Bulk burning rate in passive-reactive diffusion (Q1585774)

The authors consider a passive scalar which is advected by a prescribed mean zero divergence-free velocity field, diffuses and reacts according to a KPP-type nonlinear reaction. The quantity bulk burning rate is introduced which makes both mathematical and physical sense and extends the notion of front speed. A rigorous lower bounds are established for the bulk burning rate that are linear in the amplitude of the advecting velocity for a large class of flows. Examples are proposed of cellular flows with closed streamlines, and it is proved that these can produce only sub-linear enhancement of the bulk burning rate.