Speaker
Dhrubaditya Mitra
Description
If you look at movies of a tracer particle advected by a
turbulent flow and its time-reversed version the two movies
look very similar, although the system is not in equilibrium
but in non-equilibrium stationary state. Can one detect that
the system is indeed irreversible from this time series?
This curious question has been address by several recent
publications who proposed that the irreversibility manifests
itself in the following way: the tracer takes long to
accelerate but decelerates quickly. This has been quantified
by looking at the third moment of two random variables, the
power and the increment of energy over a time-scale $\tau$,
defined by $W(\tau) = E(t+\tau) - E(t) $. The PDF of both of
these random variables are shown to be negatively skewed.
Here we extend this result to heavy inertial particles (for
example water droplets in atmosphere) who follow a
dissipative dynamics.
We show that for the heavy inertial particles the same
measure of irreversibility works. In addition, we propose a
new measure : The PDF of time over which the power keeps the
same sign. The tail of such PDFs are found to be exponential
hence we can define a characteristic time scale of
gain and loss of energy. The characteristic time scale of
gain is slow compared to the time scale of loss.
