Nonlinear stability of parallel flows by high-order amplitude expansions
Abstract
The Landau-Stuart theory and its subsequent modifications suffer from some restrictions and from the nonuniqueness in determining higher-order terms of the amplitude expansions, which limit the range of applicability as well as the validity of the results. In the present paper, a well-defined amplitude is introduced a priori. In this way, uniqueness for terms of any order is achieved. Moreover, Watson's method is no longer restricted to almost neutral disturbances. This offers not only more accurate approximations and numerical studies on convergence but, as a consequence, a whole series of new applications. As a first example, the nonlinear equilibrium states of the plane Poiseuille flow are investigated. The numerical results are discussed in the context of the author's solutions of nonlinear equations, with special emphasis on the convergence of the Landau series.
- Publication:
-
AIAA Journal
- Pub Date:
- March 1980
- DOI:
- 10.2514/3.50755
- Bibcode:
- 1980AIAAJ..18..243H
- Keywords:
-
- Amplitudes;
- Computational Fluid Dynamics;
- Flow Stability;
- Parallel Flow;
- Series Expansion;
- Laminar Flow;
- Perturbation Theory;
- Reynolds Number;
- Fluid Mechanics and Heat Transfer