99 research outputs found

### Cascade time-scales for energy and helicity in homogeneous isotropic turbulence

We extend the Kolmogorov phenomenology for the scaling of energy spectra in
high-Reynolds number turbulence, to explicitly include the effect of helicity.
There exists a time-scale $\tau_H$ for helicity transfer in homogeneous,
isotropic turbulence with helicity. We arrive at this timescale using the
phenomenological arguments used by Kraichnan to derive the timescale $\tau_E$
for energy transfer (J. Fluid Mech. {\bf 47}, 525--535 (1971)). We show that in
general $\tau_H$ may not be neglected compared to $\tau_E$, even for rather low
relative helicity. We then deduce an inertial range joint cascade of energy and
helicity in which the dynamics are dominated by $\tau_E$ in the low wavenumbers
with both energy and helicity spectra scaling as $k^{-5/3}$; and by $\tau_H$ at
larger wavenumbers with spectra scaling as $k^{-4/3}$. We demonstrate how,
within this phenomenology, the commonly observed ``bottleneck'' in the energy
spectrum might be explained. We derive a wavenumber $k_h$ which is less than
the Kolmogorov dissipation wavenumber, at which both energy and helicity
cascades terminate due to dissipation effects. Data from direct numerical
simulations are used to check our predictions.Comment: 14 pages, 5 figures, accepted to Physical Review

### Experimental assessment of a new form of scaling law for near-wall turbulence

Scaling laws and intermittency in the wall region of a turbulent flow are
addressed by analyzing moderate Reynolds number data obtained by single
component hot wire anemometry in the boundary layer of a flat plate. The paper
aims in particular at the experimental validation of a new form of refined
similarity recently proposed for the shear dominated range of turbulence, where
the classical Kolmogorov-Oboukhov inertial range theory is inappropriate. An
approach inspired to the extended self-similarity allows for the extraction of
the different power laws for the longitudinal structure functions at several
wall normal distances. A double scaling regime is found in the logarithmic
region, confirming previous experimental results. Approaching the wall, the
scaling range corresponding to the classical cascade-dominated range tends to
disappear and, in the buffer layer, a single power law is found to describe the
available range of scales. The double scaling is shown to be associated with
two different forms of refined similarity. The classical form holds below the
shear scale L s . The other, originally introduced on the basis of DNS data for
a turbulent channel, is experimentally confirmed to set up above L s . Given
the experimental diffulties in the evaluation of the instantaneous dissipation
rate, some care is devoted to check that its one-dimensional surrogate does not
bias the results. The increased intermittency as the wall is approached is
experimentally found entirely consistent with the failure of the refined
Kolmogorov-Oboukhov similarity and the establishment of its new form near the
wall.Comment: 27 pages, 9 figure

### Generation of Large-Scale Vorticity in a Homogeneous Turbulence with a Mean Velocity Shear

An effect of a mean velocity shear on a turbulence and on the effective force
which is determined by the gradient of Reynolds stresses is studied. Generation
of a mean vorticity in a homogeneous incompressible turbulent flow with an
imposed mean velocity shear due to an excitation of a large-scale instability
is found. The instability is caused by a combined effect of the large-scale
shear motions (''skew-induced" deflection of equilibrium mean vorticity) and
''Reynolds stress-induced" generation of perturbations of mean vorticity.
Spatial characteristics, such as the minimum size of the growing perturbations
and the size of perturbations with the maximum growth rate, are determined.
This instability and the dynamics of the mean vorticity are associated with the
Prandtl's turbulent secondary flows. This instability is similar to the
mean-field magnetic dynamo instability. Astrophysical applications of the
obtained results are discussed.Comment: 8 pages, 3 figures, REVTEX4, submitted to Phys. Rev.

