This thesis covers four different problems in theunderstanding of vortex sheets, and these are presented infour chapters.
In Chapter 1, free streamline theory is used to determinethe steady solutions of an array of identical, hollowor stagnant core vortices in an inviscid, incompressiblefluid. Assuming the array is symmetric to rotation through π radians about an axis through any vortex centre, thereare two solutions or no solutions depending on whether A^(1/2)/Lis less than or greater than 0.38 where A is the area ofthe vortex and L is the separation distance. Stabilityanalysis shows that the more deformed shape is unstable toinfinitesimal symmetric disturbances which leave the centresof the vortices undisplaced.
Chapter 2 is concerned with the roll-up of vortexsheets in homogeneous fluid. The flow over conventional andring wings is used to test the method of Fink and Soh (1974).Despite modifications which improve the accuracy of themethod, unphysical results occur. A possible explanationfor this is that small scales are important and an alternatemethod based on "Cloud-in-Cell" techniques is introduced.The results show small scale growth and amalgamation intolarger structures.
The motion of a buoyant pair of line vortices ofopposite circulation is considered in Chapter 3. The densitydifference between the fluid carried by the vortices and thefluid outside is considered small, so that the Boussinesqapproximation may be used. A macroscopic model is developedwhich shows the formation of a detrainment filament and thisis included as a modification to the model. The resultsagree well with the numerical solution as developed by Hill(1975b) and show that after an initial slowdown, the vorticesbegin to accelerate downwards.
Chapter 4 reproduces completely a paper that hasalready been published (Baker, Barker, Bofah and Saffman(1974)) on the effect of "vortex wandering" on the measurementof velocity profiles of the trailing vortices behind awing.
