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

Abstract

The pair separation model of Goto and Vassilicos [New J. Phys. 6, 65 (2004)] is revisited and placed on a sound mathematical foundation. A direct numerical simulation 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 separations. Application of the present model to these 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 backward and forward cases is therefore gb/gf=(0.92±0.03), and hence exhibits a qualitatively different behavior from pair separation in three-dimensional turbulence, where gb>gf [J. Berg et al., Phys. Rev. E 74, 016304 (2006)]. 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.