This thesis is aimed at extending the spherical barotropic contour-advective semi-Lagrangian (CASL) Algorithm, written in 1996 by David Dritschel and Maarten Ambaum, to more complex test cases within the shallow-water context. This is an integral part for development of any numerical model and the accuracy obtained depends on many factors, including knowledge of the initial state of the atmosphere or ocean, the numerical methods applied, and the resolutions used. The work undertaken throughout this thesis is highly varied and produces important steps towards creating a versatile suite of programs to model all types of flow, quickly and accurately. This, as will be explained in later chapters, impacts both public safety and the world economy, since much depends on accurate medium range forecasting. There shall be an investigation of a series of tests which demonstrate certain aspects of a dynamical system and its progression into more unstable situations - including the generation and feedback of freely propagating inertia-gravity waves (hereafter “gravity waves"), which transmit throughout the system. The implications for increasing forecast accuracy will be discussed. Within this thesis two main CASL algorithms are outlined and tested, with the accuracy of the results compared with previous results. In addition, other dynamical fields (besides geopotential height and potential vorticity) are analysed in order to assess how well the models deal with gravity waves. We shall see that such waves are sensitive to the presence, or not, of sharp potential vorticity gradients, as well as to numerical parameter settings. In particular, large time-steps (convenient for semi-Lagrangian schemes) may not only seriously affect gravity waves, but may also have an adverse impact on the primary fields of height and velocity. These problems are exacerbated by a poor resolution of potential vorticity gradients, which we shall attempt to improve.

Newly released Imaging Ultraviolet Spectrograph/Mars Atmosphere and Volatile EvolutioN (IUVS/MAVEN) measurements of CO2 density in the Martian thermosphere have been used for comparison with the predictions of the Max Planck Institute Martian General Circulation Model (MPI-MGCM). The simulations reproduced (within one standard deviation) the available zonal mean density and derived temperature above 130 km. The MGCM replicated the observed dominant zonal wave number 3 nonmigrating tide and demonstrated that it represents a nonmoving imprint of the topography in the thermosphere. The comparison shows a great dependence of the simulated density and temperature to the prescribed solar flux, atomic oxygen abundances and gravity wave effects, with the former two being especially important in the thermosphere above 130 km and the latter playing a significant role both in the mesosphere and thermosphere.

Temperature measurements from the HIRDLS instrument on NASA's Aura satellite are analysed for the purposes of detecting and studying internal gravity waves in the terrestrial stratosphere. A detailed description of the methodology used to obtain these data is given, including details of the instrument correction processes used to compensate for errors introduced by a blockage in the instrument optics. A short precis of the relevant theoretical considerations related to atmospheric gravity waves is then outlined. The thesis then discusses the use of the Stockwell (time-frequency) Transform for the detection of gravity waves in HIRDLS data, together with a detailed analysis of the limitations of this method, and the results obtained from this analysis are analysed by comparison to other instruments and climatology. It is concluded that the Stockwell Transform is an appropriate method for the analysis of the HIRDLS dataset, and that the results obtained are robust. We apply these results to analyse stratospheric gravity wave activity during the 2005/06 Arctic sudden stratospheric warming. By comparing the magnitude and form of the gravity wave results to local wind data obtained from ECMWF operational analyses, we conclude that a heavily deformed stratopause observed during this period by other instruments was most probably due to wind-based filtering of the gravity wave spectrum during this period.

