Development of turbulence in physical space. (a) Formation of current sheets on the edge of the vortex. Current is normalized to . (b) Wrapping of current sheets inside the vortex and continuation of secondary instabilities. (c) Full development of turbulence. (d) Hierarchy of coherent structures as seen in close up of a region marked with a rectangle in (c). The size of each minor tick mark in Fig. 7(d) corresponds to .
(a) and (b) Omnidirectional energy (per unit mass) spectra of magnetic field and ion velocity field (Units not equated). Vertical dashed lines correspond to , , and Debye length , respectively. The magnetic spectra above show several point spectral features.
Generation of secondary tearing instabilities. (a) Plot of showing the formation of chains of tearing islands at . (b) Plot of highlighting the fact that tearing modes are formed in regions where the in-plane magnetic field is weak. Our linear tearing analysis was conducted for the two current sheets associated with these two chains of islands. Also shown are contours of vector potential . (c) Plot of showing the formation of chains of tearing islands well into the turbulent phase at and (d) corresponding plot of .
Wave excitation. (a) Plot of illustrating the launch of waves into the ambient plasma. (b) Zoomed-in region marked with a box in (a).
Wave diagnostics. (a) Frequency vs ky spectrum of magnetic fluctuations computed at the edge of the simulation away from the vortex. Superimposed on the spectrum are lines corresponding to dispersion of compressional and shear Alfven modes . (b) Compressibility diagnostic showing association of magnetosonic modes with high compressibility and shear Alfven modes with low compressibility as expected from the linear properties of these modes.
Normalized PDF of magnetic field increments, where , and is its variance. The increments are computed at spatial lag , and as is decreased beginning with large (energy containing) scales, moving through inertial range scales, and into dissipative scales, the PDFs of velocity increments are found to become increasingly non-Gaussian, acquiring “extended tails” associated with enhanced occurrence of large nearly discontinuous jumps. This phenomenon is viewed as diagnostic of intermittency or burstiness of dissipation.
is defined to be the change in the energy for each component from its initial value. (a) Time evolution of changes from their initial value of energy of the electron thermal energy, ion thermal energy, in-plane magnetic field energy, and ion flow energy. (b) Comparison of change in ion flow energy for runs that are identical except for the presence ( ) or absence ( is ) of an initial in-plane field.
Characterization of electron energization. (a) Electron distribution function in coordinates at and . Electrons are heated preferentially in the direction along the imposed magnetic field. (b) Electron energy distribution. The dashed line is drawn at times the electron thermal energy as a way to define high energy portion of the distribution function.
Dissipation in localized structures. Filamentary structure of turbulence as may be seen by spacecraft. (a) Plot of electron temperature anisotropy and a 1D cut mimicking of what a spacecraft may see in crossing such regions. (b) Density of electrons with energy in the range of where is the initial electron temperature. Energy band diagnostic consists of calculating the density of particles in each computational grid with energies in a pre-selected range of energy bands. (c) Ion temperature anisotropy.
Plot of the volume filling factor of coherent structures as measured by the volume of space that has exceeding a given threshold value on the x-axis. The x-axis is normalized to the noise level, i.e., standard deviation of in the quiet region of the simulation.
(a) Threshold plot of where values below 5 times noise level value are set to 0 (black) and those above are set to 1. (b) Plot of . (c) Overlay of the two panels, showing a close association of with intense current sheets. Bandpass filter was used to remove grid-scale noise.
3D effects. Comparison of 2D and 3D simulations of shear driven turbulence at . Intensity plot of the total current density in (a) 2D and (b) 3D. (c) Spectrum of the total magnetic energy in 2D (red) and 3D (blue), showing similar spectral index of ∼3.1. The 2D result has been re-scaled to match total magnetic energy in 3D.
Article metrics loading...
Full text loading...