D. Aaron Roberts

Anisotropic three‐dimensional MHD turbulence

Direct spectral method simulation of the three-dimensional magnetohydrodynamics (MHD) equations is used to explore anisotropy that develops from initially isotropic fluctuations as a consequence of a uniform applied magnetic field. Spectral and variance anisotropies are investigated in both compressible and incompressible MHD. The nature of the spectral anisotropy is consistent with the model of Shebalin et al. [1983] in which the spectrum broadens in the perpendicular wavenumber direction, the anisotropy being greater for smaller wavenumbers. Here this effect is seen for both incompressible and polytropic compressible MHD. In contrast, the longitudinal (compressive) velocity fluctuations remain isotropic. Variance anisotropy is observed for low plasma beta compressible MHD but not for incompressible MHD. Solar wind observations are qualitatively consistent with both variance and spectral anisotropies of the type discussed here.

Magnetohydrodynamic Turbulence in the Solar Wind

Recent work in describing the solar wind as an MHD turbulent fluid has shown that the magnetic fluctuations are adequately described as time stationary and to some extent as spatially homogeneous. Spectra of the three rugged invariants of incompressible MHD are the principal quantities used to characterize the velocity and magnetic field fluctuations. Unresolved issues concerning the existence of actively developing turbulence are discussed.

Procedural shape generation for multi-dimensional data visualization

Visualization of multi-dimensional data is a challenging task. The goal is not the display of multiple data dimensions, but user comprehension of the multi-dimensional data. This paper explores several techniques for perceptually motivated procedural generation of shapes to increase the comprehension of multi-dimensional data. Our glyph-based system allows the visualization of both regular and irregular grids of volumetric data. A glyph’s location, 3D size, color, and opacity encode up to 8 attributes of scalar data per glyph. We have extended the system’s capabilities to explore shape variation as a visualization attribute. We use procedural shape generation techniques because they allow flexibility, data abstraction, and freedom from specification of detailed shapes. We have explored three procedural shape generation techniques: fractal detail generation, superquadrics, and implicit surfaces. These techniques allow from 1 to 14 additional data dimensions to be visualized using glyph shape.

Anisotropy and minimum variance directions of solar wind fluctuations in the outer heliosphere

We systematically examine Voyager 2 magnetic field and plasma data over time intervals of 1 to 12 hours in the heliospheric range of 1 to 10 AU to study the evolution of the anisotropy of solar wind fluctuations. Consistent with previous results, we find that, on average, the directions of minimum variance vectors of magnetic fluctuations are close to the mean magnetic field direction with an increasing component of the variance along the field at larger scales. In both compression regions and rarefactions at large radial distances there is more spread in the minimum variance directions about the mean field than at smaller radial distances. The power in smaller-scale fluctuations in the magnetic field components perpendicular to the local mean field B0 is in the ratio of about 5∶1 near 1 AU (compared to the power in fluctuations parallel to the field) at the scale of 1 hour but decreases to about 3∶1 farther out. We find no evidence for selective enhancement of out-of-the-ecliptic components of fluctuations as predicted by a possible geometrical coupling between refracting Alfven waves and compressive modes. In contrast to results for field fluctuations, our analysis of fluctuations in the velocity shows that the minimum variance direction systematically remains more radially oriented and becomes increasingly less oriented along B0 with increasing heliocentric distance. The velocity fluctuations are also generally more isotropic than the magnetic fluctuations at all distances examined. Our observations cannot be explained by a superposed wave picture, and thus are consistent with the view that nonlinear turbulent evolution is responsible for the anisotropy in the fluctuations.

Is there a strange attractor in the magnetosphere

This paper reviews recent attempts to determine if some aspects of magnetospheric dynamics, and in particular substorms as measured by AE and AL geomagnetic indices, can be represented by a low-dimensional dynamical system. If true, this result would imply that a small set of ordinary differential equations could describe important aspects of substorm dynamics, greatly simplifying modeling and prediction efforts and providing significant input to more detailed modeling. The “embedding” and “correlation dimension” methods used to investigate the dimensionality of a physical process from a single time series are considered in detail with an emphasis on what can go wrong and what can be done about it. Two main conclusions of this work, which includes some new results on the particular case of AL, are (1) that a low-dimensional and probably strange attractor does exist in magnetospheric dynamics, and (2) that there is no reliable substitute for using large numbers of data points in performing analyses leading to this conclusion.

