30,909 research outputs found
Scale distributions and fractal dimensions in turbulence
A new geometric framework connecting scale distributions to coverage statistics is employed to analyze level sets arising in turbulence as well as in other phenomena. A 1D formalism is described and applied to Poisson, lognormal, and power-law statistics. A d-dimensional generalization is also presented. Level sets of 2D spatial measurements of jet-fluid concentration in turbulent jets are analyzed to compute scale distributions and fractal dimensions. Lognormal statistics are used to model the level sets at inner scales. The results are in accord with data from other turbulent flows
Optical Random Riemann Waves in Integrable Turbulence
We examine integrable turbulence (IT) in the framework of the defocusing
cubic one-dimensional nonlinear Schr\"{o}dinger equation. This is done
theoretically and experimentally, by realizing an optical fiber experiment in
which the defocusing Kerr nonlinearity strongly dominates linear dispersive
effects. Using a dispersive-hydrodynamic approach, we show that the development
of IT can be divided into two distinct stages, the initial, pre-breaking stage
being described by a system of interacting random Riemann waves. We explain the
low-tailed statistics of the wave intensity in IT and show that the Riemann
invariants of the asymptotic nonlinear geometric optics system represent the
observable quantities that provide new insight into statistical features of the
initial stage of the IT development by exhibiting stationary probability
density functions
Extreme-value statistics from Lagrangian convex hull analysis for homogeneous turbulent Boussinesq convection and MHD convection
We investigate the utility of the convex hull of many Lagrangian tracers to
analyze transport properties of turbulent flows with different anisotropy. In
direct numerical simulations of statistically homogeneous and stationary
Navier-Stokes turbulence, neutral fluid Boussinesq convection, and MHD
Boussinesq convection a comparison with Lagrangian pair dispersion shows that
convex hull statistics capture the asymptotic dispersive behavior of a large
group of passive tracer particles. Moreover, convex hull analysis provides
additional information on the sub-ensemble of tracers that on average disperse
most efficiently in the form of extreme value statistics and flow anisotropy
via the geometric properties of the convex hulls. We use the convex hull
surface geometry to examine the anisotropy that occurs in turbulent convection.
Applying extreme value theory, we show that the maximal square extensions of
convex hull vertices are well described by a classic extreme value
distribution, the Gumbel distribution. During turbulent convection,
intermittent convective plumes grow and accelerate the dispersion of Lagrangian
tracers. Convex hull analysis yields information that supplements standard
Lagrangian analysis of coherent turbulent structures and their influence on the
global statistics of the flow.Comment: 18 pages, 10 figures, preprin
Evolution of geometric structures in intense turbulence
We report measurements of the evolution of lines, planes, and volumes in an
intensely turbulent laboratory flow using high-speed particle tracking. We find
that the classical characteristic time scale of an eddy at the initial scale of
the object considered is the natural time scale for the subsequent evolution.
The initial separation may only be neglected if this time scale is much smaller
than the largest turbulence time scale, implying extremely high turbulence
levels.Comment: 10 pages, 6 figures, added more detail
Multi-scale geometric analysis of Lagrangian structures in isotropic turbulence
We report the multi-scale geometric analysis of Lagrangian structures in forced isotropic turbulence and also with a frozen turbulent field. A particle backward-tracking method, which is stable and topology preserving, was applied to obtain the Lagrangian scalar field φ governed by the pure advection equation in the Eulerian form ∂_tφ + u · ∇φ = 0. The temporal evolution of Lagrangian structures was first obtained by extracting iso-surfaces of φ with resolution 1024^3 at different times, from t = 0 to t = T_e, where T_e is the eddy turnover time. The surface area growth rate of the Lagrangian structure was quantified and the formation of stretched and rolled-up structures was observed in straining regions and stretched vortex tubes, respectively. The multi-scale geometric analysis of Bermejo-Moreno & Pullin (J. Fluid Mech., vol. 603, 2008, p. 101) has been applied to the evolution of φ to extract structures at different length scales and to characterize their non-local geometry in a space of reduced geometrical parameters. In this multi-scale sense, we observe, for the evolving turbulent velocity field, an evolutionary breakdown of initially large-scale Lagrangian structures that first distort and then either themselves are broken down or stretched laterally into sheets. Moreover, after a finite time, this progression appears to be insensible to the form of the initially smooth Lagrangian field. In comparison with the statistical geometry of instantaneous passive scalar and enstrophy fields in turbulence obtained by Bermejo-Moreno & Pullin (2008) and Bermejo-Moreno et al. (J. Fluid Mech., vol. 620, 2009, p. 121), Lagrangian structures tend to exhibit more prevalent sheet-like shapes at intermediate and small scales. For the frozen flow, the Lagrangian field appears to be attracted onto a stream-surface field and it develops less complex multi-scale geometry than found for the turbulent velocity field. In the latter case, there appears to be a tendency for the Lagrangian field to move towards a vortex-surface field of the evolving turbulent flow but this is mitigated by cumulative viscous effects
