217 research outputs found
Reynolds number effect on the velocity increment skewness in isotropic turbulence
Second and third order longitudinal structure functions and wavenumber
spectra of isotropic turbulence are computed using the EDQNM model and compared
to results of the multifractal formalism. At the highest Reynolds number
available in windtunnel experiments, , both the multifractal
model and EDQNM give power-law corrections to the inertial range scaling of the
velocity increment skewness. For EDQNM, this correction is a finite Reynolds
number effect, whereas for the multifractal formalism it is an intermittency
correction that persists at any high Reynolds number. Furthermore, the two
approaches yield realistic behavior of second and third order statistics of the
velocity fluctuations in the dissipative and near-dissipative ranges.
Similarities and differences are highlighted, in particular the Reynolds number
dependence
Gaussian multiplicative Chaos for symmetric isotropic matrices
Motivated by isotropic fully developed turbulence, we define a theory of
symmetric matrix valued isotropic Gaussian multiplicative chaos. Our
construction extends the scalar theory developed by J.P. Kahane in 1985
Metalibm: A Mathematical Functions Code Generator
International audienceThere are several different libraries with code for mathematical functions such as exp, log, sin, cos, etc. They provide only one implementation for each function. As there is a link between accuracy and performance, that approach is not optimal. Sometimes there is a need to rewrite a function's implementation with the respect to a particular specification. In this paper we present a code generator for parametrized implementations of mathematical functions. We discuss the benefits of code generation for mathematical libraries and present how to implement mathematical functions. We also explain how the mathematical functions are usually implemented and generalize this idea for the case of arbitrary function with implementation parameters. Our code generator produces C code for parametrized functions within a known scheme: range reduction (domain splitting), polynomial approximation and reconstruction. This approach can be expanded to generate code for black-box functions, e.g. defined only by differential equations
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
Intermittency of velocity time increments in turbulence
We analyze the statistics of turbulent velocity fluctuations in the time
domain. Three cases are computed numerically and compared: (i) the time traces
of Lagrangian fluid particles in a (3D) turbulent flow (referred to as the
"dynamic" case); (ii) the time evolution of tracers advected by a frozen
turbulent field (the "static" case), and (iii) the evolution in time of the
velocity recorded at a fixed location in an evolving Eulerian velocity field,
as it would be measured by a local probe (referred to as the "virtual probe"
case). We observe that the static case and the virtual probe cases share many
properties with Eulerian velocity statistics. The dynamic (Lagrangian) case is
clearly different; it bears the signature of the global dynamics of the flow.Comment: 5 pages, 3 figures, to appear in PR
Lagrangian Velocity Statistics in Turbulent Flows: Effects of Dissipation
We use the multifractal formalism to describe the effects of dissipation on
Lagrangian velocity statistics in turbulent flows. We analyze high Reynolds
number experiments and direct numerical simulation (DNS) data. We show that
this approach reproduces the shape evolution of velocity increment probability
density functions (PDF) from Gaussian to stretched exponentials as the time lag
decreases from integral to dissipative time scales. A quantitative
understanding of the departure from scaling exhibited by the magnitude
cumulants, early in the inertial range, is obtained with a free parameter
function D(h) which plays the role of the singularity spectrum in the
asymptotic limit of infinite Reynolds number. We observe that numerical and
experimental data are accurately described by a unique quadratic D(h) spectrum
which is found to extend from to , as
the signature of the highly intermittent nature of Lagrangian velocity
fluctuations.Comment: 5 pages, 3 figures, to appear in PR
Static spectroscopy of a dense superfluid
Dense Bose superfluids, as HeII, differ from dilute ones by the existence of
a roton minimum in their excitation spectrum. It is known that this roton
minimum is qualitatively responsible for density oscillations close to any
singularity, such as vortex cores, or close to solid boundaries. We show that
the period of these oscillations, and their exponential decrease with the
distance to the singularity, are fully determined by the position and the width
of the roton minimum. Only an overall amplitude factor and a phase shift are
shown to depend on the details of the interaction potential. Reciprocally, it
allows for determining the characteristics of this roton minimum from static
"observations" of a disturbed ground state, in cases where the dynamics is not
easily accessible. We focus on the vortex example. Our analysis further shows
why the energy of these oscillations is negligible compared to the kinetic
energy, which limits their influence on the vortex dynamics, except for high
curvatures.Comment: 14 pages, 4 figures, extended version, published in J. Low Temp. Phy
Probing quantum and classical turbulence analogy through global bifurcations in a von K\'arm\'an liquid Helium experiment
We report measurements of the dissipation in the Superfluid Helium high
REynold number von Karman flow (SHREK) experiment for different forcing
conditions, through a regime of global hysteretic bifurcation. Our
macroscopical measurements indicate no noticeable difference between the
classical fluid and the superfluid regimes, thereby providing evidence of the
same dissipative anomaly and response to asymmetry in fluid and superfluid
regime. %In the latter case, A detailed study of the variations of the
hysteretic cycle with Reynolds number supports the idea that (i) the stability
of the bifurcated states of classical turbulence in this closed flow is partly
governed by the dissipative scales and (ii) the normal and the superfluid
component at these temperatures (1.6K) are locked down to the dissipative
length scale.Comment: 5 pages, 5 figure
Lagrangian Diffusion Properties of a Free Shear Turbulent Jet
A Lagrangian experimental study of an axisymmetric turbulent water jet is performed to investigate the highly anisotropic and inhomogeneous flow field. Measurements are conducted within a Lagrangian exploration module, an icosahedron apparatus, to facilitate optical access of three cameras. Stereoscopic particle tracking velocimetry results in three-component tracks of position, velocity and acceleration of the tracer particles within the vertically oriented jet with a Taylor-based Reynolds number Reλ≃230. Analysis is performed at seven locations from 15 diameters up to 45 diameters downstream. Eulerian analysis is first carried out to obtain critical parameters of the jet and relevant scales, namely the Kolmogorov and large (integral) scales as well as the energy dissipation rate. Lagrangian statistical analysis is then performed on velocity components stationarised following methods inspired by Batchelor (J. Fluid Mech., vol. 3, 1957, pp. 67–80), which aim to extend stationary Lagrangian theory of turbulent diffusion by Taylor to the case of self-similar flows. The evolution of typical Lagrangian scaling parameters as a function of the developing jet is explored and results show validation of the proposed stationarisation. The universal scaling constant C0 (for the Lagrangian second-order structure function), as well as Eulerian and Lagrangian integral time scales, are discussed in this context. Constant C0 is found to converge to a constant value (of the order of C0=3) within 30 diameters downstream of the nozzle. Finally, the occurrence of finite particle size effects is investigated through consideration of acceleration-dependent quantities
Fully developed turbulence and the multifractal conjecture
We review the Parisi-Frisch MultiFractal formalism for
Navier--Stokes turbulence with particular emphasis on the issue of
statistical fluctuations of the dissipative scale. We do it for both Eulerian
and Lagrangian Turbulence. We also show new results concerning the application
of the formalism to the case of Shell Models for turbulence. The latter case
will allow us to discuss the issue of Reynolds number dependence and the role
played by vorticity and vortex filaments in real turbulent flows.Comment: Special Issue dedicated to E. Brezin and G. Paris
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