Using shape to visualize multivariate data

This paper describes our recent findings in the area of using glyph shape to display one or two data dimensions in the visualization of 3D scalar and vector fields In our glyph-based visualization system, each glyph represents a data point in 3D space Visual attributes such as size, orientation, color and transparency can be mapped to data dimensions in the 3D space We are exploring the use of glyph shape as a display dimension, using superquadric superellipses as a means of supplying a parameterizable shape A basic factor in effectively using shape for quantitative visualization is determining how many (and which) superellipse shapes people can distinguish Since the superquadric shapes parameter set is not perceptually linear, we conducted a user study to which shapes people can generally distinguish The findings show that with large superellipses, about 22 separate shapes can be distinguished on average These results provide the foundation for exploring how effective superellipses may be in quantitative shape visualization

Interactive volumetric information visualization for document corpus management

This paper describes aminimally immersive three-dimensional volumetric interactive information visualization system for management and analysis of document corpora. The system, SFA, uses glyph-based volume rendering, enabling more complex data relationships and information attributes to be visualized than traditional 2D and surface-based visualization systems. Two-handed interaction using three-space magnetic trackers and stereoscopic viewing are combined to produce aminimally immersive interactive system that enhances the user’s three-dimensional perception of the information space. This new system capitalizes on the human visual system’s pre-attentive learning capabilities to quickly analyze the displayed information. SFA is integrated with adocument management and information retrieval engine named Telltale. Together, these systems integrate visualization and document analysis technologies to solve the problem of analyzing large document corpora. We describe the usefulness of this system for the analysis and visualization of document similarity within acorpus of textual documents, and present an example exploring authorship of ancient Biblical texts.

A kinematic analysis of the role of velocity shear in expanding plasmas

We present a kinematic analysis of the effects on waves of the shear due to variations in radial flow and field-aligned propagation speeds in an expanding medium. We show that although the expansion limits the extent to which wave vectors transverse to the shear flow are produced, shear can be very effective at turning wave vectors and producing off-radial fluctuations. Any initial wave vector spectrum will become spread in wave vector space with no change in spectral index. For typical spectra of the sheared radial speeds, the small-scale variability in the speed is more important than the large-scale in the sense of effectively turning the wave vectors. Radial spectra will be unchanged by stream or microstream shear, and although field-aligned Alfven speed changes will produce some observable effects, nonlinear processes are still needed to fully explain observations. This work suggests a model for near-Sun solar wind turbulence in which modes are “driven” nonlocally at all scales rather than the Kolmogoroff model, in which only large-scale driving is important; this is consistent with well-developed turbulence spectra in highly structured regions farther out in the wind.

Interactive lens visualization techniques

The paper describes new techniques for minimally immersive visualization of 3D scalar and vector fields, and visualization of document corpora. In our glyph based visualization system, the user interacts with the 3D volume of glyphs using a pair of button-enhanced 3D position and orientation trackers. The user may also examine the volume using an interactive lens, which is a rectangle that slices through the 3D volume and displays scalar information on its surface. A lens allows the display of scalar data in the 3D volume using a contour diagram, and a texture based volume rendering.

An evolving MHD vortex street model for quasi‐periodic solar wind fluctuations

We use magnetohydrodynamic (MHD) simulation to provide a dynamical basis for the “vortex street” model of the quasi-periodic meridional flow observed by Voyager 2 in the outer heliosphere. Various observations suggest that near the current sheet at solar minimum one can expect to find a vorticity distribution of two opposite shear layers with an antisymmetric staggered vorticity pattern due to structured high-speed wind surrounding low-speed equatorial flow. We show that this flow pattern leads to the formation of a highly stable vortex street through the nonlinear interaction of the two shear layers. Spatial profiles of various simulated parameters (velocity, density, meridional flow angle and the location of magnetic sector boundaries) and their relative locations in the quasi-steady vortex street are generally in good agreement with the observations. A strong, flow-aligned magnetic field, such as would occur in the inner heliosphere, inhibits the development of the street which would then be masked by the background interplanetary turbulence. The flow produced by the street induces a (relatively small) transport of plasma and magnetic flux as a result of the meridional flow away from the ecliptic region.