Abstract
We develop a threedimensional numerical model for the EF region ionosphere and study the Lagrangian dynamics for plasma flows in this region. Our interest rests on the chargeneutral interactions and the statistics associated with stochastic Lagrangian motion. In particular, we examine the organizing mixing patterns for plasma flows due to polarized gravity wave excitations in the neutral field, using Lagrangian coherent structures (LCS). LCS objectively depict the flow topology—the extracted attractors indicate generation of ionospheric density gradients, due to accumulation of plasma. Using Lagrangian measures such as the finitetime Lyapunov exponents, we locate the Lagrangian skeletons for mixing in plasma, hence where charged fronts are expected to appear. With polarized neutral wind, we find that the corresponding plasma velocity is also polarized. Moreover, the polarized velocity alone, coupled with stochastic Lagrangian motion, may give rise to polarized density fronts in plasma. Statistics of these trajectories indicate high level of nonGaussianity. This includes clear signatures of variance, skewness, and kurtosis of displacements taking polarized structures aligned with the gravity waves, and being anisotropic.
The authors are partially supported by the Grant No. AFOSR FA95501110220.
I. INTRODUCTION
II. BACKGROUND
A. Mathematical formulation and numerical details
B. Lagrangian coherent structures
III. NUMERICAL RESULTS
A. Initialization at equilibrium
B. Deterministic dynamics
C. Stochastic Lagrangian dynamics
IV. DISCUSSIONS AND CONCLUSIONS
Key Topics
 Diffusion
 39.0
 Lagrangian mechanics
 29.0
 Plasma flows
 15.0
 Liquid crystals
 14.0
 E region
 12.0
Figures
Initial profiles in dimensional units. (a) Plasma temperature. Black solid curve: ion temperature. Red dashed curve: electron temperature. (b) Ion density. (c)Normalized collision frequency. Black solid curve: ion. Red dashed curve: electron. (d) Reaction parameters. Black solid curve: production rate, coordinate at bottom of figure. Red dashed curve: recombination rate, coordinate at top of figure. Vertical axes are the same in all panels.
Initial profiles in dimensional units. (a) Plasma temperature. Black solid curve: ion temperature. Red dashed curve: electron temperature. (b) Ion density. (c)Normalized collision frequency. Black solid curve: ion. Red dashed curve: electron. (d) Reaction parameters. Black solid curve: production rate, coordinate at bottom of figure. Red dashed curve: recombination rate, coordinate at top of figure. Vertical axes are the same in all panels.
(a) Current density divergence scaled by . (b) The resulting electrostatic potential. Eight wave periods are shown. y is the vertical coordinate (altitude), and z is the meridional direction.
(a) Current density divergence scaled by . (b) The resulting electrostatic potential. Eight wave periods are shown. y is the vertical coordinate (altitude), and z is the meridional direction.
(a) Normalized density in log scale. (b) Zonal velocity. (c) Vertical velocity. (d) Meridional velocity. (e)Electrostatic potential. (b)–(e) are indimensional units. Snapshot is at t = T/4, a quarter wave period.
(a) Normalized density in log scale. (b) Zonal velocity. (c) Vertical velocity. (d) Meridional velocity. (e)Electrostatic potential. (b)–(e) are indimensional units. Snapshot is at t = T/4, a quarter wave period.
(a) Normalized density in log scale. (b) Zonal velocity. (c) Vertical velocity. (d) Meridional velocity. (e)Electrostatic potential. (b)–(e) are indimensional units. Snapshot is at t = 3 T/4, three quarters of a wave period.
(a) Normalized density in log scale. (b) Zonal velocity. (c) Vertical velocity. (d) Meridional velocity. (e)Electrostatic potential. (b)–(e) are indimensional units. Snapshot is at t = 3 T/4, three quarters of a wave period.
Trajectory comparison for initial conditions of plasma parcels released at x = 1 km, z = 19 km and y between 80 and 220 km. The dots denote the end position of trajectories after integration for a wave period. (a) Deterministic. The three red dots denote trajectories started at , and 220 km, respectively. (b) Random case 1 with diagonal diffusivity. The three red layers denote trajectories started at , and 220 km, respectively. (c) Random case 2 with field aligned diffusivity. The three red layers denote trajectories started at , and 220 km, respectively. Note that the z scale is much larger than the x scale, thus the spread is more in z as compared to in x.
Trajectory comparison for initial conditions of plasma parcels released at x = 1 km, z = 19 km and y between 80 and 220 km. The dots denote the end position of trajectories after integration for a wave period. (a) Deterministic. The three red dots denote trajectories started at , and 220 km, respectively. (b) Random case 1 with diagonal diffusivity. The three red layers denote trajectories started at , and 220 km, respectively. (c) Random case 2 with field aligned diffusivity. The three red layers denote trajectories started at , and 220 km, respectively. Note that the z scale is much larger than the x scale, thus the spread is more in z as compared to in x.
Statistics of displacements subject to diagonal diffusivity. Row a: first four moments in the xdirection. Row b: first four moments in the zdirection. Row c: first four moments in the ydirection. First column: mean displacement, in km. Second column: standard deviation, in km. Third column: skewness. Fourth column: Kurtosis.
Statistics of displacements subject to diagonal diffusivity. Row a: first four moments in the xdirection. Row b: first four moments in the zdirection. Row c: first four moments in the ydirection. First column: mean displacement, in km. Second column: standard deviation, in km. Third column: skewness. Fourth column: Kurtosis.
Statistics of displacements subject to field aligned diffusivity. Row a: first four moments in the xdirection. Row b: first four moments in the zdirection. Row c: first four moments in the ydirection. First column: mean displacement, in km. Second column: standard deviation, in km. Third column: skewness. Fourth column: Kurtosis.
Statistics of displacements subject to field aligned diffusivity. Row a: first four moments in the xdirection. Row b: first four moments in the zdirection. Row c: first four moments in the ydirection. First column: mean displacement, in km. Second column: standard deviation, in km. Third column: skewness. Fourth column: Kurtosis.
Probability density function compared to the mean trajectory. The initial condition is chosen at x = 0 km, y = 43 km, and z = 220 km, where nontrivial skewness and kurtosis are present. (a) Diagonal diffusion. (b) Field aligned diffusion. The blue solid curve is the pdf for x displacement. The black dashed curve is the pdf for z displacement, and the red dashdotted curve is the pdf for y displacement. The three crosses correspond to the mean value for x, y, and z, respectively. Their vertical coordinates are chosen so the location and the peak density are easily comparable.
Probability density function compared to the mean trajectory. The initial condition is chosen at x = 0 km, y = 43 km, and z = 220 km, where nontrivial skewness and kurtosis are present. (a) Diagonal diffusion. (b) Field aligned diffusion. The blue solid curve is the pdf for x displacement. The black dashed curve is the pdf for z displacement, and the red dashdotted curve is the pdf for y displacement. The three crosses correspond to the mean value for x, y, and z, respectively. Their vertical coordinates are chosen so the location and the peak density are easily comparable.
(a) Deterministic attractors. (b) Stochastic attractors for the diagonal diffusion case. (c) Stochastic attractors for the fieldaligned case.
(a) Deterministic attractors. (b) Stochastic attractors for the diagonal diffusion case. (c) Stochastic attractors for the fieldaligned case.
Number density of stochastic realization at end of one wave period. (a) The diagonal diffusion case. (b) The fieldaligned diffusion case.
Number density of stochastic realization at end of one wave period. (a) The diagonal diffusion case. (b) The fieldaligned diffusion case.
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