Speaker
Prof.
Haitao Xu
(University of Gottingen)
Description
In fluid turbulence, there is a wide separation between the scales
at which the fluid is forced into motion and the scales at which
the dissipation dominates. In between, energy is transferred
through scales. This energy cascade dictates that turbulence
statistics are not time-reversible, as reflected in the celebrated
Karman-Howarth-Kolmogorov equation, which relates the energy
flux with velocity differences in space (Eulerian statistics). This
can be further extended to statistics along trajectories of fluid
particles in turbulence (Lagrangian statistics). The energy flux
can also be related to the relative motion between fluid particles.
The interesting question is then: Can one detect irreversibility
from the motion of single fluid particles, where an intrinsic length
scale is missing? Using data from both experiments and direct
numerical simulations in a large set of flow conditions, we show
that the irreversibility induced by the energy flux through spatial
scales can be revealed and quantified by following the change of
the kinetic energy of single fluid particles. We find that fluid
particles decelerate harder than they accelerate, i.e., they tend
to lose kinetic energy faster than they gain it. The third moment
of the power fluctuations along a trajectory, nondimensionalized
by the energy flux, displays a remarkable power law as a function
of the Reynolds number, both in two and in three spatial
dimensions. This establishes a relation between the irreversibility
of the system and the range of active scales.
