64 research outputs found
A statistical conservation law in two and three dimensional turbulent flows
Particles in turbulence live complicated lives. It is nonetheless sometimes
possible to find order in this complexity. It was proposed in [Falkovich et
al., Phys. Rev. Lett. 110, 214502 (2013)] that pairs of Lagrangian tracers at
small scales, in an incompressible isotropic turbulent flow, have a statistical
conservation law. More specifically, in a d-dimensional flow the distance
between two neutrally buoyant particles, raised to the power and
averaged over velocity realizations, remains at all times equal to the initial,
fixed, separation raised to the same power. In this work we present evidence
from direct numerical simulations of two and three dimensional turbulence for
this conservation. In both cases the conservation is lost when particles exit
the linear flow regime. In 2D we show that, as an extension of the conservation
law, a Evans-Cohen-Morriss/Gallavotti-Cohen type fluctuation relation exists.
We also analyse data from a 3D laboratory experiment [Liberzon et al., Physica
D 241, 208 (2012)], finding that although it probes small scales they are not
in the smooth regime. Thus instead of \left, we look for a
similar, power-law-in-separation conservation law. We show that the existence
of an initially slowly varying function of this form can be predicted but that
it does not turn into a conservation law. We suggest that the conservation of
\left, demonstrated here, can be used as a check of isotropy,
incompressibility and flow dimensionality in numerical and laboratory
experiments that focus on small scales
Moth-inspired navigation algorithm in a turbulent odor plume from a pulsating source
Some female moths attract male moths by emitting series of pulses of
pheromone filaments propagating downwind. The turbulent nature of the wind
creates a complex flow environment, and causes the filaments to propagate in
the form of patches with varying concentration distributions. Inspired by moth
navigation capabilities, we propose a navigation strategy that enables a flier
to locate a pulsating odor source in a windy environment using a single
threshold-based detection sensor. The strategy is constructed based on the
physical properties of the turbulent flow carrying discrete puffs of odor and
does not involve learning, memory, complex decision making or statistical
methods. We suggest that in turbulent plumes from a pulsating point source, an
instantaneously measurable quantity referred as a "puff crossing time",
improves the success rate as compared to the navigation strategy based on
"internal counter" that does not use this information. Using computer
simulations of fliers navigating in turbulent plumes of the pulsating point
source for varying flow parameters: turbulent intensities, plume meandering and
wind gusts, we obtained trajectories qualitatively resembling male moths
flights towards the pheromone sources. We quantified the probability of a
successful navigation as well as the flight parameters such as the time spent
searching and the total flight time, with respect to different turbulent
intensities, meandering or gusts. The concepts learned using this model may
help to design odor-based navigation of miniature airborne autonomous vehicles
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