The onset of vortex turbulence
Abstract
The goal is to investigate some of the unusual and spectacular properties near the transition to turbulence in a twodimensional field of limitcycle oscillators. Of particular interest are the dynamics of topological defects (vortices) associated with the onset of turbulence. The complex GinzburgLandau equation describes an extended reactiondiffusion system close to the bifurcation of a steady state into a stable, periodic orbit. In the jargon of nonlinear dynamics, it is the amplitude equation corresponding to a Hopf bifurcation. Because of the generality of the assumptions under which it is derived, the complex GinzburgLandau equation describes systems in contexts other than chemical reactions with diffusion. Examples include RayleighBenard convection and the phase fields of multimode lasers. The reactiondiffusion model is however, a sufficiently general model to frame our discussion.
 Publication:

Ph.D. Thesis
 Pub Date:
 December 1992
 Bibcode:
 1992PhDT........68H
 Keywords:

 Chemical Reactions;
 Diffusion Theory;
 LandauGinzburg Equations;
 Turbulent Flow;
 Two Dimensional Flow;
 Vortices;
 Branching (Mathematics);
 ConvectionDiffusion Equation;
 RayleighBenard Convection;
 Turbulence;
 Fluid Mechanics and Heat Transfer