Computational Studies on Fluid and Particle Dynamics

This dissertation is divided into two parts. The first part includes chapter 2 to 4, which focus on development and application of numerical algorithm on particle and fluid simulation. Starting with a pure granular system in a driven cavity setup (Chapter 2), we move on to the immersed boundary simulation of fluid solid interaction (Chapter 3). This part ends with a coupled immersed boundary-discrete particle implementation. The second part includes Chapter 5 and Appendix A, each deals with an independent problem and focuses more on the theoretical aspects. Chapter 5 deals with a classic fluid dynamics problem of thermal wave induced net flux. Appendix A studies the underestimation of solver accuracy when the solution has singularities, and analyzes the cause of the underestimation using a simple theoretical model

High Frequency Monitoring and Three-Dimensional Modelling of Temporal Variations in Water Quality of Lake Rotorua, New Zealand

Over the last few decades, anthropogenic eutrophication has become a significant problem in New Zealand and other parts of the world. Lake Rotorua is located in the central North Island, New Zealand. It is a lake with significant historical, cultural and recreational values that has undergone anthropogenic eutrophication. Lake Rotorua has been exposed to anthropogenic impacts through conversion of forested land to agricultural use within its catchment, and the discharge of domestic sewage into the lake. Cyanobacterial blooms have become a common occurrence in the lake each summer. These blooms not only reduce aesthetic appeal but also have potential to affect human health. Lake stratification and physical mixing events are the most important factors influencing nutrient availability and phytoplankton growth in Lake Rotorua. The main objective of this study was to use high frequency monitoring data to investigate the significance of lake stratification events and how these events interact with the development of the cyanobacteria population and changes in nutrient concentrations in Lake Rotorua. The second objective was to use an ecological model to understand the relationship between physical, chemical and biological variables, and phytoplankton dynamics. Data from a high frequency real-time water quality monitoring buoy was used as the basis for 12 sampling trips to Lake Rotorua timed around stratification and mixing events. Water samples were collected from five different sites for nutrient analysis, chlorophyll a analysis, and phytoplankton and zooplankton identification at depth intervals of 6 meters. Profiles were taken for temperature, dissolved oxygen and fluorescence. Total suspended solids and volatile suspended solids were also analysed. The data provided by the buoy, combined with additional sampling and measurements around stratification events, were used to calibrate a three-dimensional ecosystem model, ELCOM-CAEDYM. Periods consisting of a few days of high solar radiation and low winds caused Lake Rotorua to become stratified between 26 January 2009 and 20 February 2009. During this stratification period the bottom waters became deoxygenated and there were large increases in of phosphorus and nitrogen concentrations in bottom waters, which were subsequently dispersed through the water column when the lake mixed again. Ammonium and phosphate were the dominant species of inorganic nitrogen and phosphorus in bottom waters during the periods of stratification. Upon mixing there was rapid growth of cyanobacteria (Microcystis sp. and Anabaena sp.). For the zooplankton community, copepod and rotifer densities increased significantly after the stratification event and replaced the previously dominant cladocerans. In the study high frequency modelling with ELCOM-CADYM simulated the general trends of water temperature, dissolved oxygen and nutrient concentrations in Lake Rotorua. The model captured the water temperature fluctuation before, during, and after lake stratification as well as subsequent dissolved oxygen changes over time and space. Simulated nutrient concentrations were close to the field measurements, in particular NH4, TN and TP. Some issues occurred with high frequency simulations such as being unable to capture the strong fluctuations of lake surface temperature, and the magnitude of the decreases in dissolved oxygen under strong stratification

Effect of hurricane forward speed and approach angle on coastal storm surge

Hurricane induced storm surges can be destructive and can pose great threats to coastal communities. There are many factors affecting storm surges, including the hurricane’s intensity and movement, the bathymetry and coastline of affected area, rainfall, tide, and river stage. This thesis focuses on the effects of hurricane approach angle (θ) and forward speed (U), which together describe the hurricane’s motion. The problem is approached through several numerical experiments with increasing complexity. First are some process studies of long wave propagations near the coast, followed by examination of the generation of long waves by a traveling wind field. The central part consists of a systematic experiment looking into the two hurricane parameters θ and U, with additional tests on bottom friction and hurricane size. In the end is an experiment with more realistic bathymetry and inundation treatment. Storm surge is a surface wave caused by atmospheric forcing. In the open ocean it has small amplitude and propagates at the speed of a shallow water gravity wave once it is away from the area of generation. After reaching the coast, it increases to a more dangerous level and extends up and down-coast. It is found in this study that θ and U have significant effects on storm surge. The mechanism is related to Kelvin wave’s characteristics of propagation. Because of the boundary-confinement and the unidirectional propagation of the Kelvin wave, certain hurricane movements defined by a combination of θ and U may either be favorable or non-favorable for storm surge development. It was also found that hurricane size can have important effects on storm surge amplitude. When more realistic bathymetry is used, experiments suggest that the conclusions made with simplified experiments are still valid and should not be overlooked

"Asymmetric Market Shares, Advertising, and Pricing: Equilibrium with an Information Gatekeeper"

We analyze the impact of market share on advertising and pricing decisions by firms that sell to loyal, non-shopping customers and can advertise to shoppers through an information intermediary or "gatekeeper." In equilibrium the firm with the smaller loyal market advertises more aggressively but prices less competitively than the firm with the larger loyal market, and there is no equilibrium in which both firms advertise with probability 1. The results differ significantly from earlier literature which assumes all prices are revealed to shoppers and finds that the firm with the smaller loyal market adopts a more competitive pricing strategy. The predictions of the model are consistent with advertising and pricing behavior observed on price comparison websites such as Shopper.com.online markets, E-commerce, market share, information gatekeeper, equilibrium price dispersion, advertising