  In a highly turbulent medium characterized by a low Damk\"ohler number Da,
reactions are commonly considered to occur in distributed zones broadened by
small-scale turbulent eddies. In the present communication, an alternative
regime of propagation of reaction waves in a highly turbulent medium is
introduced and studied theoretically and numerically. More specifically,
propagation of an infinitely thin reaction sheet in a turbulent medium is
analyzed, with molecular mixing of the reactant and product being allowed in
wide layers. In this limiting case, an increase in the consumption velocity by
turbulence is solely controlled by an increase in the reaction-sheet area.
Based on physical reasoning and estimates, the area is hypothesized to be close
to the mean area of an inert iso-scalar surface at the same turbulent Reynolds
number. This hypothesis leads to a relation for the turbulent consumption
velocity, which is similar to the well-known Damk\"ohler scaling associated
commonly with distributed reaction zones at a low Da. The obtained theoretical
results are validated by analyzing a big database (23 cases characterized by
0.01<Da<1) created recently in 3D direct numerical simulations of propagation
of a statistically planar, one-dimensional, dynamically passive reaction wave
in statistically stationary, homogeneous, isotropic turbulence. The DNS data
well support the aforementioned relation. They also show that the reaction is
localized to thin zones even at Da as low as 0.01, with a ratio of the
turbulent and laminar consumption velocities being mainly controlled by the
reaction-zone-surface area.