by Lai Chi Wai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves [104]-107). / Text in English; abstract also in Chinese. / by Lai Chi Wai. / Abstract --- p.i / Acknowledgment --- p.iv / List of Figures --- p.xi / List of Tables --- p.xii / Chapter 1 --- Introduction to Numerical Relativity --- p.1 / Chapter 1.1 --- The need for numerical approach --- p.2 / Chapter 1.2 --- A brief history of numerical relativity --- p.3 / Chapter 1.3 --- What this thesis concern --- p.4 / Chapter 2 --- Mathematical Formulation --- p.6 / Chapter 2.1 --- The initial value problem --- p.6 / Chapter 2.2 --- The space-plus-time (3+1) formalism --- p.8 / Chapter 3 --- Methods in Numerical Relativity --- p.17 / Chapter 3.1 --- General numerical methods --- p.17 / Chapter 3.2 --- Consistency and stability --- p.18 / Chapter 3.3 --- Difficulties and limitations --- p.20 / Chapter 3.4 --- Strategies specific to numerical relativity --- p.21 / Chapter 3.5 --- Boundary conditions --- p.27 / Chapter 4 --- Detweiler's Scheme --- p.29 / Chapter 4.1 --- Constrainted evolution in numerical relativity --- p.29 / Chapter 4.2 --- Detweiler's Scheme --- p.31 / Chapter 5 --- Constraint Enforcement in Plane Waves --- p.36 / Chapter 5.1 --- General solution for a linearized plane wave --- p.36 / Chapter 5.2 --- Code test --- p.40 / Chapter 5.3 --- Comparison of results with and without Detweiler's scheme --- p.41 / Chapter 5.4 --- Stability of evolution --- p.46 / Chapter 5.5 --- Comparison of Detweiler's scheme and simple diffusion method --- p.50 / Chapter 5.6 --- Two parameter extension of Detweiler's scheme --- p.55 / Chapter 5.7 --- Long time behavior --- p.59 / Chapter 5.8 --- Comparison of Hamiltonian and momentum constraint --- p.63 / Chapter 5.9 --- Indicator of Detweiler's scheme --- p.67 / Chapter 5.10 --- The maximal slicing condition --- p.70 / Chapter 5.11 --- The leaking problem --- p.73 / Chapter 5.12 --- The near-linear plane waves --- p.75 / Chapter 6 --- Constraint Enforcement in MTW Waves --- p.83 / Chapter 6.1 --- MTW waves --- p.83 / Chapter 6.2 --- Linear regime --- p.85 / Chapter 6.3 --- Comparison of results with and without Detweiler's scheme --- p.85 / Chapter 6.4 --- The indicator --- p.90 / Chapter 6.5 --- A comparison of simple diffusion method and Detweiler's scheme with a large amplitude wave --- p.92 / Chapter 7 --- Summary and Conclusion --- p.97 / Chapter A --- The Numerical Scheme of the Code --- p.98 / Chapter B --- Convergence Test --- p.100 / Chapter B.1 --- Plane wave --- p.100 / Chapter B.2 --- MTW wave --- p.102 / Bibliography --- p.104

This thesis studies the scattering properties of different types of imperfections in large Arctic and Antarctic ice sheets. Such irregularities include cracks, pressure ridges and both open and refrozen leads. The scattering by a transition region between sea ice and a very thick ice shelf, for example as is found in the Ross Sea in Antarctica, is also treated. Methods of solution are based on applications of Green�s theorem to the appropriate situation, which leads to either a single integral equation or a pair of coupled integral equations to be solved at the boundary between the ice and the sea water. Those equations over a finite interval are solved using numerical quadrature, while those over semi-infinite ranges are solved using the Wiener-Hopf method. Results calculated using different techniques are able to be checked against each other, giving us great confidence in their accuracy. In particular, the scattering by three ice sheets of different thicknesses is confirmed analytically by mode-matching coupled with the residue calculus technique. The scattering by the single irregularities is investigated partly for its own sake, and partly with the aim of using it to treat the scattering when large numbers of features are included in a single ice sheet. The principal objective of doing this is to observe the change in the general amounts of reflection and transmission as the background ice thickness is changed. There is enough variation in our results for us to conclude that there is definite potential for using the change in an incident wave spectrum after passing through a given ice field to estimate the background ice thickness.

