  Cross-jet transport of passive scalars in a kinematic model of the meandering
laminar two-dimensional incompressible flow which is known to produce chaotic
mixing is studied. We develop a method for detecting barriers to cross-jet
transport in the phase space which is a physical space for our model. Using
tools from theory of nontwist maps, we construct a central invariant curve and
compute its characteristics that may serve good indicators of the existence of
a central transport barrier, its strength, and topology. Computing fractal
dimension, length, and winding number of that curve in the parameter space, we
study in detail change of its geometry and its destruction that are caused by
local bifurcations and a global bifurcation known as reconnection of
separatrices of resonances. Scenarios of reconnection are different for odd and
even resonances. The central invariant curves with rational and irrational
(noble) values of winding numbers are arranged into hierarchical series which
are described in terms of continued fractions. Destruction of central transport
barrier is illustrated for two ways in the parameter space: when moving along
resonant bifurcation curves with rational values of the winding number and
along curves with noble (irrational) values.
