45 research outputs found
Universal Model of Finite-Reynolds Number Turbulent Flow in Channels and Pipes
In this Letter we suggest a simple and physically transparent analytical
model of the pressure driven turbulent wall-bounded flows at high but finite
Reynolds numbers Re. The model gives accurate qualitative description of the
profiles of the mean-velocity and Reynolds-stresses (second order correlations
of velocity fluctuations) throughout the entire channel or pipe in the wide
range of Re, using only three Re-independent parameters. The model sheds light
on the long-standing controversy between supporters of the century-old log-law
theory of von-K\`arm\`an and Prandtl and proposers of a newer theory promoting
power laws to describe the intermediate region of the mean velocity profile.Comment: 4 pages, 6 figs, re-submitted PRL according to referees comment
Phenomenology of Wall Bounded Newtonian Turbulence
We construct a simple analytic model for wall-bounded turbulence, containing
only four adjustable parameters. Two of these parameters characterize the
viscous dissipation of the components of the Reynolds stress-tensor and other
two parameters characterize their nonlinear relaxation. The model offers an
analytic description of the profiles of the mean velocity and the correlation
functions of velocity fluctuations in the entire boundary region, from the
viscous sub-layer, through the buffer layer and further into the log-layer. As
a first approximation, we employ the traditional return-to-isotropy hypothesis,
which yields a very simple distribution of the turbulent kinetic energy between
the velocity components in the log-layer: the streamwise component contains a
half of the total energy whereas the wall-normal and the cross-stream
components contain a quarter each. In addition, the model predicts a very
simple relation between the von-K\'arm\'an slope and the turbulent
velocity in the log-law region (in wall units): . These
predictions are in excellent agreement with DNS data and with recent laboratory
experiments.Comment: 15 pages, 11 figs, included, PRE, submitte
The Scaling Structure of the Velocity Statistics in Atmospheric Boundary Layer
The statistical objects characterizing turbulence in real turbulent flows
differ from those of the ideal homogeneous isotropic model.They
containcontributions from various 2d and 3d aspects, and from the superposition
ofinhomogeneous and anisotropic contributions. We employ the recently
introduceddecomposition of statistical tensor objects into irreducible
representations of theSO(3) symmetry group (characterized by and
indices), to disentangle someof these contributions, separating the universal
and the asymptotic from the specific aspects of the flow. The different
contributions transform differently under rotations and so form a complete
basis in which to represent the tensor objects under study. The experimental
data arerecorded with hot-wire probes placed at various heights in the
atmospheric surfacelayer. Time series data from single probes and from pairs of
probes are analyzed to compute the amplitudes and exponents of different
contributions to the second order statistical objects characterized by ,
and . The analysis shows the need to make a careful distinction
between long-lived quasi 2d turbulent motions (close to the ground) and
relatively short-lived 3d motions. We demonstrate that the leading scaling
exponents in the three leading sectors () appear to be different
butuniversal, independent of the positions of the probe, and the large
scaleproperties. The measured values of the exponent are , and .
