Structural stability of threedimensional vortex flows
Abstract
Topological approaches which permit the description of threedimensional flowfields in terms of nonlinear dynamical systems are discussed. The basic idea is to treat unsteady flow phenomena as steady topological flow structures (TPS). This requires tracking the evolution of the TPS over time by means of empirical measurements of locally measured quantities which can be correlated with changes in the TPS. For twodimensional flows, the changes that occur are either a local or a global bifurcation, forming, e.g., a separation bubble, vortex flows and interactions of vortices. Twodimensional flows are actually structurally unstable, transient states of threedimensional flows. Analytical techniques are defined for modeling the formation of elementary topological structures and applied to describing TPS which appear in RayleighBenard convection. It is noted that the comparison of results for different nonlinear dynamical systems depends on the characterization of topologically equivalent structures and structural changes and their relationship to an invariant flow quantity.
 Publication:

IN: Nonlinear dynamics of transcritical flows; Proceedings of the International Colloquium
 Pub Date:
 1985
 Bibcode:
 1985ndtf.proc...81D
 Keywords:

 Computational Fluid Dynamics;
 Flow Distribution;
 Flow Stability;
 Three Dimensional Flow;
 Vortices;
 Dynamical Systems;
 Nonlinear Equations;
 RayleighBenard Convection;
 Temporal Distribution;
 Two Dimensional Flow;
 Fluid Mechanics and Heat Transfer