Ionospheric Gravity Wave Interactions and Their Representation in Terms of Stochastic Partial Differential Equations

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Nijimbere, Victor




Phenomena in nature that involve diffusion and convection of matter and propagation
of waves, e.g., the propagation of waves in geophysical flows, can exhibit randomness
properties and thus need to be modeled by stochastic partial differential equations
(SPDEs). For example in the ionosphere, the region in the upper atmosphere where
there are high concentrations of ions and electrons, wave interactions are influenced
by electromagnetic forces that fluctuate randomly in time, and are thus modeled by

In this thesis we model interactions between atmospheric waves and the
ionosphere induced by upward propagating atmospheric gravity waves (AGWs) starting
with the equations of conservation of mass, momentum and energy, and Maxwell's
equations. Two important problems are examined: the problem in which the ionosphere is treated as a deterministic medium and the wave interactions are governed
by nonlinear partial differential equations (PDEs), and the problem in which the
ionosphere is a random medium and the governing equations are nonlinear stochastic
partial differential equation (SPDEs) driven by the Brownian motion.

In the stochastic case we make
use of numerical methods based on Wiener Chaos
expansions (WCE) which are effective methods for solving SPDEs driven by Brownian
motion. The accuracy of this method is accessed by comparing the results with the
exact analytical or semi-analytical solutions for some problems involving stochastic
evolution equations comprising the stochastic heat and stochastic advection-diffusion
equations, and the stochastic Burgers' equation. In the the deterministic case, we
derive analytical solutions for some special simplified configurations and then carry
out numerical simulations for
time-dependent nonlinear configurations.

The results of the simulations of our analytical and numerical models are compared
with the conclusions from previous studies which are mainly observations. Our results
explain several observed phenomena arising from the interactions of the atmospheric
gravity waves with the ionosphere.


Atmospheric Science
Physics - Fluid and Plasma




Carleton University

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