The Breakdown to Turbulence of a Forced Vortex Flow at a Pipe Orifice: The Non-Linear Evolution of Initially Axisymmetric Vortices

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

Molecular reponses of cell adhesion upon cell-cell contact initiation in a 2-D ultrasound standing wave trap

This thesis explores the interactions of cells and particles brought into contact in suspension in an ultrasound standing wave trap as aggregates or monolayers. The influence of CaCb , and hence modulation of electrostatic particle interaction force, on the growth and morphology of aggregates of 25 urn latex spheres was initially characterised by techniques including fractal dimension, and void analysis. At low CaCb additions highly hexagonally ordered structures were formed while with increasing CaCb additions the aggregate morphology gradually 'crossed over' from being essentially closely packed to a dendritic, highly disordered one. The physical environment of cells aggregating in the trap was then examined to assess the extent to which ultrasound might influence cell viability and function. The temperature rise was < 0.5 K. The drag due to acoustic streaming was smaller than the stress imposed by gentle preparative cell centrifugation. The attractive acoustic force between cells was small compared to the force required to reverse a single receptor- receptor bond and to the attractive van der Waals force. Acoustic spectrum analysis detected no cavitation activity in the suspensions. Fluorescent indicators showed that the number of viable cells (99 %) did not change during 1 h in the trap. The progression of cell-cell interactions i.e. length of membrane-membrane contact, and the integral intensities of stained cadherin/catenin complex molecules, the actin cytoskeleton and (for chondrocytes) gap junctions were examined over 60 min in primary chondrocytes, and in neural, prostate epithelial and prostate cancer cell lines. The aggregate form changed concurrently from hexagonally ordered cells to a continuous sheet of mostly quadrilateral and pentagonal cells. Rapid molecular responses to cell contact in other systems are reviewed. The cells in this work progressed from physical aggregation, through molecular adhesion, to displaying the intracellular consequences of receptor interactions. The ability to form mechanically strong confluent cell monolayers that can be monitored in situ or harvested from the trap provides a technique with general potential for monitoring the synchronous development of cell responses to receptor-triggered adhesion