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.

Learning and using taxonomies for visual and olfactory classification

Humans are able of distinguishing more than 5000 visual categories even in complex environments using a variety of different visual systems all working in tandem. We seem to be capable of distinguishing thousands of different odors as well. In the machine learning community, many commonly used multi-class classifiers do not scale well to such large numbers of categories. This thesis demonstrates a method of automatically creating application-specific taxonomies to aid in scaling classification algorithms to more than 100 cate- gories using both visual and olfactory data. The visual data consists of images collected online and pollen slides scanned under a microscope. The olfactory data was acquired by constructing a small portable sniffing apparatus which draws air over 10 carbon black polymer composite sensors. We investigate performance when classifying 256 visual categories, 8 or more species of pollen and 130 olfactory categories sampled from common household items and a standardized scratch-and-sniff test. Taxonomies are employed in a divide-and-conquer classification framework which improves classification time while allowing the end user to trade performance for specificity as needed. Before classification can even take place, the pollen counter and electronic nose must filter out a high volume of background “clutter” to detect the categories of interest. In the case of pollen this is done with an efficient cascade of classifiers that rule out most non-pollen before invoking slower multi-class classifiers. In the case of the electronic nose, much of the extraneous noise encountered in outdoor environments can be filtered using a sniffing strategy which preferentially samples the visensor response at frequencies that are relatively immune to background contributions from ambient water vapor. This combination of efficient background rejection with scalable classification algorithms is tested in detail for three separate projects: 1) the Caltech-256 Image Dataset, 2) the Caltech Automated Pollen Identification and Counting System (CAPICS) and 3) a portable electronic nose specially constructed for outdoor use.