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

TL;DR

This paper revisits the pair separation model in 2D turbulence using DNS data, revealing a unique time asymmetry linked to inverse energy cascade and challenging previous explanations based on strain tensor eigenvalues.

Contribution

It provides a mathematically grounded analysis of pair separation in 2D turbulence, highlighting the role of inverse cascade in time asymmetry and refining the understanding of Richardson constants.

Findings

Richardson constants for forward and backward separation are approximately 1.066 and 0.999.

The ratio of Richardson constants g_b/g_f is about 0.92, indicating reversed asymmetry compared to 3D turbulence.

Inverse cascade effects lead to merging eddies, explaining the observed time asymmetry.

Abstract

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.