  (Abridged) A series of three-dimensional numerical simulations is used to
study the intrinsic stability of high-speed turbulent flames. Calculations
model the interaction of a fully-resolved premixed flame with a highly
subsonic, statistically steady, homogeneous, isotropic turbulence. We consider
a wide range of turbulent intensities and system sizes, corresponding to the
Damk\"ohler numbers Da = 0.1-6.0. These calculations show that turbulent flames
in the regimes considered are intrinsically unstable. In particular, we find
three effects. 1) Turbulent flame speed develops pulsations with the observed
peak-to-peak amplitude > 10 and a characteristic time scale close to a
large-scale eddy turnover time. Such variability is caused by the interplay
between turbulence, which continuously creates the flame surface, and highly
intermittent flame collisions, which consume the flame surface. 2) Unstable
burning results in the periodic pressure build-up and the formation of pressure
waves or shocks, when the flame speed approaches or exceeds the speed of a
Chapman-Jouguet deflagration. 3) Coupling of pressure gradients formed during
pulsations with density gradients across the flame leads to the anisotropic
amplification of turbulence inside the flame volume and flame acceleration.
Such process, which is driven by the baroclinic term in the vorticity transport
equation, is a reacting-flow analog of the mechanism underlying the
Richtmyer-Meshkov instability. With the increase in turbulent intensity, the
limit-cycle instability discussed here transitions to the regime described in
our previous work, in which the growth of the flame speed becomes unbounded and
produces a detonation.
