Stability of mean flows over an infinite flat plate
Abstract
The present investigation is mainly concerned with a stability analysis for the linearized NavierStokes equations for parallel and nonparallel mean flows over an infinite flat plate. The system of equations for parallel flows is presented. The system is viewed as a generalized OrrSommerfeld equation. Attention is given to an explicit criterion characterizing the case when the stability of all physically reasonable solutions is determined by the eigenvalues. The proof given in the investigation is applicable to both the generalized OrrSomerfeld equations and the modified equations for nonparallel flow. The fact that the criterion is independent of the completeness or incompleteness of eigenfunctions is contrary to some expectations.
 Publication:

Archive for Rational Mechanics and Analysis
 Pub Date:
 March 1982
 DOI:
 10.1007/BF00251524
 Bibcode:
 1982ArRMA..80...57M
 Keywords:

 Computational Fluid Dynamics;
 Flat Plates;
 Flow Stability;
 NavierStokes Equation;
 Parallel Flow;
 Eigenvalues;
 Eigenvectors;
 Flow Equations;
 Linear Equations;
 OrrSommerfeld Equations;
 Reynolds Number;
 Small Perturbation Flow;
 Fluid Mechanics and Heat Transfer