Global geometry and coarse-grained formulation of the evolution of pointwise intermaterial interface measure in chaotic flows

The article develops a coarse-grained model for the evolution of the interm aterial contact interface measure (length in 2d, area in 3d) in chaotic flo ws, starting from the global geometric properties characterizing these flow s. The model reduces to a finite-volume formulation for the balance equatio ns expressing the evolution in time and space of the interface measure, whe re its local growth rate within chaotic regions is controlled by the averag e (D(x, t) : e(u)(x, t)), D(x, t)), D(x, t) being the deformation tenser an d e(u)(x, t) the unit vector spanning the unstable invariant subspace at th e point x. The analysis is developed for two- and three-dimensional flows, and is useful not only for short-cut analysis of interface measures but als o as a tool in the development of coarse-grained models of reaction/diffusi on kinetics in chaotic flows accounting for the complex lamellar structure generated in such systems. (C) 2001 Elsevier Science Ltd. All rights reserv ed.