  Chaotic variations in flow speed up mixing of scalar fields via intensified
stirring. This paper addresses the statistical properties of a passive scalar
field mixing in a regular shear flow with random fluctuations against its
background. We consider two-dimensional flow with shear component dominating
over smooth fluctuations. Such flow is supposed to model passive scalar mixing
e.g. inside a large-scale coherent vortex forming in two-dimensional turbulence
or in elastic turbulence in a micro-channel. We examine both the decaying case
and the case of the continuous forcing of the scalar variances. In both cases
dynamics possesses strong intermittency, that can be characterized via the
single-point moments and correlation functions calculated in our work. We
present general qualitative properties of pair correlation function as well as
certain quantitative results obtained in the framework of the model with
fluctuations that are short correlated in time.
