  The turbulent energy flux through scales, $\bar{\epsilon}$, remains constant
and non vanishing in the limit of zero viscosity, which results in the
fundamental anomaly of time irreversibility. It was considered straightforward
to deduce from this the Lagrangian velocity anomaly, $\left< d u^2/dt\right>=-4
\bar{\epsilon}$ at $t=0$, where $\vec{u}$ is the velocity difference of a pair
of particles, initially separated by a fixed distance. In this letter we
demonstrate that this derivation assumed first taking the limit $t \to 0$ and
then $\nu \to 0$, while the true anomaly requires taking viscosity to zero
first. For compressible turbulence we find that the limits $t \to 0$ and $\nu
\to 0$ do not commute and the Lagrangian anomaly is completely altered: $\left<
d u^2/dt\right>$ has different values forward and backward in time. We show
that this new anomaly is related to the particles entering/exiting shocks
forward/backward in time. For incompressible flows, on the other hand, we show
that the limits can be interchanged and the Lagrangian anomaly is still induced
by the flux law, apparently due to a homogeneous distribution of fluid
particles at all times.
