  The method of Lagrangian descriptors has been already applied in many
different contexts, specially in geophysical flows. In this paper we analyze
the performance of this methodology in incompressible flows. We demonstrate
that barriers to transport are not always coded by singular features of the $M$
function as Mancho, Wiggins and their co-workers conjectured. The techniques
presented here are not restricted to incompressible flows. In fact, by our
approach, one can infer that the method of Lagrangian descriptors is not useful
in most linear systems.
