INVESTIGATIONS INTO MECHANISMS UNDERLYING EXTREME WAVE FORMATIONS AND COMPUTATIONALLY INTENSIVE SIMULATIONS

Various mechanisms have been proposed to explain extreme waves or rogue waves in an oceanic environment including directional focusing, dispersive focusing, wave-current interaction, and nonlinear modulational instability. The Benjamin-Feir instability (nonlinear modulational instability), however, is considered to be one of the primary mechanisms for rogue-wave occurrence. The nonlinear Schrodinger equation is a well-established approximate model based on the same assumptions as required for the derivation of the Benjamin-Feir theory. Solutions of the nonlinear Schrodinger equation, including new rogue-wave type solutions are presented in the author's dissertation work. The solutions are obtained by using a predictive eigenvalue map based predictor-corrector procedure developed by the author. Features of the predictive map are explored and the influences of certain parameter variations are investigated. The solutions are rescaled to match the length scales of waves generated in a wave tank. Based on the information provided by the map and the details of physical scaling, a framework is developed that can serve as a basis for experimental investigations into a variety of extreme waves as well localizations in wave fields. To derive further fundamental insights into the complexity of extreme wave conditions, Smoothed Particle Hydrodynamics (SPH) simulations are carried out on an advanced Graphic Processing Unit (GPU) based parallel computational platform. Free surface gravity wave simulations have successfully characterized water-wave dispersion in the SPH model while demonstrating extreme energy focusing and wave growth in both linear and nonlinear regimes. A virtual wave tank is simulated wherein wave motions can be excited from either side. Focusing of several wave trains and isolated waves has been simulated. With properly chosen parameters, dispersion effects are observed causing a chirped wave train to focus and exhibit growth. By using the insights derived from the study of the nonlinear Schrodinger equation, modulational instability or self-focusing has been induced in a numerical wave tank and studied through several numerical simulations. Due to the inherent dissipative nature of SPH models, simulating persistent progressive waves can be problematic. This issue has been addressed and an observation-based solution has been provided. The efficacy of SPH in modeling wave focusing can be critical to further our understanding and predicting extreme wave phenomena through simulations. A deeper understanding of the mechanisms underlying extreme energy localization phenomena can help facilitate energy harnessing and serve as a basis to predict and mitigate the impact of energy focusing.

EXPOSURE TO EXTREME HEAT EVENTS AND CHRONIC RESPIRATORY DISEASES AMONG A NATIONALLY REPRESENTATIVE SAMPLE OF THE UNITED STATES POPULATION

Previous studies have shown that extreme weather events are on the rise in response to our changing climate. Such events are projected to become more frequent, more intense, and longer lasting. A consistent exposure metric for measuring these extreme events as well as information regarding how these events lead to ill health are needed to inform meaningful adaptation strategies that are specific to the needs of local communities. Using federal meteorological data corresponding to 17 years (1997-2013) of the National Health Interview Survey, this research: 1) developed a location-specific exposure metric that captures individuals’ “exposure” at a spatial scale that is consistent with publicly available county-level health outcome data; 2) characterized the United States’ population in counties that have experienced higher numbers of extreme heat events and thus identified population groups likely to experience future events; and 3) developed an empirical model describing the association between exposure to extreme heat events and hay fever. This research confirmed that the natural modes of forcing (e.g., El Niño-Southern Oscillation), seasonality, urban-rural classification, and division of country have an impact on the number extreme heat events recorded. Also, many of the areas affected by extreme heat events are shown to have a variety of vulnerable populations including women of childbearing age, people who are poor, and older adults. Lastly, this research showed that adults in the highest quartile of exposure to extreme heat events had a 7% increased odds of hay fever compared to those in the lowest quartile, suggesting that exposure to extreme heat events increases risk of hay fever among US adults.