Fourier spectral and pseudospectral methods are used in the numerical modeling of processes that produce ionospheric irregularities; namely the evolution of the Kelvin-Helmholtz instability (KHI) is studied. The simulation model consists of two-dimensional, electrostatic, nonlinear, and time dependent fluid equations that describe the KHI evolution. Spectral and pseudospectral methods are used to solve the spatial dependence of these self-consistent equations. They are chosen over the widely used finite difference technique since spectral methods are straightforward to implement on nonlinear equations. Time integration is accomplished using a combination of predictor-corrector, leapfrog, and leapfrog-trapezoidal methods. A FO RTRAN program is developed to implement the simulation model. All calculations are performed in the Fourier domain.

The process of how the KHI evolves is discussed in theory, and observed in simulation. The simulation data is displayed and studied by utilizing various diagnostics and visualization techniques. These include two dimensional images and three dimensional surface plots of the electron density and electric potential. The transverse velocity is also monitored, as well as the density power spectrum. The simulation is performed for different velocity shear scale lengths to observe how varying the shear length effects the development of the KHI. The simulation results agree with and expand upon similar results obtained using finite difference methods. The results also shed light on some recent experimental observations of ionospheric irregularities thought to be produced by the KHI.