Unsteady processes in the solar wind–magnetosphere interaction,
such as vortices developed at the magnetopause boundary by the
Kelvin–Helmholtz instability, may contribute to the process of mass, momentum
and energy transfer into the Earth's magnetosphere. The research described in
this paper validates an algorithm to automatically detect and characterize
vortices based on velocity data from simulations. The vortex identification
algorithm (VIA) systematically searches the 3-D velocity fields to
identify critical points where the magnitude of the velocity vector vanishes.
The velocity gradient tensor is computed and its invariants are used to
assess vortex structure in the flow field. We use the Community Coordinated
Modeling Center (CCMC) Runs on Request capability to create a series of model
runs initialized from the conditions observed by the Cluster mission in the
Large eddy structures or vortices can mark regions of intense flow activity
and are important in understanding physical transport processes. Coherent
vortical structures are often the most important physical mechanisms for
generating and sustaining turbulent motion. One important mechanism of vortex
generation is the Kelvin–Helmholtz instability. When the different layers of
a stratified fluid are in relative motion, the shear causes a wrinkling of
their interface, which is amplified by nonlinearities to produce vortical
motion. Such a situation exists when the solar wind passes the Earth's
magnetopause. Finding and studying these vortices is important for
understanding the Sun–Earth connection. Even in the initial stages, these
vortices can transfer momentum, energy and mass from the solar wind to the
Earth's magnetosphere (
Streamlines are mapped to show an example of the method used to
identify vortices in the data. If the norm of
Recently
Figure from Hwang et al. (2011) where vortices were found using the
BATS-R-US simulation. The region of the dawnside flank magnetopause is blown
up (
The vortices found in the second study were not linked to specific observed
vortices in satellite data. The present paper goes a step further, and it
validates the algorithm by a direct comparison of VIA-found vortices with
independently vetted vortices. Using the CCMC's Runs on Request capability,
we used the model runs initialized from the same conditions observed by the
Cluster mission in the
Taking advantage of this capability, we analyze further the properties of the
identified vortices, including speed and extent. We also analyze the velocity
changes within their motion across the magnetosheath, and we establish the
potential of our tool to characterize other transient features that have
vortical internal structures like some flux transfer events (FTEs). Section 2
describes the methodology and how the algorithm works. Section 3 describes
the data analysis of the features found and the comparison with those from
Solar wind conditions used for the MHD simulation used by
In this paper, we focus our attention on the simulation run employed by
For these points, we transform the velocity field to a coordinate system with
Properties of the vortices found with our algorithm separated into
time step, cluster size, transformed coordinate system, vortex coordinates,
vorticity vector and
We used MHD model runs available at the CCMC website, specifically the run
for 28 July 2006 used by
The white dots mark where the vortex centers were found using our
VIA and they are visualized using Mathematica software for the same
time steps as shown in Fig.
3-D representation of the vorticity vectors from the structure found
on the
For several boundary crossing observations by Cluster,
Having already noted the location of the vortices determined by
Table
Close-up view of a flux transfer event in the MHD simulation at
02:23 UTC (centered at
3-D display of the FTE shown in Fig.
Our tool also yields more information concerning the 3-D extent and duration
of the vortices. Our algorithm identified a coherent structure at the
The extension along the
We found that our tool could also identify such features of FTEs due to their
vortical structure in the simulation. Using the Space Weather Explorer
visualization tool available at the CCMC, we analyzed information about the
topology of the first vortical structure (center at
Close-up of the
To study the vortex properties in more depth, we visualized how the structure
of the vortices changed in the
With our algorithm we find that there are vortices present at the
These figures verify that our VIA is able to locate vortices created by the Kelvin–Helmholtz instability and vortical structures formed by bursty magnetic reconnection in the form of flux transfer events. This actually demonstrates that at least some FTEs have vortical velocity structures. Our tool can be used to find how common these vortical FTE structures are. Scientific modeling of the magnetosphere is of special importance since observational data are sparse and relegated to point observations. However, as numerical models increase in spatial resolution, analysis of their results becomes more difficult and time consuming, and it requires an automated search mechanism to focus on important transient features for model validation and inter-comparison. This is a great data mining tool for research purposes since it minimizes the time spent searching for such signatures, in this case on the Earth's magnetosphere.
Close-up of the
Figure
Output from our code that shows the velocity magnitude as the
background color with no vortices detected at 03:55 UTC on the
To determine whether the accelerated flows are only seen when the vortices are
present, we need to compare times where vortices are found near the boundary
with times when they are not. No vortex is visible in the diagram shown in
Fig.
Figure
These results could indicate that vortices could contribute to such localized
acceleration as they convect antisunward. By contrast,
The large data sets that are now available through magnetospheric simulations and also spacecraft missions require an automated search algorithm to focus on specific areas or features such as transients on the magnetopause boundary. It is really difficult to visually identify small-scale features in a 3-D vector field, both from the aspect of visualization and sheer data volume, without an automatic search algorithm like the one described in this paper.
We have leveraged a technique used in fluid dynamics to automatically detect vortical structure and elucidate its properties. The algorithm provides information on the 3-D properties and extent of the identified vortical structures. We have identified vortical structures not only attributed to the Kelvin–Helmholtz instability, but to flux transfer events. The magnetic topology seen in this vortical structures confirms this.
Our data demonstrate that the algorithm can identify vortical structures in
a simulation based on solar wind conditions where Kelvin–Helmholtz vortices
were found in observations by the Cluster mission for southward IMF
(
We have also demonstrated that the Kelvin–Helmholtz vortices, analyzed and
formed under southward IMF for the case shown, are associated with the
accelerated flows observed on the magnetosheath side, with speeds higher than
the solar wind speed observed at the bow shock. No such accelerated flows were
visible when no vortices were present at the boundary. These accelerated
flows can be attributed to the draping of the magnetic field lines in
conjunction with the super-Alfvénic shear occurring at the boundary due
to the Kelvin–Helmholtz vortices. Inspection shows that the
In the near future, we plan to leverage this capability to include the magnetic field topology and delve into the specific vortex characteristics to increase the science return from the data. We also want to compare the simulation results with in situ observations by different spacecraft data for algorithm validation. One promising application of our VIA is the possibility to search vortical structures in data from missions like the Magnetospheric Multiscale Mission (MMS), in which four satellites fly in a tetrahedral formation with a small separation.
Simulation results were provided by the Community
Coordinated Modeling Center at Goddard Space Flight Center through their
public Runs on Request system (
The supplement related to this article is available online at:
YMCV wrote the manuscript, helped with the algorithm development and analyzed the algorithm output data. VLK developed the algorithm, processed the simulation data, created custom visualizations for the algorithm results, and helped with the editing of the manuscript. DGS helped with the analysis and editing of the manuscript. KJH is the author of a previous analysis used in the paper. LR helped with the simulations used.
The authors declare that they have no conflict of interest.
This work was supported by the FY2015 Science Innovation Fund from NASA Headquarters. The authors would like to thank Jay Friedlander for his amazing help with the manuscript figures. The topical editor, Elias Roussos, thanks two anonymous referees for help in evaluating this paper.