### Hysteresis phenomenon in turbulent convection

Coherent large-scale circulations of turbulent thermal convection in air have
been studied experimentally in a rectangular box heated from below and cooled
from above using Particle Image Velocimetry. The hysteresis phenomenon in
turbulent convection was found by varying the temperature difference between
the bottom and the top walls of the chamber (the Rayleigh number was changed
within the range of $10^7 - 10^8$). The hysteresis loop comprises the one-cell
and two-cells flow patterns while the aspect ratio is kept constant ($A=2 -
2.23$). We found that the change of the sign of the degree of the anisotropy of
turbulence was accompanied by the change of the flow pattern. The developed
theory of coherent structures in turbulent convection (Elperin et al. 2002;
2005) is in agreement with the experimental observations. The observed coherent
structures are superimposed on a small-scale turbulent convection. The
redistribution of the turbulent heat flux plays a crucial role in the formation
of coherent large-scale circulations in turbulent convection.Comment: 10 pages, 9 figures, REVTEX4, Experiments in Fluids, 2006, in pres

### Persistence of small-scale anisotropies and anomalous scaling in a model of magnetohydrodynamics turbulence

The problem of anomalous scaling in magnetohydrodynamics turbulence is
considered within the framework of the kinematic approximation, in the presence
of a large-scale background magnetic field. The velocity field is Gaussian,
$\delta$-correlated in time, and scales with a positive exponent $\xi$.
Explicit inertial-range expressions for the magnetic correlation functions are
obtained; they are represented by superpositions of power laws with
non-universal amplitudes and universal (independent of the anisotropy and
forcing) anomalous exponents. The complete set of anomalous exponents for the
pair correlation function is found non-perturbatively, in any space dimension
$d$, using the zero-mode technique. For higher-order correlation functions, the
anomalous exponents are calculated to $O(\xi)$ using the renormalization group.
The exponents exhibit a hierarchy related to the degree of anisotropy; the
leading contributions to the even correlation functions are given by the
exponents from the isotropic shell, in agreement with the idea of restored
small-scale isotropy. Conversely, the small-scale anisotropy reveals itself in
the odd correlation functions : the skewness factor is slowly decreasing going
down to small scales and higher odd dimensionless ratios (hyperskewness etc.)
dramatically increase, thus diverging in the $r\to 0$ limit.Comment: 25 pages Latex, 1 Figur

### Bottleneck effect in three-dimensional turbulence simulations

At numerical resolutions around $512^3$ and above, three-dimensional energy
spectra from turbulence simulations begin to show noticeably shallower spectra
than $k^{-5/3}$ near the dissipation wavenumber (`bottleneck effect'). This
effect is shown to be significantly weaker in one-dimensional spectra such as
those obtained in wind tunnel turbulence. The difference can be understood in
terms of the transformation between one-dimensional and three-dimensional
energy spectra under the assumption that the turbulent velocity field is
isotropic. Transversal and longitudinal energy spectra are similar and can both
accurately be computed from the full three-dimensional spectra. Second-order
structure functions are less susceptible to the bottleneck effect and may be
better suited for inferring the scaling exponent from numerical simulation
data.Comment: 8 pages, 6 figure

### Anomalous scaling of a passive scalar in the presence of strong anisotropy

Field theoretic renormalization group and the operator product expansion are
applied to a model of a passive scalar field, advected by the Gaussian strongly
anisotropic velocity field. Inertial-range anomalous scaling behavior is
established, and explicit asymptotic expressions for the n-th order structure
functions of scalar field are obtained; they are represented by superpositions
of power laws with nonuniversal (dependent on the anisotropy parameters)
anomalous exponents. In the limit of vanishing anisotropy, the exponents are
associated with tensor composite operators built of the scalar gradients, and
exhibit a kind of hierarchy related to the degree of anisotropy: the less is
the rank, the less is the dimension and, consequently, the more important is
the contribution to the inertial-range behavior. The leading terms of the even
(odd) structure functions are given by the scalar (vector) operators. For the
finite anisotropy, the exponents cannot be associated with individual operators
(which are essentially ``mixed'' in renormalization), but the aforementioned
hierarchy survives for all the cases studied. The second-order structure
function is studied in more detail using the renormalization group and
zero-mode techniques.Comment: REVTEX file with EPS figure

### Statistical Properties of Turbulence: An Overview

We present an introductory overview of several challenging problems in the
statistical characterisation of turbulence. We provide examples from fluid
turbulence in three and two dimensions, from the turbulent advection of passive
scalars, turbulence in the one-dimensional Burgers equation, and fluid
turbulence in the presence of polymer additives.Comment: 34 pages, 31 figure

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