Abstract

Being able to predict the properties of a decaying vortex is of value to various technological and scientific problems. The hazards presented by the vortices shed by large, heavily loaded, aircraft to an incoming plane are well known. A safe separation distance makes sure that the vortices shed by the first aircraft have been decayed to a level that is safe for the following aircraft. The decay of geophysical vortices is a highly complex phenomenon. Nevertheless, simplified time-dependent vortex models, like the one presented in this thesis, do elaborate on the basic processes involved during the energy dissipative phase. The general approach also provides a method that enables us to study the transient flow development in a plethora of swirling flow problems that evolve by starting or halting a pair of circular cylinders. In the present thesis, a novel analytical method is developed to study the decay of a strong, concentrated vortex. Based on the equations representing the transient fluid motion and using a standard solution formulation via Fourier-Bessel expansions will show that different initial profiles of the velocity produce distinct velocity time distributions. Three initial velocity shapes will be explored here. The first deals with the decay of a potential vortex. This type presents the known theoretical discrepancy of infinite velocity and vorticity in the center at the start. The second case considers an initial velocity distribution of a Rankine's vortex. The latter although possess a continuous velocity and static pressure distributions, it is also theoretically dubious since in this situation the vorticity presents a jump discontinuity at the core radius. The final distribution will assume the Vatistas' n = 2 vortex