How jets and eddies influence the speed of propagation of plankton blooms: an idealised view

We investigate the influence of flows on the propagation of chemical pulsating fronts evolving inside an infinite channel domain. We focus on the sharp  front  obtained in Fisher--Kolmogorov--Petrovskii--Piskunov (FKPP) type models  in the limit of small  molecular diffusivity and fast reaction (large P\'eclet and Damk\"ohler numbers). This problem arises naturally in oceanographic applications when studying interacting chemical or biological species, such as plankton blooms in the ocean. We introduce a new formulation that expresses the front speed  in terms of trajectories minimising the time of travel across a characteristic length scale of the flow subject to a time-averaged constraint that depends on both the P\'eclet and Damk\"ohler numbers. We calculate the front speed for a flow consisting of an infinite array of vortices rotating in alternating directions and investigate how this changes in the presence of a jet.