On the non-local geometry of turbulence

A multi-scale methodology for the study of the non-local geometry of eddy structures in turbulence is developed. Starting from a given three-dimensional field, this consists of three main steps: extraction, characterization and classification of structures. The extraction step is done in two stages. First, a multi-scale decomposition based on the curvelet transform is applied to the full three-dimensional field, resulting in a finite set of component three-dimensional fields, one per scale. Second, by iso-contouring each component field at one or more iso-contour levels, a set of closed iso-surfaces is obtained that represents the structures at that scale. The characterization stage is based on the joint probability density function (p.d.f.), in terms of area coverage on each individual iso-surface, of two differential-geometry properties, the shape index and curvedness, plus the stretching parameter, a dimensionless global invariant of the surface. Taken together, this defines the geometrical signature of the iso-surface. The classification step is based on the construction of a finite set of parameters, obtained from algebraic functions of moments of the joint p.d.f. of each structure, that specify its location as a point in a multi-dimensional ‘feature space’. At each scale the set of points in feature space represents all structures at that scale, for the specified iso-contour value. This then allows the application, to the set, of clustering techniques that search for groups of structures with a common geometry. Results are presented of a first application of this technique to a passive scalar field obtained from 5123 direct numerical simulation of scalar mixing by forced, isotropic turbulence (Reλ = 265). These show transition, with decreasing scale, from blob-like structures in the larger scales to blob- and tube-like structures with small or moderate stretching in the inertial range of scales, and then toward tube and, predominantly, sheet-like structures with high level of stretching in the dissipation range of scales. Implications of these results for the dynamical behaviour of passive scalar stirring and mixing by turbulence are discussed

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

Geometry of enstrophy and dissipation, grid resolution effects and proximity issues in turbulence

We perform a multi-scale non-local geometrical analysis of the structures extracted from the enstrophy and kinetic energy dissipation-rate, instantaneous fields of a numerical database of incompressible homogeneous isotropic turbulence decaying in time obtained by DNS in a periodic box. Three different resolutions are considered: 256^3, 512^3 and 1024^3 grid points, with k_(max)η(overbar) approximately 1, 2 and 4, respectively, the same initial conditions and Re_λ ≈ 77. This allows a comparison of the geometry of the structures obtained for different resolutions. For the highest resolution, structures of enstrophy and dissipation evolve in a continuous distribution from blob-like and moderately stretched tube-like shapes at the large scales to highly stretched sheet-like structures at the small scales. The intermediate scales show a predominance of tube-like structures for both fields, much more pronounced for the enstrophy field. The dissipation field shows a tendency towards structures with lower curvedness than those of the enstrophy, for intermediate and small scales. The 256^3 grid resolution case (k_(max)η(overbar) ≈ 1) was unable to detect the predominance of highly stretched sheet-like structures at the smaller scales in both fields. The same non-local methodology for the study of the geometry of structures, but without the multi-scale decomposition, is applied to two scalar fields used by existing local criteria for the eduction of tube- and sheet-like structures in turbulence, Q and [A_ij]_+, respectively, obtained from invariants of the velocity-gradient tensor and alike in the 1024^3 case. This adds the non-local geometrical characterization and classification to those local criteria, assessing their validity in educing particular geometries. Finally, we introduce a new methodology for the study of proximity issues among structures of different fields, based on geometrical considerations and non-local analysis, by taking into account the spatial extent of the structures. We apply it to the four fields previously studied. Tube-like structures of Q are predominantly surrounded by sheet-like structures of [A_ij]_+, which appear at closer distances. For the enstrophy, tube-like structures at an intermediate scale are primarily surrounded by sheets of smaller scales of the enstrophy and structures of dissipation at the same and smaller scales. A secondary contribution results from tubes of enstrophy at smaller scales appearing at farther distances. Different configurations of composite structures are presented

VIOLA - A multi-purpose and web-based visualization tool for neuronal-network simulation output

Neuronal network models and corresponding computer simulations are invaluable tools to aid the interpretation of the relationship between neuron properties, connectivity and measured activity in cortical tissue. Spatiotemporal patterns of activity propagating across the cortical surface as observed experimentally can for example be described by neuronal network models with layered geometry and distance-dependent connectivity. The interpretation of the resulting stream of multi-modal and multi-dimensional simulation data calls for integrating interactive visualization steps into existing simulation-analysis workflows. Here, we present a set of interactive visualization concepts called views for the visual analysis of activity data in topological network models, and a corresponding reference implementation VIOLA (VIsualization Of Layer Activity). The software is a lightweight, open-source, web-based and platform-independent application combining and adapting modern interactive visualization paradigms, such as coordinated multiple views, for massively parallel neurophysiological data. For a use-case demonstration we consider spiking activity data of a two-population, layered point-neuron network model subject to a spatially confined excitation originating from an external population. With the multiple coordinated views, an explorative and qualitative assessment of the spatiotemporal features of neuronal activity can be performed upfront of a detailed quantitative data analysis of specific aspects of the data. Furthermore, ongoing efforts including the European Human Brain Project aim at providing online user portals for integrated model development, simulation, analysis and provenance tracking, wherein interactive visual analysis tools are one component. Browser-compatible, web-technology based solutions are therefore required. Within this scope, with VIOLA we provide a first prototype.Comment: 38 pages, 10 figures, 3 table

VisIVO - Integrated Tools and Services for Large-Scale Astrophysical Visualization

VisIVO is an integrated suite of tools and services specifically designed for the Virtual Observatory. This suite constitutes a software framework for effective visual discovery in currently available (and next-generation) very large-scale astrophysical datasets. VisIVO consists of VisiVO Desktop - a stand alone application for interactive visualization on standard PCs, VisIVO Server - a grid-enabled platform for high performance visualization and VisIVO Web - a custom designed web portal supporting services based on the VisIVO Server functionality. The main characteristic of VisIVO is support for high-performance, multidimensional visualization of very large-scale astrophysical datasets. Users can obtain meaningful visualizations rapidly while preserving full and intuitive control of the relevant visualization parameters. This paper focuses on newly developed integrated tools in VisIVO Server allowing intuitive visual discovery with 3D views being created from data tables. VisIVO Server can be installed easily on any web server with a database repository. We discuss briefly aspects of our implementation of VisiVO Server on a computational grid and also outline the functionality of the services offered by VisIVO Web. Finally we conclude with a summary of our work and pointers to future developments

09251 Abstracts Collection -- Scientific Visualization

From 06-14-2009 to 06-19-2009, the Dagstuhl Seminar 09251 ``Scientific Visualization \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, over 50 international participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general

Spectral Mapping Reconstruction of Extended Sources

Three dimensional spectroscopy of extended sources is typically performed with dedicated integral field spectrographs. We describe a method of reconstructing full spectral cubes, with two spatial and one spectral dimension, from rastered spectral mapping observations employing a single slit in a traditional slit spectrograph. When the background and image characteristics are stable, as is often achieved in space, the use of traditional long slits for integral field spectroscopy can substantially reduce instrument complexity over dedicated integral field designs, without loss of mapping efficiency -- particularly compelling when a long slit mode for single unresolved source followup is separately required. We detail a custom flux-conserving cube reconstruction algorithm, discuss issues of extended source flux calibration, and describe CUBISM, a tool which implements these methods for spectral maps obtained with ther Spitzer Space Telescope's Infrared Spectrograph.Comment: 11 pages, 8 figures, accepted by PAS