February 11, 2011 Alexandra Tzella, Cambridge University
Title: Mixing of reacting tracers: spatial structures
Motivated by the spatial heterogeneity observed in plankton distributions in the meso-scale ocean, we examine a class of reacting tracers advected by a globally mixing flow, whose structure is maintained by a large-scale source. Previous theoretical investigations have shown that in a regime where diffusion can be neglected (large Peclet number), the structures are filamental and characterized by a single scaling regime that depends on the rate of convergence of the reactive processes and the strength of the stirring measured by the average stretching rate (Lyapunov exponent). In the presence of delay terms, we show that for sufficiently small scales all interacting fields should share the same spatial structure, as found in the absence of delay terms. However, depending on the strength of the stirring and the magnitude of the delay time, two further scaling regimes that are unique to the delay system may appear at intermediate length-scales. An expression for the transition length-scale dividing small-scale and intermediate-scale regimes is obtained and the scaling behavior of the tracer field is explained.