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Time irreversibility is a basic property of turbulence. Its Eulerian
footprint is the energy flux, $\epsilon$, through the inertial range
of scales. It can also be expressed in Lagrangian form, relating the
temporal change in the energy of relative motion of pairs to the
energy flux. In this talk I will present new manifestations of time
irreversibility for fluid particle pairs at short times. For an
incompressible flow, we find a unique function of the separation
between particles proportional to $\epsilon t^3$ to leading order,
with opposite signs in 2d and 3d. For other moments of separation in
the inertial interval, this term is hidden by an even in time
ballistic contribution. In the dissipative range, the analogous
function is found to be a statistically conserved quantity - it
remains equal to its initial value throughout the pairs motion within
the dissipative range. In this case ballistics controls the leading
order dynamics, obscuring time irreversibility. Finally, I will
consider tracers in 1d Burgers turbulence - a compressible flow for
which there exists an analogue of the energy flux law in its Eulerian
and Lagrangian forms. In the inviscid limit, we find that the latter
relation is changed, with a new type of time irreversibility emerging-
a finite jump upon time reversal. This jump is due to compressibility
of the flow, and is absent in incompressible turbulence.
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