  In this paper we consider a recent theoretical prediction (Bragg \emph{et
al.}, Phys. Fluids \textbf{28}, 013305 (2016)) that for inertial particles in
2D turbulence, the nature of the irreversibility of the particle-pair
dispersion inverts when the particle inertia exceeds a certain value. In
particular, when the particle Stokes number, ${\rm St}$, is below a certain
value, the forward-in-time (FIT) dispersion should be faster than the
backward-in-time (BIT) dispersion, but for ${\rm St}$ above this value, this
should invert so that BIT becomes faster than FIT dispersion. This non-trivial
behavior arises because of the competition between two physically distinct
irreversibility mechanisms that operate in different regimes of ${\rm St}$. In
3D turbulence, both mechanisms act to produce faster BIT than FIT dispersion,
but in 2D turbulence, the two mechanisms have opposite effects because of the
flux of energy from the small to the large scales. We supplement the
qualitative argument given by Bragg \emph{et al.} (Phys. Fluids \textbf{28},
013305 (2016)) by deriving quantitative predictions of this effect in the short
time limit. We confirm the theoretical predictions using results of inertial
particle dispersion in a direct numerical simulation of 2D turbulence. A more
general finding of this analysis is that in turbulent flows with an inverse
energy flux, inertial particles may yet exhibit a net downscale flux of kinetic
energy because of their non-local in-time dynamics.
