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The pair separation model of Goto and Vassilicos (S Goto and J C Vassilicos,2004, New J.Phys., 6, p.65) is revisited and placed on a sound mathematicalfoundation. A DNS of two dimensional homogeneous isotropic turbulence with aninverse energy cascade and a k^{-5/3} power law is used to investigateproperties of pair separation in two dimensional turbulence. A special focuslies on the time asymmetry observed between forward and backward separation.Application of the present model to this data suffers from finite inertialrange effects and thus, conditional averaging on scales rather than on time hasbeen employed to obtain values for the Richardson constants and their ratio.The Richardson constants for the forward and backward case are found to be(1.066 +/- 0.020) and (0.999 +/- 0.007) respectively. The ratio of Richardsonconstants for the backwards and forwards case is therefore g_b/g_f = (0.92 +/-0.03), and hence exhibits a qualitatively different behavior from pairseparation in three dimensional turbulence, where g_b > g_f (J Berg et al.,2006, Phys.Rev.E, 74(1), p.016304). This indicates that previously proposedexplanations for this time asymmetry based on the strain tensor eigenvalues arenot sufficient to describe this phenomenon in two dimensional turbulence. Wesuggest an alternative qualitative explanation based on the time asymmetryrelated to the inverse versus forward energy cascade. In two dimensionalturbulence, this asymmetry manifests itself in merging eddies due to theinverse cascade, leading to the observed ratio of Richardson constants.

Turbulent pair separation due to multi scale stagnation point structure and its time asymmetry in two-dimensional turbulence