  We review and test twelve different approaches to the detection of
finite-time coherent material structures in two-dimensional, temporally
aperiodic flows. We consider both mathematical methods and diagnostic scalar
fields, comparing their performance on three benchmark examples: the
quasiperiodically forced Bickley jet, a two-dimensional turbulence simulation,
and an observational wind velocity field from Jupiter's atmosphere. A close
inspection of the results reveals that the various methods often produce very
different predictions for coherent structures, once they are evaluated beyond
heuristic visual assessment. As we find by passive advection of the coherent
set candidates, false positives and negatives can be produced even by some of
the mathematically justified methods due to the ineffectiveness of their
underlying coherence principles in certain flow configurations. We summarize
the inferred strengths and weaknesses of each method, and make general
recommendations for minimal self-consistency requirements that any Lagrangian
coherence detection technique should satisfy.
