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The primary purpose of this research is to investigate non-linear and chaotic behaviour of water in a pipeline at the transition region from laminar to turbulent flow. Turbulence was generated in the flow by the use of an orifice plate which generated coherent vortices and subsequent break-down into turbulence, downstream of the orifice. The flow regime was pulsatile. This was decided specifically to obtain better control of the experimental apparatus, better control of the frequency of vortices shedding from the orifice, and because of its wider range of practical applications discussed in section 1.3. The mechanism of vortex breakdown has been addressed many times over the past century. The process by which vortices interact and degenerate is essentially non- inear. New techniques from the field of non-linear dynamics have emerged which can yield some quantitative information about the complexity of non-linear phenomena. This thesis aims to test some of these techniques, together with more traditional methods, on the experimental time series data obtained from axisymmetric vortex breakdown of a pulsed flow at a pipe orifice. An experimental rig was designed and constructed in the Civil Engineering Department, at the University of Glasgow, to produce, accurately controllable, pulsed flows within a pipe system at an orifice plate. The apparatus was designed to allow a range of parameters to be varied over the course of the investigation. Computer algorithms were written by the author to analyse the resulting data, obtained from Laser Doppler Anemometry readings. Flow visualisation techniques were also used to give a qualitative understanding of the system. Evidence was found for the development of initially axisymmetric pulsed vortex flows to a relatively low dimensional chaotic state prior to breaking down to a more complex turbulent state. The flow complexity was probed by investigating the dynamics of phase space attractors reconstructed from time series taken at various spatial locations within the developing flow field. The two techniques used for this were the Grassberger- Procaccia dimension and the Lyapunov exponent. Reconstruction of the attractors was performed using the minimum mutual information function. The flow complexity was used in conjunction with Turbulent Intensitites within the flow and the development of the flow velocity profile, to provide a comprehensive picture of the flow field development for pulsed vortex flows. In addition, the techniques from the field of non-linear dynamics were thoroughly tested in the experimental environment. The problem of noise, and its effect on the results produced has been analysed in detail.