  The structure of the concentration field of a decaying substance produced by
chemical sources and advected by a smooth incompressible two-dimensional flow
is investigated. We focus our attention on the non-uniformities of the H\"older
exponent of the resulting filamental chemical field. They appear most evidently
in the case of open flows where irregularities of the field exhibit strong
spatial intermittency as they are restricted to a fractal manifold.
Non-uniformities of the H\"older exponent of the chemical field in closed flows
appears as a consequence of the non-uniform stretching of the fluid elements.
We study how this affects the scaling exponents of the structure functions,
displaying anomalous scaling, and relate the scaling exponents to the
distribution of finite-time Lyapunov exponents of the advection dynamics.
Theoretical predictions are compared with numerical experiments.
