  In fluids and plasmas with zonal flow reversed shear, a peculiar kind of
transport barrier appears in the shearless region, one that is associated with
a proper route of transition to chaos. Using a symplectic nontwist maps, which
model such zonal flows, we investigate these barriers. In particular, the
standard nontwist map, a paradigm of nontwist systems, is used to analyze the
parameter dependence of the transport through a broken shearless barrier.
Varying a proper control parameter, we identify the onset of structures with
high stickiness that give rise to an effective barrier near the broken
shearless curve. Several diagnostics are used: stickiness is measured by escape
time and transmissivity plots, while barriers that separate different regions
of stickiness are identified by employing two indicators in the phase space,
the finite-time rotation number and the finite-time Lyapunov exponent.
