Performance of Lagrangian descriptors and their variants in incompressible flows.

The method of Lagrangian Descriptors has been applied in many different contexts, specially in geophysical flows. In this paper, we analyze their performance in incompressible flows. We construct broad families of systems where this diagnostic fails in the detection of barriers to transport. Another aim of this manuscript is to illustrate the same deficiencies in the recent diagnostic proposed by Craven and Hernández.