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Abstract: The stationary-state spatial structure of reacting scalar fields, chaoticallyadvected by a two-dimensional large-scale flow, is examined for the case forwhich the reaction equations contain delay terms. Previous theoreticalinvestigations have shown that, in the absence of delay terms and in a regimewhere diffusion can be neglected large P\-eclet number, the emergent spatialstructures are filamental and characterized by a single scaling regime with aH\-older exponent that depends on the rate of convergence of the reactiveprocesses and the strength of the stirring measured by the average stretchingrate. In the presence of delay terms, we show that for sufficiently smallscales all interacting fields should share the same spatial structure, as foundin the absence of delay terms. Depending on the strength of the stirring andthe magnitude of the delay time, two further scaling regimes that are unique tothe delay system may appear at intermediate length scales. An expression forthe transition length scale dividing small-scale and intermediate-scale regimesis obtained and the scaling behavior of the scalar field is explained. Thetheoretical results are illustrated by numerical calculations for two types ofreaction models, both based on delay differential equations, coupled to atwo-dimensional chaotic advection flow. The first corresponds to a singlereactive scalar and the second to a nonlinear biological model that includesnutrients, phytoplankton and zooplankton. As in the no-delay case, the presenceof asymmetrical couplings among the biological species results in a non-genericscaling behavior.

Autor: Alexandra Tzella, Peter H. Haynes



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