the flame position are found to scale anomalously, with exponents
that saturate at higher-orders. This signature of small-scale inner
intermittency is shown to originate from high-curvature, cusp-like structures
on the flame surface, which have significance for modeling the heat release
rate and other key properties of premixed turbulent flames.