A three-field photometer has been employed at the University of Adelaide's Buckland Park field site to collect optical observations of the 557.7nm OI and 730nm OH airglow emissions. Data have been collected on an almost continuous basis since May 1995 through to May 2000, with observations made whenever the moon was not up. Techniques and analysis procedures have been developed which allow routine extraction of the parameters of gravity waves observed each night. A cross-spectral analysis was performed on processed data from the photometer to identify short period (less than 3 hours) wave activity on nights where the impact of clouds on the data was minimal. The resulting wave parameters are analysed for seasonal variability and used to build up a climatology of wave parameters over the 5 years of observation. No consistent seasonal variation was observed, although there was a strong eastward perference to the wave's propagation direction. Implications of this finding are discussed. A co-located MF radar has been operating in spaced antenna mode providing wind data concurrent with the optical observations for most of the acquisition period. When available the wind data allowed calculation of the intrinsic parameters for waves identified in the optical data. The seasonal variablility of these parameters was investigated. An evaluation of energy and momentum fluxes estimated using the method of Swenson et al (1998b) was carried out. Approximations made in this method were found to be inappropriate for the waves detected by the photometer, and a refined procedure was therefore developed. This gave more realistic results, although large number of physically unreasonable momentum flux measurements were reported. Possible reasons for these were explored, and the need for further investigations emphasised. The five year dataset also allowed investigation of the long-term behaviour of the airglow. Both the intensity and variance were analysed using the Lomb-Scargle method across the complete dataset to identify the dominant periods present. Following similar treatment, the MF spaced antenna winds were compared with the optical results; this utilised a complex spectrum extension to the basic Lomb algorithm. Seasonally related periodicities of two years, one year, one half of a year and one third of a year were observed in the optical data, along with a possible signature of a five and a half year period potentially linked to the eleven year solar cycle. The radar data did not have stong signatures of the one third of a year periodicity although the presence of an five and a half year periodicity could not be ruled out. Gravity wave activity, as measured by the optical intensity variance, reached a maximum during autumn with a secondary maximum occurring in spring. The annual variability of the wave spectrum detected by the photometer was also studied which showed a falloff in the wave energy at short periods (less than thirty minutes) during autumn and spring. This suggested that the enhanced wave activity at these times consisted mainly of waves with periods greater than thirty minutes. / Thesis (Ph.D.)--Department of Physics and Mathematical Physics, 2000.

Includes reprint of author's article, `HF Doppler measurements of mesospheric gravity wave momentum fluxes`, from Journal of the atmospheric sciences, vol. 40, no. 5, May 1983 Bibliography: Last 6 unnumbered leaves

Graduation date: 1991

Thesis (M. Sc.)--College of William and Mary. / Typescript (photocopy). Vita. Includes bibliographical references (leaves 96-100).

The majority of internal gravity wave energy in the ocean is produced by tidal flow over bottom topography. Regions of critical topography, where the topographic slope is equal to the slope of the internal gravity waves, is often believed to contribute most significantly to the radiated internal gravity wave power. Here, we present 2D computational studies of internal gravity wave generation by tidal flow over several types of topographic ridges. We vary the criticality parameter [epsilon], which is the ratio of the topographic slope to the wave beam slope, by independently changing the tidal frequency, stratification and topographic slope, which allows to study subcritical ([epsilon] < 1), critical ([epsilon] = 1), and supercritical ([epsilon] > 1) topography. This parameter variation allows us to explore a large range of criticality parameter, namely 0.1< [epsilon] < 10, as well as beam slope S, 0.05< S < 10. As in prior work [Zhang et al., Phys. Rev. Lett. (2008)], we observe resonant boundary currents for [epsilon] = 1. However, we find that the normalized radiated power monotonically increases with internal wave beam slope. We show that an appropriate normalization condition leads to a universal scaling of the radiated power that is proportional to the inverse of the beam slope 1/S and the tidal intensity I[subscript tide], except near [epsilon] = 1 where the behavior undergoes a transition. We characterize this transition and the overall scaling with the criticality parameter f([epsilon]), which is weak compared to the scalings mentioned before and only varies by a factor of two over the entire range of criticality parameter that we explored. Our results therefore suggest that estimates of the ocean energy budget must account for the strong scaling with the local beam slope, which dominates the conversion of tidal motions to internal wave energy. Thus we argue that detailed characterization of the stratification in the ocean is more important for global ocean models than high-resolution bathymetry to determine the criticality parameter. / text