156 research outputs found
Condensate in quasi two-dimensional turbulence
We investigate the process of formation of large-scale structures in a
turbulent flow confined in a thin layer. By means of direct numerical
simulations of the Navier-Stokes equations, forced at an intermediate scale, we
obtain a split of the energy cascade in which one fraction of the input goes to
small scales generating the three-dimensional direct cascade. The remaining
energy flows to large scales producing the inverse cascade which eventually
causes the formation of a quasi two-dimensional condensed state at the largest
horizontal scale. Our results shows that the connection between the two actors
of the split energy cascade in thin layers is tighter than what was established
before: the small scale three-dimensional turbulence acts as an effective
viscosity and dissipates the large-scale energy thus providing a
viscosity-independent mechanism for arresting the growth of the condensate.
This scenario is supported by quantitative predictions of the saturation energy
in the condensate
Split energy cascade in turbulent thin fluid layers
We discuss the phenomenology of the split energy cascade in a
three-dimensional thin fluid layer by mean of high resolution numerical
simulations of the Navier-Stokes equations. We observe the presence of both an
inverse energy cascade at large scales, as predicted for two-dimensional turbu-
lence, and of a direct energy cascade at small scales, as in three-dimensional
turbulence. The inverse energy cascade is associated with a direct cascade of
enstrophy in the intermediate range of scales. Notably, we find that the
inverse cascade of energy in this system is not a pure 2D phenomenon, as the
coupling with the 3D velocity field is necessary to guarantee the constancy of
fluxes
Inertial floaters in stratified turbulence
We investigate numerically the dynamics and statistics of inertial particles
transported by stratified turbulence, in the case of particle density
intermediate in the average density profile of the fluid. In these conditions,
particles tend to form a thin layer around the corresponding fluid isopycnal.
The thickness of the resulting layer is determined by a balance between
buoyancy (which attracts the particle to the isopycnal) and inertia (which
prevents them from following it exactly). By means of extensive numerical
simulations, we explore the parameter space of the system and we find that in a
range of parameters particles form fractal cluster within the layer.Comment: 6 pages, 6 figure
Irreversibility-inversions in 2 dimensional turbulence
In this paper we consider a recent theoretical prediction (Bragg \emph{et
al.}, Phys. Fluids \textbf{28}, 013305 (2016)) that for inertial particles in
2D turbulence, the nature of the irreversibility of the particle-pair
dispersion inverts when the particle inertia exceeds a certain value. In
particular, when the particle Stokes number, , is below a certain
value, the forward-in-time (FIT) dispersion should be faster than the
backward-in-time (BIT) dispersion, but for above this value, this
should invert so that BIT becomes faster than FIT dispersion. This non-trivial
behavior arises because of the competition between two physically distinct
irreversibility mechanisms that operate in different regimes of . In
3D turbulence, both mechanisms act to produce faster BIT than FIT dispersion,
but in 2D turbulence, the two mechanisms have opposite effects because of the
flux of energy from the small to the large scales. We supplement the
qualitative argument given by Bragg \emph{et al.} (Phys. Fluids \textbf{28},
013305 (2016)) by deriving quantitative predictions of this effect in the short
time limit. We confirm the theoretical predictions using results of inertial
particle dispersion in a direct numerical simulation of 2D turbulence. A more
general finding of this analysis is that in turbulent flows with an inverse
energy flux, inertial particles may yet exhibit a net downscale flux of kinetic
energy because of their non-local in-time dynamics
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
Gyrotactic phytoplankton in laminar and turbulent flows: a dynamical systems approach
Gyrotactic algae are bottom heavy, motile cells whose swimming direction is
determined by a balance between a buoyancy torque directing them upwards and
fluid velocity gradients. Gyrotaxis has, in recent years, become a paradigmatic
model for phytoplankton motility in flows. The essential attractiveness of this
peculiar form of motility is the availability of a mechanistic description
which, despite its simplicity, revealed predictive, rich in phenomenology,
easily complemented to include the effects of shape, feed-back on the fluid and
stochasticity (e.g. in cell orientation). In this review we consider recent
theoretical, numerical and experimental results to discuss how, depending on
flow properties, gyrotaxis can produce inhomogeneous phytoplankton
distributions on a wide range of scales, from millimeters to kilometers, in
both laminar and turbulent flows. In particular, we focus on the phenomenon of
gyrotactic trapping in nonlinear shear flows and in fractal clustering in
turbulent flows. We shall demonstrate the usefulness of ideas and tools
borrowed from dynamical systems theory in explaining and interpreting these
phenomena
Clustering and Turbophoresis in a Shear Flow without Walls
We investigate the spatial distribution of inertial particles suspended in
the bulk of a turbulent inhomogeneous flow. By means of direct numerical
simulations of particle trajectories transported by the turbulent Kolmogorov
flow, we study large and small scale mechanisms inducing inhomogeneities in the
distribution of heavy particles. We discuss turbophoresis both for large and
weak inertia, providing heuristic arguments for the functional form of the
particle density profile. In particular, we argue and numerically confirm that
the turbophoretic effect is maximal for particles of intermediate inertia. Our
results indicate that small-scale fractal clustering and turbophoresis peak in
different ranges in the particles' Stokes number and the separation of the two
peaks increases with the flow's Reynolds number.Comment: 13 pages, 5 figure
Geotropic tracers in turbulent flows: a proxy for fluid acceleration
We investigate the statistics of orientation of small, neutrally buoyant,
spherical tracers whose center of mass is displaced from the geometrical
center. If appropriate-sized particles are considered, a linear relation can be
derived between the horizontal components of the orientation vector and the
same components of acceleration. Direct numerical simulations are carried out,
showing that such relation can be used to reconstruct the statistics of
acceleration fluctuations up to the order of the gravitational acceleration.
Based on such results, we suggest a novel method for the local experimental
measurement of accelerations in turbulent flows.Comment: 14 pages, 6 figure
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