  This paper outlines a theoretical approach for predicting the onset of
detonation in unconfined turbulent flames which is relevant both to problems of
terrestrial combustion and to thermonuclear burning in Type Ia supernovae. Two
basic assumuptions are made: 1) the gradient mechanism is the inherent
mechanism that leads to DDT in unconfined conditions, and 2) the sole mechanism
for preparing the gradient in induction time is by turbulent mixing and local
flame quenching. The criterion for DDT is derived in terms of the
one-dimensional detonation wave thickness, the laminar flame speed, and the
laminar flame thickness in the reactive gas. This approach gives a lower-bound
criterion for DDT for conditions where shock preheating, wall effects, and
interactions with obstacles are absent. Regions in parameter space where
unconfined DDT can and cannot occur are determined. A subsequent paper will
address these issues specifically in the astrophysical context.
