The Matalon–Matkowsky–Clavin–Joulin theory refers to a theoretical hydrodynamic model of a premixed flame with a large-amplitude flame wrinkling, developed independently by Moshe Matalon & Bernard J. Matkowsky and Paul Clavin & Guy Joulin,[1][2] following the pioneering study by Paul Clavin and Forman A. Williams[3] and by Pierre Pelcé and Paul Clavin.
are the laminar burning speed and thickness of a planar flame (and
being the thermal diffusivity in the unburnt gas), then the burning speed
for the curved flame with respect to the unburnt gas is given by[6][page needed] where
is the unit normal to the flame surface (pointing towards the burnt gas side),
is the flow velocity field evalauted at the flame surface and
are the two Markstein numbers, associated with the curvature term
corresponding to flow strain imposed on the flame.