Spatial structures of chaotically advected scalars: the role of a delay time
Alexandra Tzella (Laboratoire de Meteorologie Dynamique, Paris)
Friday 29th May, 2009 02:00-03:00 325
This talk concerns the spatial structure of reactive scalar ﬁelds in two-dimensional, incompressible chaotic advection ﬂows. Considerations of such ﬁelds arise naturally when studying interacting chemical or biological species, such as ozone in the atmosphere and plankton populations in the ocean, where the dominant ﬂow is large-scale and quasi-horizontal. The emerging spatial structures are ﬁlamental and characterised by a single scaling regime that depends on the rate of convergence of the reactive processes involved and the stirring induced by the ﬂow, as measured by the average rate of divergence of the distance of neighbouring ﬂuid parcels. Motivated by models of the evolution of complex organisms such as oceanic zooplankton, we consider the eﬀect of introducing a delay time into the reaction term. For suﬃciently small scales, all interacting ﬁelds share the same spatial structure, as found in the absence of a delay time. 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 behaviour of the scalar ﬁeld is explained.