352 research outputs found
Generalized Knudsen number for unsteady fluid flow
We explore the scaling behavior of an unsteady flow that is generated by an oscillating body of finite size in a gas. If the gas is gradually rarefied, the Navier-Stokes equations begin to fail and a kinetic description of the flow becomes more appropriate. The failure of the Navier-Stokes equations can be thought to take place via two different physical mechanisms: either the continuum hypothesis breaks down as a result of a finite size effect or local equilibrium is violated due to the high rate of strain. By independently tuning the relevant linear dimension and the frequency of the oscillating body, we can experimentally observe these two different physical mechanisms. All the experimental data, however, can be collapsed using a single dimensionless scaling parameter that combines the relevant linear dimension and the frequency of the body. This proposed Knudsen number for an unsteady flow is rooted in a fundamental symmetry principle, namely, Galilean invariance
Mean- Field Approximation and a Small Parameter in Turbulence Theory
Numerical and physical experiments on two-dimensional (2d) turbulence show
that the differences of transverse components of velocity field are well
described by a gaussian statistics and Kolmogorov scaling exponents. In this
case the dissipation fluctuations are irrelevant in the limit of small
viscosity. In general, one can assume existence of critical
space-dimensionality , at which the energy flux and all odd-order
moments of velocity difference change sign and the dissipation fluctuations
become dynamically unimportant. At the flow can be described by the
``mean-field theory'', leading to the observed gaussian statistics and
Kolmogorov scaling of transverse velocity differences. It is shown that in the
vicinity of the ratio of the relaxation and translation
characteristic times decreases to zero, thus giving rise to a small parameter
of the theory. The expressions for pressure and dissipation contributions to
the exact equation for the generating function of transverse velocity
differences are derived in the vicinity of . The resulting equation
describes experimental data on two-dimensional turbulence and demonstrate onset
of intermittency as and in three-dimensional flows in
close agreement with experimental data. In addition, some new exact relations
between correlation functions of velocity differences are derived. It is also
predicted that the single-point pdf of transverse velocity difference in
developing as well as in the large-scale stabilized two-dimensional turbulence
is a gaussian.Comment: 25 pages, 1 figur
Self-sustained oscillations in homogeneous shear flow
Generation of the large-scale coherent vortical structurs in homogeneous
shear flow couples dynamical processes of energy and enstrophy production. In
the large rate of strain limit, the simple estimates of the contributions to
the energy and enstrophy equations result in a dynamical system, describing
experimentally and numerically observed self-sustained non-linear oscillations
of energy and enstrophy. It is shown that the period of these oscilaltions is
independent upon the box size and the energy and enstrophy fluctuations are
strongly correlated.Comment: 10 pages 6 figure
Anomalous Scaling of Structure Functions and Dynamic Constraints on Turbulence Simulations
The connection between anomalous scaling of structure functions
(intermittency) and numerical methods for turbulence simulations is discussed.
It is argued that the computational work for direct numerical simulations (DNS)
of fully developed turbulence increases as , and not as
expected from Kolmogorov's theory, where is a large-scale Reynolds number.
Various relations for the moments of acceleration and velocity derivatives are
derived. An infinite set of exact constraints on dynamically consistent subgrid
models for Large Eddy Simulations (LES) is derived from the Navier-Stokes
equations, and some problems of principle associated with existing LES models
are highlighted.Comment: 18 page
Mean- Field Approximation and Extended Self-Similarity in Turbulence
Recent experimental discovery of extended self-similarity (ESS) was one of
the most interesting developments, enabling precise determination of the
scaling exponents of fully developed turbulence. Here we show that the ESS is
consistent with the Navier-Stokes equations, provided the pressure -gradient
contributions are expressed in terms of velocity differences in the mean field
approximation (Yakhot, Phys.Rev. E{\bf 63}, 026307, (2001)). A sufficient
condition for extended self-similarity in a general dynamical systemComment: 8 pages, no figure
Kolmogorov turbulence in a random-force-driven Burgers equation
The dynamics of velocity fluctuations, governed by the one-dimensional
Burgers equation, driven by a white-in-time random force with the spatial
spectrum \overline{|f(k)|^2}\proptok^{-1}, is considered. High-resolution
numerical experiments conducted in this work give the energy spectrum
with . The observed two-point
correlation function reveals with the
"dynamical exponent" . High-order moments of velocity differences
show strong intermittency and are dominated by powerful large-scale shocks. The
results are compared with predictions of the one-loop renormalized perturbation
expansion.Comment: 13 LaTeX pages, psfig.sty macros, Phys. Rev. E 51, R2739 (1995)
Closure of two dimensional turbulence: the role of pressure gradients
Inverse energy cascade regime of two dimensional turbulence is investigated
by means of high resolution numerical simulations. Numerical computations of
conditional averages of transverse pressure gradient increments are found to be
compatible with a recently proposed self-consistent Gaussian model. An
analogous low order closure model for the longitudinal pressure gradient is
proposed and its validity is numerically examined. In this case numerical
evidence for the presence of higher order terms in the closure is found. The
fundamental role of conditional statistics between longitudinal and transverse
components is highlighted.Comment: 4 pages, 2 figures, in press on PR
Turbulence without pressure in d dimensions
The randomly driven Navier-Stokes equation without pressure in d-dimensional
space is considered as a model of strong turbulence in a compressible fluid. We
derive a closed equation for the velocity-gradient probability density
function. We find the asymptotics of this function for the case of the gradient
velocity field (Burgers turbulence), and provide a numerical solution for the
two-dimensional case. Application of these results to the velocity-difference
probability density function is discussed.Comment: latex, 5 pages, revised and enlarge
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