Structures in magnetohydrodynamic turbulence: detection and scaling
We present a systematic analysis of statistical properties of turbulent
current and vorticity structures at a given time using cluster analysis. The
data stems from numerical simulations of decaying three-dimensional (3D)
magnetohydrodynamic turbulence in the absence of an imposed uniform magnetic
field; the magnetic Prandtl number is taken equal to unity, and we use a
periodic box with grids of up to 1536^3 points, and with Taylor Reynolds
numbers up to 1100. The initial conditions are either an X-point configuration
embedded in 3D, the so-called Orszag-Tang vortex, or an
Arn'old-Beltrami-Childress configuration with a fully helical velocity and
magnetic field. In each case two snapshots are analyzed, separated by one
turn-over time, starting just after the peak of dissipation. We show that the
algorithm is able to select a large number of structures (in excess of 8,000)
for each snapshot and that the statistical properties of these clusters are
remarkably similar for the two snapshots as well as for the two flows under
study in terms of scaling laws for the cluster characteristics, with the
structures in the vorticity and in the current behaving in the same way. We
also study the effect of Reynolds number on cluster statistics, and we finally
analyze the properties of these clusters in terms of their velocity-magnetic
field correlation. Self-organized criticality features have been identified in
the dissipative range of scales. A different scaling arises in the inertial
range, which cannot be identified for the moment with a known self-organized
criticality class consistent with MHD. We suggest that this range can be
governed by turbulence dynamics as opposed to criticality, and propose an
interpretation of intermittency in terms of propagation of local instabilities.Comment: 17 pages, 9 figures, 5 table
Geometric study of Lagrangian and Eulerian structures in turbulent channel flow
We report the detailed multi-scale and multi-directional geometric study of both evolving Lagrangian and instantaneous Eulerian structures in turbulent channel flow at low and moderate Reynolds numbers. The Lagrangian structures (material surfaces) are obtained by tracking the Lagrangian scalar field, and Eulerian structures are extracted from the swirling strength field at a time instant. The multi-scale and multi-directional geometric analysis, based on the mirror-extended curvelet transform, is developed to quantify the geometry, including the averaged inclination and sweep angles, of both structures at up to eight scales ranging from the half-height δ of the channel to several viscous length scales δ_ν. Here, the inclination angle is on the plane of the streamwise and wall-normal directions, and the sweep angle is on the plane of streamwise and spanwise directions. The results show that coherent quasi-streamwise structures in the near-wall region are composed of inclined objects with averaged inclination angle 35°–45°, averaged sweep angle 30°–40° and characteristic scale 20δ_ν, and 'curved legs' with averaged inclination angle 20°–30°, averaged sweep angle 15°–30° and length scale 5δ_ν–10δ_ν. The temporal evolution of Lagrangian structures shows increasing inclination and sweep angles with time, which may correspond to the lifting process of near-wall quasi-streamwise vortices. The large-scale structures that appear to be composed of a number of individual small-scale objects are detected using cross-correlations between Eulerian structures with large and small scales. These packets are located at the near-wall region with the typical height 0.25δ and may extend over 10δ in the streamwise direction in moderate-Reynolds-number, long channel flows. In addition, the effects of the Reynolds number and comparisons between Lagrangian and Eulerian structures are discussed
Path lengths in turbulence
By tracking tracer particles at high speeds and for long times, we study the
geometric statistics of Lagrangian trajectories in an intensely turbulent
laboratory flow. In particular, we consider the distinction between the
displacement of particles from their initial positions and the total distance
they travel. The difference of these two quantities shows power-law scaling in
the inertial range. By comparing them with simulations of a chaotic but
non-turbulent flow and a Lagrangian Stochastic model, we suggest that our
results are a signature of turbulence.Comment: accepted for publication in Journal of Statistical Physic
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