Three-Dimensional Fluid Simulations of Mid-Latitude Ionospheric Processes with Hybrid Chebyshev/Fourier Pseudo-Spectral Methods

Ionospheric irregularities are small-scale plasma density structures driven by instabilities arising from combinations of plasma drifts, density gradients, and electric fields. These irregularities can cause mid-latitude GPS scintillations, characterized by amplitude and phase fluctuations that degrade communication link performance. However, the processes behind these scintillations remain poorly understood due to limited models and observations. This thesis explores the Gradient Drift Instability (GDI) and Kelvin-Helmholtz Instability (KHI) to understand their potential roles in driving mid-latitude ionospheric turbulence and irregularities.par Initial investigations involved a two-dimensional (2D) numerical model to study density irregularities in the Subauroral Polarization Streams (SAPS). This model analyzed the turbulence spectra of the GDI. Previous work identified GDI as a key mechanism for generating ionospheric irregularities in SAPS, emphasizing the role of background electric fields and velocity shear in shaping turbulence. Using a fixed background density profile and varying latitudinal velocity profiles, the model explored how velocity shear location and neutral wind direction affect turbulence spectra of the GDI and their associated power laws. Turbulence spectra for cases with no velocity profile and with different neutral wind directions are analyzed. The impact of velocity shear is studied by translating the velocity shear location relative to the density gradient. Numerical spectral analysis results are presented and compared to recent experimental observations.par A newly developed three-dimensional (3D) electrostatic fluid model extends these investigations to capture the behavior and evolution of ionospheric plasma clouds. Historically, these artificial plasma clouds have served as a case study for understanding irregularity evolution in the textit{F} region. The GDI, driven by the (mathbf{E}timesmathbf{B}) drift, was identified as the primary mechanism causing rapid structuring of these clouds, cascading energy to smaller scales transverse to the magnetic field. Nonlinear 2D and 3D simulations were conducted across three regimes: highly collisional ((approx 200 , si{km})), collisional ((approx 300 , si{km})), and inertial ((approx 450 , si{km})). The results show that structuring evolves more slowly in 3D simulations due to additional dynamics, particularly the ambipolar potential in the current closure equation, which introduces an azimuthal "twist" around the magnetic field axis. In the collisional regime, this twist disrupts flute-like perturbations ((k_{parallel} neq 0)), while in the inertial regime, the cloud rapidly diffuses, retaining flute-like perturbations ((k_{parallel} = 0)).par Building on this 3D model, altitude-dependent neutral and plasma density profiles were incorporated to better represent ionospheric parallel dynamics. This enhanced model captures ionospheric irregularities, their generation mechanisms, and their altitudinal variations. It was used to examine the dominance and interplay of GDI and KHI within SAPS across varying altitudes, advancing our understanding of mid- to high-latitude ionospheric turbulence processes.par This work was supported by NASA under Grant Number $NASAMAG162-0050$, the Kevin T. Crofton Department of Aerospace and Ocean Engineering, and the Bradley Department of Electrical Engineering at Virginia Tech.