Six topics in incompressible, inviscid fluid flow involvingvortex motion are presented. The stability of the unsteady flow fielddue to the vortex filament expanding under the influence of an axialcompression is examined in the first chapter as a possible model ofthe vortex bursting observed in aircraft contrails. The filament witha 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, butthe compression causes the disturbance to undergo a rapid increase inamplitude. The time at which the increase occurs is, however, laterthan the observed bursting times, indicating the bursting phenomenonis not caused by this type of instability.
In the second and third chapters the stability of a steady vortexfilament deformed by two-dimensional strain and shear flows, respectively,is examined. The steady deformations are in the plane of thevortex cross-section. Disturbances which deform the filament centerlineinto a wave which does not propagate along the filament are shownto be unstable and a method is described to calculate the wave numberand corresponding growth rate of the amplified waves for a general distributionof vorticity in the vortex core.
In Chapter Four exact solutions are constructed for two-dimensionalpotential flow over a wing with a free ideal vortex standingover the wing. The loci of positions of the free vortex are found andthe lift is calculated. It is found that the lift on the wing can besignificantly increased by the free vortex.
The two-dimensional trajectories of an ideal vortex pair near anorifice are calculated in Chapter Five. Three geometries are examined,and the criteria for the vortices to travel away from the orifice aredetermined.
Finally, Chapter Six reproduces completely the paper, "Structureof a linear array of hollow vortices of finite cross-section," co-authoredwith G. R. Baker and P. G. Saffman. Free streamline theory is employedto construct an exact steady solution for a linear array of hollow, orstagnant cored vortices. If each vortex has area A and the separationis L, then there are two possible shapes if A^(1/2)/L is less than 0.38and none if it is larger. The stability of the shapes to two-dimensional, periodic and symmetric disturbances is considered for hollowvortices. The more deformed of the two possible shapes is found to beunstable, while the less deformed shape is stable.