We present theoretical arguments for the values of these exponents usingthe
Clebsch representation of the Euler equations; neglecting anomalous
corrections, the values obtained are 2/3, 1 and 4/3 respectively.Comment: PRE, submitted. RevTex, 38 pages, 8 figures included . Online (HTML)
version of this paper is avaliable at http://lvov.weizmann.ac.il
Correlation functions in isotropic and anisotropic turbulence: the role of the symmetry group
The theory of fully developed turbulence is usually considered in an
idealized homogeneous and isotropic state. Real turbulent flows exhibit the
effects of anisotropic forcing. The analysis of correlation functions and
structure functions in isotropic and anisotropic situations is facilitated and
made rational when performed in terms of the irreducible representations of the
relevant symmetry group which is the group of all rotations SO(3). In this
paper we firstly consider the needed general theory and explain why we expect
different (universal) scaling exponents in the different sectors of the
symmetry group. We exemplify the theory context of isotropic turbulence (for
third order tensorial structure functions) and in weakly anisotropic turbulence
(for the second order structure function). The utility of the resulting
expressions for the analysis of experimental data is demonstrated in the
context of high Reynolds number measurements of turbulence in the atmosphere.Comment: 35 pages, REVTEX, 1 figure, Phys. Rev. E, submitte
Identification and Calculation of the Universal Maximum Drag Reduction Asymptote by Polymers in Wall Bounded Turbulence
Drag reduction by polymers in wall turbulence is bounded from above by a
universal maximal drag reduction (MDR) velocity profile that is a log-law,
estimated experimentally by Virk as . Here
and are the mean streamwise velocity and the distance from the
wall in "wall" units. In this Letter we propose that this MDR profile is an
edge solution of the Navier-Stokes equations (with an effective viscosity
profile) beyond which no turbulent solutions exist. This insight rationalizes
the universality of the MDR and provides a maximum principle which allows an
ab-initio calculation of the parameters in this law without any viscoelastic
experimental input.Comment: 4 pages, 1 fig. Phys. Rev. Letts., submitte
Drag Reduction by Bubble Oscillations
Drag reduction in stationary turbulent flows by bubbles is sensitive to the
dynamics of bubble oscillations. Without this dynamical effect the bubbles only
renormalize the fluid density and viscosity, an effect that by itself can only
lead to a small percentage of drag reduction. We show in this paper that the
dynamics of bubbles and their effect on the compressibility of the mixture can
lead to a much higher drag reduction.Comment: 7 pages, 1 figure, submitted to Phys. Rev.
Symmetries and Interaction coefficients of Kelvin waves
We considered symmetry restriction on the interaction coefficients of Kelvin
waves and demonstrated that linear in small wave vector asymptotic is not
forbidden, as one can expect by naive reasoning.Comment: 4 pages, submitted to J. of Low Temp. Phy
A Model of Intra-seasonal Oscillations in the Earth atmosphere
We suggest a way of rationalizing an intra-seasonal oscillations (IOs) of the
Earth atmospheric flow as four meteorological relevant triads of interacting
planetary waves, isolated from the system of all the rest planetary waves.
Our model is independent of the topography (mountains, etc.) and gives a
natural explanation of IOs both in the North and South Hemispheres. Spherical
planetary waves are an example of a wave mesoscopic system obeying discrete
resonances that also appears in other areas of physics.Comment: 4 pages, 2 figs, Submitted to PR
Finite-Dimensional Turbulence of Planetary Waves
Finite-dimensional wave turbulence refers to the chaotic dynamics of
interacting wave `clusters' consisting of finite number of connected wave
triads with exact three-wave resonances. We examine this phenomenon using the
example of atmospheric planetary (Rossby) waves. It is shown that the dynamics
of the clusters is determined by the types of connections between neighboring
triads within a cluster; these correspond to substantially different scenarios
of energy flux between different triads. All the possible cases of the energy
cascade termination are classified. Free and forced chaotic dynamics in the
clusters are investigated: due to the huge fluctuations of the energy exchange
between resonant triads these two types of evolution have a lot in common. It
is confirmed that finite-dimensional wave turbulence in finite wave systems is
fundamentally different from kinetic wave turbulence in infinite systems; the
latter is described by wave kinetic equations that account for interactions
with overlapping quasi-resonances of finite amplitude waves. The present
results are directly applicable to finite-dimensional wave turbulence in any
wave system in finite domains with 3-mode interactions as encountered in
hydrodynamics, astronomy, plasma physics, chemistry, medicine, etc.Comment: 29 pages, 21 figures, submitted to PR
Energy Spectra of Quantum Turbulence: Large-scale Simulation and Modeling
In simulation of quantum turbulence within the Gross-Pitaevskii
equation we demonstrate that the large scale motions have a classical
Kolmogorov-1941 energy spectrum E(k) ~ k^{-5/3}, followed by an energy
accumulation with E(k) ~ const at k about the reciprocal mean intervortex
distance. This behavior was predicted by the L'vov-Nazarenko-Rudenko bottleneck
model of gradual eddy-wave crossover [J. Low Temp. Phys. 153, 140-161 (2008)],
further developed in the paper.Comment: (re)submitted to PRB: 5.5 pages, 4 figure