249 research outputs found
Lagrangian Refined Kolmogorov Similarity Hypothesis for Gradient Time-evolution in Turbulent Flows
We study the time evolution of velocity and pressure gradients in isotropic
turbulence, by quantifying their decorrelation time scales as one follows fluid
particles in the flow. The Lagrangian analysis uses data in a public database
generated using direct numerical simulation of the Naiver-Stokes equations, at
a Reynolds number 430. It is confirmed that when averaging over the entire
domain, correlation functions decay on timescales on the order of the mean
Kolmogorov turnover time scale, computed from the globally averaged rate of
dissipation and viscosity. However, when performing the analysis in different
subregions of the flow, turbulence intermittency leads to large spatial
variability in the decay time scales. Remarkably, excellent collapse of the
auto-correlation functions is recovered when using the `local Kolmogorov
time-scale' defined using the locally averaged, rather than the global,
dissipation-rate. This provides new evidence for the validity of Kolmogorov's
Refined Similarity Hypothesis, but from a Lagrangian viewpoint that provides a
natural frame to describe the dynamical time evolution of turbulence.Comment: 4 Pages, 4 figure
Multifractal PDF analysis for intermittent systems
The formula for probability density functions (PDFs) has been extended to
include PDF for energy dissipation rates in addition to other PDFs such as for
velocity fluctuations, velocity derivatives, fluid particle accelerations,
energy transfer rates, etc, and it is shown that the formula actually explains
various PDFs extracted from direct numerical simulations and experiments
performed in a wind tunnel. It is also shown that the formula with appropriate
zooming increment corresponding to experimental situation gives a new route to
obtain the scaling exponents of velocity structure function, including
intermittency exponent, out of PDFs of velocity fluctuations.Comment: 10 pages, 5 figure
Lagrangian dynamics and statistical geometric structure of turbulence
The local statistical and geometric structure of three-dimensional turbulent
flow can be described by properties of the velocity gradient tensor. A
stochastic model is developed for the Lagrangian time evolution of this tensor,
in which the exact nonlinear self-stretching term accounts for the development
of well-known non-Gaussian statistics and geometric alignment trends. The
non-local pressure and viscous effects are accounted for by a closure that
models the material deformation history of fluid elements. The resulting
stochastic system reproduces many statistical and geometric trends observed in
numerical and experimental 3D turbulent flows, including anomalous relative
scaling.Comment: 5 pages, 5 figures, final version, publishe
Chaotic Cascades with Kolmogorov 1941 Scaling
We define a (chaotic) deterministic variant of random multiplicative cascade
models of turbulence. It preserves the hierarchical tree structure, thanks to
the addition of infinitesimal noise. The zero-noise limit can be handled by
Perron-Frobenius theory, just as the zero-diffusivity limit for the fast dynamo
problem. Random multiplicative models do not possess Kolmogorov 1941 (K41)
scaling because of a large-deviations effect. Our numerical studies indicate
that deterministic multiplicative models can be chaotic and still have exact
K41 scaling. A mechanism is suggested for avoiding large deviations, which is
present in maps with a neutrally unstable fixed point.Comment: 14 pages, plain LaTex, 6 figures available upon request as hard copy
(no local report #
Multiscale theory of turbulence in wavelet representation
We present a multiscale description of hydrodynamic turbulence in
incompressible fluid based on a continuous wavelet transform (CWT) and a
stochastic hydrodynamics formalism. Defining the stirring random force by the
correlation function of its wavelet components, we achieve the cancellation of
loop divergences in the stochastic perturbation expansion. An extra
contribution to the energy transfer from large to smaller scales is considered.
It is shown that the Kolmogorov hypotheses are naturally reformulated in
multiscale formalism. The multiscale perturbation theory and statistical
closures based on the wavelet decomposition are constructed.Comment: LaTeX, 27 pages, 3 eps figure
Multi-Zone Shell Model for Turbulent Wall Bounded Flows
We suggested a \emph{Multi-Zone Shell} (MZS) model for wall-bounded flows
accounting for the space inhomogeneity in a "piecewise approximation", in which
cross-section area of the flow, , is subdivided into "-zones". The area
of the first zone, responsible for the core of the flow, , and
areas of the next -zones, , decrease towards the wall like . In each -zone the statistics of turbulence is assumed to be space
homogeneous and is described by the set of "shell velocities" for
turbulent fluctuations of the scale . The MZS-model includes a
new set of complex variables, , , describing the
amplitudes of the near wall coherent structures of the scale
and responsible for the mean velocity profile. Suggested MZS-equations of
motion for and preserve the actual conservations laws
(energy, mechanical and angular momenta), respect the existing symmetries
(including Galilean and scale invariance) and account for the type of the
non-linearity in the Navier-Stokes equation, dimensional reasoning, etc. The
MZS-model qualitatively describes important characteristics of the wall bounded
turbulence, e.g., evolution of the mean velocity profile with increasing
Reynolds number, \RE, from the laminar profile towards the universal
logarithmic profile near the flat-plane boundary layer as \RE\to \infty.Comment: 27 pages, 17 figs, included, PRE, submitte
Universal Scaling Properties in Large Assemblies of Simple Dynamical Units Driven by Long-Wave Random Forcing
Large assemblies of nonlinear dynamical units driven by a long-wave
fluctuating external field are found to generate strong turbulence with scaling
properties. This type of turbulence is so robust that it persists over a finite
parameter range with parameter-dependent exponents of singularity, and is
insensitive to the specific nature of the dynamical units involved. Whether or
not the units are coupled with their neighborhood is also unimportant. It is
discovered numerically that the derivative of the field exhibits strong spatial
intermittency with multifractal structure.Comment: 10 pages, 7 figures, submitted to PR
Time-reversible Dynamical Systems for Turbulence
Dynamical Ensemble Equivalence between hydrodynamic dissipative equations and
suitable time-reversible dynamical systems has been investigated in a class of
dynamical systems for turbulence. The reversible dynamics is obtained from the
original dissipative equations by imposing a global constraint. We find that,
by increasing the input energy, the system changes from an equilibrium state to
a non-equilibrium stationary state in which an energy cascade, with the same
statistical properties of the original system, is clearly detected.Comment: 16 pages Latex, 4 PS figures, on press on J. Phy
Dynamical Organization around Turbulent Bursts
The detailed dynamics around intermittency bursts is investigated in
turbulent shell models. We observe that the amplitude of the high wave number
velocity modes vanishes before each burst, meaning that the fixed point in zero
and not the Kolmogorov fixed point determines the intermittency. The phases of
the field organize during the burst, and after a burst the field oscillates
back to the laminar level. We explain this behavior from the variations in the
values of the dissipation and the advection around the zero fixed point.Comment: 4 pages, REVTex, 3 figures in one ps-fil
Maximal blood flow velocity in severe coronary stenosis measured with a doppler guidewire. Limitations for the application of the continuity equation in the assessment of stenosis severity
In vitro and animal experiments have shown that the severity of coronary stenoses can be assessed using the continuity equation if the maximal blood flow velocity of the stenotic jet is measured. The large diameter and the low range of velocities measurable without frequency aliasing with the conventional intracoronary Doppler catheters precluded the clinical application of this method for hemodynamically significant coronary stenoses in humans. This article reports the results obtained using a 12 MHz steerable angioplasty guidewire in a consecutive se
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