Spatial structure of Reactive scalars in chaotic advection flows

  • IFISC Seminar

  • Alexandra Tzella
  • Department of Applied Mathematics and Theoretical Physics (DAMTP
  • 21 de Noviembre de 2007 a las 15:00
  • Sala Multiusos, Ed. Cientifíco-Técnico
  • Announcement file

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. In a regime where diffusion can be neglected
(large P´eclet number), the scalar concentration in any fluid parcel is determined by
the time history of that parcel. The emerging spatial structures are filamental and
characterised by a single scaling regime with a H¨older exponent that depends on the
rate of convergence of the reactive processes involved and the stirring induced by
the flow, measured by the average rate of divergence of the distance of neighbouring
fluid parcels.
A theoretical analysis, based on the behaviour of nonlinear ordinary and delay
dynamical systems, asymptotic analysis and statistical methods, is developed to
understand two distinct problems, both concerned with the scaling behaviour of
the spatial structure of the emerging scalar field. The results are confirmed by
numerical simulations.
The first problem is motivated by models of the evolution of complex organisms
such as oceanic zooplankton and considers 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. For larger scales,
depending on the strength of the stirring and the magnitude of the delay time, a
second scaling regime, that is unique to the delay system, may appear.
The second problem takes into account the inhomogeneous nature of the recent
stretching histories of the parcel ensemble in order to improve previous quantitative
understanding. The average scaling exponent of the scalar field is modified from
previously obtained results with the corrections maximised when the strength of
the reactions are comparable to the strength of the flow. The point of transition
from a filamental to a smooth field behaviour is re-examined and a new diagnostic
for when the transition occurs is developed.


Detalles de contacto:

Damià Gomila

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