On the linear and nonlinear stability of nonparallel flow
Abstract
Due to theoretical and practical demands, the stability of nonparallel flows have received increasing attention recently. Two nonparallel exact solutions to the NavierStokes equations are chosen as the basic flow: the Taylor vortex array and the Kovasznay flow. In Part 1, the linear stability analysis of the Taylor vortex array is formulated. By use of the spectral Galerkin method, we reduced the governing equation of linear into 4 independent modes. In each mode, vortices break down in a different manner. The time evolution of the streamline patterns of the decaying vortices under the influence of disturbances are given. In Part 2, the linear and nonlinear stability analyses of another nonparallel exact solution to the NavierStokes equations, the Kovasznay flow, are also formulated. A new approach to the problem is given. For the semiinfinite computational domain, the rational Chebyshev function was used as the base functions. The linear stability analysis of the Kovasznay flow is performed with respect to the oddrational Chebyshev mode and the evenrational Chebyshev mode. An organized structure seems to develop after the onset of instability. The importance of the secondary stability is recognized through this work. Several general characteristics of nonparallel flow stability are found.
 Publication:

Ph.D. Thesis
 Pub Date:
 March 1989
 Bibcode:
 1989PhDT........38C
 Keywords:

 Chebyshev Approximation;
 Flow Stability;
 NavierStokes Equation;
 Nonlinearity;
 Stability;
 Vortices;
 Rational Functions;
 Vortex Breakdown;
 Vortex Sheets;
 Fluid Mechanics and Heat Transfer