  The stationary-state spatial structure of reacting scalar fields, chaotically
advected by a two-dimensional large-scale flow, is examined for the case for
which the reaction equations contain delay terms. Previous theoretical
investigations have shown that, in the absence of delay terms and in a regime
where diffusion can be neglected (large P\'eclet number), the emergent spatial
structures are filamental and characterized by a single scaling regime with a
H\"older exponent that depends on the rate of convergence of the reactive
processes and the strength of the stirring measured by the average stretching
rate. 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. 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 scalar field is explained. The
theoretical results are illustrated by numerical calculations for two types of
reaction models, both based on delay differential equations, coupled to a
two-dimensional chaotic advection flow. The first corresponds to a single
reactive scalar and the second to a nonlinear biological model that includes
nutrients, phytoplankton and zooplankton. As in the no-delay case, the presence
of asymmetrical couplings among the biological species results in a non-generic
scaling behavior.
