171 research outputs found
On the Global Regularity of a Helical-decimated Version of the 3D Navier-Stokes Equations
We study the global regularity, for all time and all initial data in
, of a recently introduced decimated version of the incompressible 3D
Navier-Stokes (dNS) equations. The model is based on a projection of the
dynamical evolution of Navier-Stokes (NS) equations into the subspace where
helicity (the scalar product of velocity and vorticity) is sign-definite.
The presence of a second (beside energy) sign-definite inviscid conserved
quadratic quantity, which is equivalent to the Sobolev norm, allows
us to demonstrate global existence and uniqueness, of space-periodic solutions,
together with continuity with respect to the initial conditions, for this
decimated 3D model. This is achieved thanks to the establishment of two new
estimates, for this 3D model, which show that the and the time
average of the square of the norms of the velocity field remain
finite. Such two additional bounds are known, in the spirit of the work of H.
Fujita and T. Kato \cite{kato1,kato2}, to be sufficient for showing
well-posedness for the 3D NS equations. Furthermore, they are directly linked
to the helicity evolution for the dNS model, and therefore with a clear
physical meaning and consequences
Role of helicity for large- and small-scale turbulent fluctuations
The effect of the helicity on the dynamics of the turbulent flows is
investigated. The aim is to disentangle the role of helicity in fixing the
direction, the intensity and the fluctuations of the energy transfer across the
inertial range of scales. We introduce an external parameter, , that
controls the mismatch between the number of positive and negative helically
polarized Fourier modes. We present the first set of direct numerical
simulations of Navier-Stokes equations from the fully symmetrical case,
, to the fully asymmetrical case, , when only helical modes
of one sign survive. We found a singular dependency of the direction of the
energy cascade on , measuring a positive forward flux as soon as only a
few modes with different helical polarities are present. On the other hand,
small-scales fluctuations are sensitive only to the degree of mode-reduction,
leading to a vanishing intermittency already for values of
and independently of the degree of mirror symmetry-breaking. Our findings
suggest that intermittency is the result of a global mode-coupling in Fourier
space.Comment: 4 Fig
A note on the fluctuation of dissipative scale in turbulence
We present an application of the multifractal formalism able to predict the whole shape of the probability density function (pdf) of the dissipative scale, Ξ·. We discuss both intense velocity fluctuations, leading to dissipative scales smaller than the Kolmogorov scale, where the formalism gives a pdf decaying as a superposition of stretched exponential, and smooth velocity fluctuations, where the formalism predicts a power-law decay. Both trends are found to be in good agreement with recent direct numerical simulations [J. Schumacher, "Sub-Kolmogorov-scale fluctuations in fluid turbulence," Europhys. Lett.β80, 54001 (2007)]
Intermittency in Turbulence: Multiplicative random process in space and time
We present a simple stochastic algorithm for generating multiplicative
processes with multiscaling both in space and in time. With this algorithm we
are able to reproduce a synthetic signal with the same space and time
correlation as the one coming from shell models for turbulence and the one
coming from a turbulent velocity field in a quasi-Lagrangian reference frame.Comment: 23 pages, 12 figure
A closure theory for the split energy-helicity cascades in homogeneous isotropic homochiral turbulence
We study the energy transfer properties of three dimensional homogeneous and
isotropic turbulence where the non-linear transfer is altered in a way that
helicity is made sign-definite, say positive. In this framework, known as
homochiral turbulence, an adapted eddy-damped quasi-normal Markovian (EDQNM)
closure is derived to analyze the dynamics at very large Reynolds numbers, of
order based on the Taylor scale. In agreement with previous findings, an
inverse cascade of energy with a kinetic energy spectrum like is found for scales larger than the forcing one. Conjointly, a
forward cascade of helicity towards larger wavenumbers is obtained, where the
kinetic energy spectrum scales like . By following the
evolution of the closed spectral equations for a very long time and over a huge
extensions of scales, we found the developing of a non monotonic shape for the
front of the inverse energy flux. The very long time evolution of the kinetic
energy and integral scale in both the forced and unforced cases is analyzed
also.Comment: 8 pages, 3 figure
The statistical properties of turbulence in the presence of a smart small-scale control
By means of high-resolution numerical simulations, we compare the statistical
properties of homogeneous and isotropic turbulence to those of the
Navier-Stokes equation where small-scale vortex filaments are strongly
depleted, thanks to a non-linear extra viscosity acting preferentially on high
vorticity regions. We show that the presence of such smart small-scale drag can
strongly reduce intermittency and non-Gaussian fluctuations. Our results pave
the way towards a deeper understanding on the fundamental role of degrees of
freedom in turbulence as well as on the impact of (pseudo)coherent structures
on the statistical small-scale properties. Our work can be seen as a first
attempt to develop smart-Lagrangian forcing/drag mechanisms to control
turbulence.Comment: 5 pages, 5 figure
Deformation statistics of sub-Kolmogorov-scale ellipsoidal neutrally buoyant drops in isotropic turbulence
Small droplets in turbulent flows can undergo highly variable deformations
and orientational dynamics. For neutrally buoyant droplets smaller than the
Kolmogorov scale, the dominant effects from the surrounding turbulent flow
arise through Lagrangian time histories of the velocity gradient tensor. Here
we study the evolution of representative droplets using a model that includes
rotation and stretching effects from the surrounding fluid, and restoration
effects from surface tension including a constant droplet volume constraint,
while assuming that the droplets maintain an ellipsoidal shape. The model is
combined with Lagrangian time histories of the velocity gradient tensor
extracted from DNS of turbulence to obtain simulated droplet evolutions. These
are used to characterize the size, shape and orientation statistics of small
droplets in turbulence. A critical capillary number, is identified
associated with unbounded growth of one or two of the droplet's semi-axes.
Exploiting analogies with dynamics of polymers in turbulence, the number
can be predicted based on the large deviation theory for the largest Finite
Time Lyapunov exponent. Also, for sub-critical the theory enables
predictions of the slope of the power-law tails of droplet size distributions
in turbulence. For cases when the viscosities of droplet and outer fluid differ
in a way that enables vorticity to decorrelate the shape from the straining
directions, the large deviation formalism based on the stretching properties of
the velocity gradient tensor loses validity and its predictions fail. Even
considering the limitations of the assumed ellipsoidal droplet shape, the
results highlight the complex coupling between droplet deformation, orientation
and the local fluid velocity gradient tensor to be expected when small viscous
drops interact with turbulent flows
Statistics of small scale vortex filaments in turbulence
We study the statistical properties of coherent, small-scales,
filamentary-like structures in Turbulence. In order to follow in time such
complex spatial structures, we integrate Lagrangian and Eulerian measurements
by seeding the flow with light particles. We show that light particles
preferentially concentrate in small filamentary regions of high persistent
vorticity (vortex filaments). We measure the fractal dimension of the
attracting set and the probability that two particles do not separate for long
time lapses. We fortify the signal-to-noise ratio by exploiting multi-particles
correlations on the dynamics of bunches of particles. In doing that, we are
able to give a first quantitative estimation of the vortex-filaments
life-times, showing the presence of events as long as the integral correlation
time. The same technique introduced here could be used in experiments as long
as one is capable to track clouds of bubbles in turbulence for a relatively
long period of time, at high Reynolds numbers; shading light on the dynamics of
small-scale vorticity in realistic turbulent flows.Comment: 5 pages, 5 figure
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