Bulk burning rate in passive-reactive diffusion

Journal Article (Journal Article)

We consider a passive scalar that is advected by a prescribed mean zero divergence-free velocity field, diffuses, and reacts according to a KPP-type nonlinear reaction. We introduce a quantity, the bulk burning rate, that makes both mathematical and physical sense in general situations and extends the often ill-defined notion of front speed. We establish rigorous lower bounds for the bulk burning rate that are linear in the amplitude of the advecting velocity for a large class of flows. These "percolating" flows are characterized by the presence of tubes of streamlines connecting distant regions of burned and unburned material and generalize shear flows. The bound contains geometric information on the velocity streamlines and degenerates when these oscillate on scales that are finer than the width of the laminar burning region. We give also examples of very different kind of flows, cellular flows with closed streamlines, and rigorously prove that these can produce only sub-linear enhancement of the bulk burning rate.

Full Text

Duke Authors

Cited Authors

  • Constantin, P; Kiselev, A; Oberman, A; Ryzhik, L

Published Date

  • January 1, 2000

Published In

Volume / Issue

  • 154 / 1

Start / End Page

  • 53 - 91

International Standard Serial Number (ISSN)

  • 0003-9527

Digital Object Identifier (DOI)

  • 10.1007/s002050000090

Citation Source

  • Scopus