  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 mathematical
foundation. A DNS of two dimensional homogeneous isotropic turbulence with an
inverse energy cascade and a k^{-5/3} power law is used to investigate
properties of pair separation in two dimensional turbulence. A special focus
lies on the time asymmetry observed between forward and backward separation.
Application of the present model to this data suffers from finite inertial
range effects and thus, conditional averaging on scales rather than on time has
been 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 Richardson
constants for the backwards and forwards case is therefore g_b/g_f = (0.92 +/-
0.03), and hence exhibits a qualitatively different behavior from pair
separation 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 proposed
explanations for this time asymmetry based on the strain tensor eigenvalues are
not sufficient to describe this phenomenon in two dimensional turbulence. We
suggest an alternative qualitative explanation based on the time asymmetry
related to the inverse versus forward energy cascade. In two dimensional
turbulence, this asymmetry manifests itself in merging eddies due to the
inverse cascade, leading to the observed ratio of Richardson constants.
