Some applications of the qualitative theory of differential equations in fluid dynamics
Abstract
The qualitative theory of differential equations is used along with topological considerations to discuss problems in fluid dynamics and gasdynamics. Special attention is given to the qualitative aspects of flow fields, in particular to the geometry, the shape, and the structural stability of streamline patterns. The theory relies much on critical point analyses and on bifurcations in vector fields. Local solutions of the flow equations are derived to dicuss changes in flow topology in conjuntion with bifurcations of critical points. The theory is applied to inviscid, nonlinear conical flows and steady viscous flows over plane walls.
 Publication:

Ph.D. Thesis
 Pub Date:
 June 1988
 Bibcode:
 1988PhDT........43B
 Keywords:

 Computational Fluid Dynamics;
 Differential Equations;
 Flow Distribution;
 Flow Equations;
 Gas Flow;
 Separated Flow;
 Critical Point;
 Flow Stability;
 Inviscid Flow;
 Laminar Flow;
 Topology;
 Viscous Flow;
 Fluid Mechanics and Heat Transfer