A new flow-type measure based on the triple decomposition method – application to two-dimensional flows

Flow-type indicators serve to distinguish among the three principal patterns of flow: elongation, shear and rotation. Such indicators are extremely useful to aid in the analysis of flows that are either measured experimentally or obtained from numerical simulations. A suitably normalised flow-type-indicator field varies continuously through those flow patterns, with values usually ranging from +1, for pure elongational flow, to 0, for simple shear flow, and tending to − 1 , for pure solid-body rotation. Those indicators are usually evaluated on the basis of invariant quantities of the rates of deformation and rotation tensors, although we here propose what we feel is a far better alternative based on the actual rates of elongation, shear and rotation extracted locally from the so-called “triple decomposition” method. We show how different the results from those two approaches can be, and we also deal with the issue of objectivity by devising a simple method to make the flow-type indicator independent of the relative motion of the observer.