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Recent works have shown that the rate of kinetic-energy change of
small fluid elements has a non-trivial Reynolds dependence and,
moreover, is characterized by a negatively skewed distribution, a fact
that can be put in relation with the irreversibility of turbulent
flows. Irreversibility in turbulence originates both from the fact of
being far from equilibrium and from the viscous term which explicitly
break the time reversal symmetry.
Here the Lagrangian power statistics is investigated in the framework
of the shell models for turbulence. It will be shown that the power
statistics can be rationalized in the framework of the multifractal
model of turbulence. Moreover, it will be shown that the left tail of
the power gives rise to a Re dependence that is subleading with
respect to the symmetric part of the distribution. It will be also
discussed a variant of the shell model where the viscous term is
modified such us to preserve the time reversal symmetry so that the
only source of irreversibility is the out-of-equilibrium nature of the
turbulent state.
Finally, Lagrangian power in Navier-Stokes turbulence will be
revisited on the light of these results.
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