Topics in vortex motion

Six topics in incompressible, inviscid fluid flow involving vortex motion are presented. The stability of the unsteady flow field due to the vortex filament expanding under the influence of an axial compression is examined in the first chapter as a possible model of the vortex bursting observed in aircraft contrails. The filament with a stagnant core is found to be unstable to axisymmetric disturbances. For initial disturbances with the form of axisymmetric Kelvin waves, the filament with a uniformly rotating core is neutrally stable, but the compression causes the disturbance to undergo a rapid increase in amplitude. The time at which the increase occurs is, however, later than the observed bursting times, indicating the bursting phenomenon is not caused by this type of instability.

In the second and third chapters the stability of a steady vortex filament deformed by two-dimensional strain and shear flows, respectively, is examined. The steady deformations are in the plane of the vortex cross-section. Disturbances which deform the filament centerline into a wave which does not propagate along the filament are shown to be unstable and a method is described to calculate the wave number and corresponding growth rate of the amplified waves for a general distribution of vorticity in the vortex core.

In Chapter Four exact solutions are constructed for two-dimensional potential flow over a wing with a free ideal vortex standing over the wing. The loci of positions of the free vortex are found and the lift is calculated. It is found that the lift on the wing can be significantly increased by the free vortex.

The two-dimensional trajectories of an ideal vortex pair near an orifice are calculated in Chapter Five. Three geometries are examined, and the criteria for the vortices to travel away from the orifice are determined.

Finally, Chapter Six reproduces completely the paper, "Structure of a linear array of hollow vortices of finite cross-section," co-authored with G. R. Baker and P. G. Saffman. Free streamline theory is employed to construct an exact steady solution for a linear array of hollow, or stagnant cored vortices. If each vortex has area A and the separation is L, then there are two possible shapes if A^(1/2)/L is less than 0.38 and none if it is larger. The stability of the shapes to two-dimensional, periodic and symmetric disturbances is considered for hollow vortices. The more deformed of the two possible shapes is found to be unstable, while the less deformed shape is stable.

Studies in vortex motion

This thesis covers four different problems in the understanding of vortex sheets, and these are presented in four chapters.

In Chapter 1, free streamline theory is used to determine the steady solutions of an array of identical, hollow or stagnant core vortices in an inviscid, incompressible fluid. Assuming the array is symmetric to rotation through π radians about an axis through any vortex centre, there are two solutions or no solutions depending on whether A^(1/2)/L is less than or greater than 0.38 where A is the area of the vortex and L is the separation distance. Stability analysis shows that the more deformed shape is unstable to infinitesimal symmetric disturbances which leave the centres of the vortices undisplaced.

Chapter 2 is concerned with the roll-up of vortex sheets in homogeneous fluid. The flow over conventional and ring wings is used to test the method of Fink and Soh (1974). Despite modifications which improve the accuracy of the method, unphysical results occur. A possible explanation for this is that small scales are important and an alternate method based on "Cloud-in-Cell" techniques is introduced. The results show small scale growth and amalgamation into larger structures.

The motion of a buoyant pair of line vortices of opposite circulation is considered in Chapter 3. The density difference between the fluid carried by the vortices and the fluid outside is considered small, so that the Boussinesq approximation may be used. A macroscopic model is developed which shows the formation of a detrainment filament and this is included as a modification to the model. The results agree well with the numerical solution as developed by Hill (1975b) and show that after an initial slowdown, the vortices begin to accelerate downwards.

Chapter 4 reproduces completely a paper that has already been published (Baker, Barker, Bofah and Saffman (1974)) on the effect of "vortex wandering" on the measurement of velocity profiles of the trailing vortices behind a wing.

Contributions of parietal cortex to reach planning

Sensory-motor circuits course through the parietal cortex of the human and monkey brain. How parietal cortex manipulates these signals has been an important question in behavioral neuroscience. This thesis presents experiments that explore the contributions of monkey parietal cortex to sensory-motor processing, with an emphasis on the area's contributions to reaching. First, it is shown that parietal cortex is organized into subregions devoted to specific movements. Area LIP encodes plans to make saccadic eye movements. A nearby area, the parietal reach region (PRR), plans reaches. A series of experiments are then described which explore the contributions of PRR to reach planning. Reach plans are represented in an eye-centered reference frame in PRR. This representation is shown to be stable across eye movements. When a sequence of reaches is planned, only the impending movement is represented in PRR, showing that the area is more related to movement planning than to storing the memory of reach targets. PRR resembles area LIP in each of these properties: the two areas may provide a substrate for hand-eye coordination. These findings yield new perspectives on the functions of the parietal cortex and on the organization of sensory-motor processing in primate brains.

Impacts of climate change of seaports: A survey of knowledge, perceptions, and planning efforts among port administrators

Port authorities from around the world were surveyed to ascertain how administrators feel climate change might impact their operations, what level of change would be problematic, and how they plan to adapt to new conditions. The survey was distributed to 350 major ports through two leading international port organizations, the International Association of Ports and Harbors and the American Association of Port Authorities. (PDF contains 4 pages)

Climate change adaptation and planning: An example from Kailua Beach, Oahu, Hawaii

The University of Hawaii Sea Grant College Program (UHSG) in partnership with the Hawaii Department of Land and Natural Resources (DLNR), Office of Conservation and Coastal Lands (OCCL) is developing a beach and dune management plan for Kailua Beach on the eastern shoreline of Oahu. The objective of the plan is to develop a comprehensive beach management and land use development plan for Kailua Beach that reflects the state of scientific understanding of beach processes in Kailua Bay and abutting shoreline areas and is intended to provide long-term recommendations to adapting to climate change including potential coastal hazards such as sea level rise. The development of the plan has lead to wider recognition of the significance of projected sea level rise to the region and provides the rational behind some of the land use conservation strategies. The plan takes on a critical light given global predictions for continued, possibly accelerated, sea-level rise and the ongoing focus of intense development along the Hawaiian shoreline. Hawaii’s coastal resource managers are faced with the daunting prospect of managing the effects of erosion while simultaneously monitoring and regulating high-risk coastal development that often impacts the shoreline. The beach and dune preservation plan is the first step in a more comprehensive effort prepare for and adapt to sea level rise and ensure the preservation of the beach and dune ecosystem for the benefit of present and future generations. The Kailua Beach and Dune Management plan is intended to be the first in a series of regional plans in Hawaii to address climate change adaptation through land use planning. (PDF contains 3 pages)

Applying hedonic property models in the planning and evaluation of shoreline management

According to the Millennium Ecosystem Assessment’s chapter “Coastal Systems” (Agardy and Alder 2005), 40% of the world population falls within 100 km of the coast. Agardy and Alder report that population densities in coastal regions are three times those of inland regions and demographic forecasts suggest a continued rise in coastal populations. These high population levels can be partially traced to the abundance of ecosystem services provided in the coastal zone. While populations benefit from an abundance of services, population pressure also degrades existing services and leads to increased susceptibility of property and human life to natural hazards. In the face of these challenges, environmental administrators on the coast must pursue agendas which reflect the difficult balance between private and public interests. These decisions include maintaining economic prosperity and personal freedoms, protecting or enhancing the existing flow of ecosystem services to society, and mitigating potential losses from natural hazards. (PDF contains 5 pages)