The Earth's atmosphere is described theoretically as a "fluid".  Atmospheric gravity waves (GWs) are linear pertubations in this fluid.  GWs are not static, but propagate vertically and horizontally at the same time as coherent waves.  In this project, we examined the GWs propagating in the upper Earth's atmosphere (called the "thermosphere").  This region of the Earth's atmosphere is located 100-600 km (or 60-360 miles) above the Earth's surface.  The thermosphere consists of neutral fluid molecules (meaning that each molecule has a complete set of electron(s)).  Overlapping the thermosphere is the ionosphere, which consists of ionized molecules (meaning that each molecule is missing at least one electron).  These molecules are ionized by high-energy particles from the Sun.  The neutral molecules in the thermosphere consist mainly of oxygen, hydrogen, helium and nitrogen. Although double nitrogen is the dominant neutral molecule in the lower atmosphere, single oxygen is the dominant neutral molecule in the thermosphere at 200-500 km (or 120-300 miles) above the Earth's surface.  Although the neutral molecules in the thermosphere are generally difficult to observe, the ions and electrons can more-easily be observed.  Observatories such as Poker Flat ISR (PFISR) routinely observe ions and electrons.  However, although the ions are relatively easy to observe at heights of 100-400 km (or 60-240 miles), they constitute less than a few percent of the total mass in that region.  Thus, it is important to quantify how the neutral and ionized molecules interact with each other in order to relate the movements and properties of the waves in the ionized fluid with the movements and properties of the waves in the neutral fluid.

When GWs propagate in the thermosphere, they push and pull the ions along the Earth's magnetic field via collisions between the neutral and ionized molecules.  For this project, we derived analytic expressions to determine the ion velocity and electron density oscillations created by GWs.  These expressions are valid where single oxygen dominates (above 200 km (or 120 mile) height).  These perturbations in the ions "travel" with the GW, although they cannot propagate on their own, and are called travelling ionospheric disturbances (TIDs).  These ion and electron oscillations occur in time and space.

We also derived new solutions for the GWs and acoustic (sound) waves excited by generalized heatings in the Earth's atmosphere.  These solutions were derived using techniques developed by the French mathmeticians Joseph Fourier and Pierre-Simon Laplace.  These solutions can be used to determine the GWs excited by heatings from the aurora and other geomagnetic processes that occur above PFISR.  These GWs make up a spectrum of waves having different wavelengths and frequencies.

For this project, we also calculated the GWs excited by ocean surface waves, propagated these waves into the middle thermosphere (250 km (or 150 miles) height) using "ray tracing" and a unique new "sprinkling" method for the GW spectra, and allowed these GWs to dissipate from molecular viscosity.  Molecular viscosity acts like honey or molasses in damping wave motions, and is caused by interactions or collisions between the neutral molecules.  Because the thermosphere is characterized by rapidly increasing viscosity with height, all GWs are eventually dissipated from viscosity.  We found that all of the excited GWs have the same horizontal wavelength as that of the ocean surface wave, and travel in the same direction as the ocean surface wave.  Additionally, most of the GWs are excited with horizontal (phase) speeds equal to that of the ocean surface wave.  However, some of the excited GWs have horizontal speeds that are much faster th...

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