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Two problems in computational wave dynamics are considered: (i) the use of Klemp-Wilhelmson time splitting at large scales and (ii) analysis of wave-wave instabilities in nonhydrostatic and rotating mountain waves. The use of Klemp-Wilhelmson (KW) time splitting for large-scale and global modeling is assessed through a series of von Neumann accuracy and stability analyses. Two variations of the KW splitting are evaluated in particular: the original acousticmode splitting of Klemp and Wilhelmson (KW78) and a modified splitting due to Skamarock and Klemp (SK92) in which the buoyancy and vertical stratification terms are treated as fast-mode terms. The large-scale cases of interest are the problem of Rossby wave propagation on a resting background state and the classic baroclinic Eady problem. The results show that the original KW78 splitting is surprisingly inaccurate when applied to large-scale wave modes. The source of this inaccuracy is traced to the splitting of the hydrostatic balance terms between the small and large time steps. The errors in the KW78 splitting are shown to be largely absent from the SK92 scheme. Resonant wave-wave instability in rotating mountain waves is examined using a linear stability analysis based on steady-state solutions for flow over an isolated ridge. The analysis is performed over a parameter space spanned by the mountain height (Nh/U) and the Rossby number (U/fL). Steady solutions are found using a newly developed solver based on a nonlinear Newton iteration. Results from the steady solver show that the critical heights for wave overturning are smallest for the hydrostatic case and generally increase in the rotating wave regime. Results of the stability analyses show that the wave-wave instability exists at mountain heights even below the critical overturning values. The most unstable cases are found in the nonrotating regime while the range of unstable mountain heights between initial onset and critical overturning is largest for intermediate Rossby number.

Atmospheric mountain waves form in the lee of mountainous terrain under appropriate conditions of the vertical structure of wind speed and atmospheric stability. Trapped lee waves can extend hundreds of kilometers downwind from the mountain range, and they can extend tens of kilometers vertically into the stratosphere. Mountain waves are of importance in meteorology as they affect the general circulation of the atmosphere, can influence the vertical structure of wind speed and temperature fields, produce turbulence and downdrafts that can be an aviation hazard, and affect the vertical transport of aerosols and trace gasses, and ozone concentration. Sailplane pilots make extensive use of mountain lee waves as a source of energy with which to climb. There are many sailplane wave flights conducted every year throughout the world and they frequently cover large distances and reach high altitudes. Modern sailplanes frequently carry flight recorders that record their position at regular intervals during the flight. There is therefore potential to use this recorded data to determine the 3D wind velocity at positions on the sailplane flight path. This would provide an additional source of information on mountain waves to supplement other measurement techniques that might be useful for studies on mountain waves. The recorded data are limited however, and determination of wind velocities is not straightforward. This thesis is concerned with the development and application of techniques to determine the vector wind field in atmospheric mountain waves using the limited flight data collected during sailplane flights. A detailed study is made of the characteristics, uniqueness, and sensitivity to errors in the data, of the problem of estimating the wind velocities from limited flight data consisting of ground velocities, possibly supplemented by air speed or heading data. A heuristic algorithm is developed for estimating 3D wind velocities in mountain waves from ground velocity and air speed data, and the algorithm is applied to flight data collected during “Perlan Project” flights. The problem is then posed as a statistical estimation problem and maximum likelihood and maximum a posteriori estimators are developed for a variety of different kinds of flight data. These estimators are tested on simulated flight data and data from Perlan Project flights.

Look up! Travelling over your head in the air are waves. They are present all the time in the atmosphere all over the Earth. Now imagine throwing a small rock in a pond and watching the ripples spread out around it. The same thing happens in the atmosphere except the rock is a thunderstorm, the wind blowing over a mountain, or another disturbance. As the wave (known as a gravity wave) travels upwards the thinning air allows the wave to grow larger and larger. Eventually the gravity wave gets too large – and like waves on the beach – it crashes causing whitewater or turbulence. If you are in the shallow water when the ocean wave crashes or breaks, you would feel the energy and momentum from the wave as it pushes or even knocks you over. In the atmosphere, when waves break they transfer their energy and momentum to the background wind changing its speed and even direction. This affects the circulation of the atmosphere. These atmospheric waves are not generally visible to the naked eye but by using special instruments we can observe their effects on the wind, temperature, density, and pressure of the atmosphere. This dissertation discusses the use of a specialized camera to study gravity waves as they travel through layers of the atmosphere 50 miles above the Andes Mountains and change the temperature. First, we introduce the layers of the atmosphere, the techniques used for observing these waves, and the mathematical theory and properties of these gravity waves. We then discuss the camera, its properties, and its unique feature of acquiring temperatures in the middle layer of the atmosphere. We introduce the observatory high in the Andes Mountains and why it was selected. We will look at the nightly fluctuations (or willy-nillyness) and long-term trends from August 2009 until December 2017. We compare measurements from the camera with similar measurements obtained from a satellite taken at the same altitude and measurements from the same camera when it was used at a different location, over Hawaii. Next, we measure the amount of change in the temperature and compare it to a nearby location on the other side of the Andes Mountains. Finally, we look for a specific type of gravity wave caused by wind blowing over the mountains called a mountain wave and perform statistics of those observed events over a period of six years. By understanding the changes in atmospheric properties caused by gravity waves we can learn more about their possible sources. By knowing their sources, we can better understand how much energy is being transported in the atmosphere, which in turn helps with better weather and climate models. Even now –all of this is going on over your head!

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