A new kind of Lagrangian diagnostic family is proposed and a specific form of it is suggested for characterizing mixing: the extreme (maximal/minimal) extent of a trajectory and some of its variants. It enables the detection of coherent structures and their dynamics in two- (and potentially three-) dimensional unsteady flows in both bounded and open domains. Its computation is simple and provides new insights regarding the mixing properties on both short and long time scales and on both spatial plots and distribution diagrams. We demonstrate its applicability to two dimensional flows using two toy models and a data set of surface currents from the South Atlantic. (C) 2014 AIP Publishing LLC.
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