Stability Analysis for Wake Flow Behind a Flat Plate

Neutral stability limits for wake flow behind a flat plate is studied using spectral method. First, Orr-Sommerfeld equation was changed to matrix form, covering the whole domain of solution. Next, each term of matrix was expanded using Chebyshev expansion series, a series very much equivalent to the Fourier cosine series. A group of functions and conditions are applied to start and end points in the mathematical domain of the solution so as to avoid error accomulation at these points. The scheme ends with two matrices which result from the Orr-Sommerfeld equation. These matrices are solved, in conjunction, with boundary conditions ending up with a curve of neutral points of stability for an assumed velocity profile. Results are compared with other existing numerical methods and experiments, and the accuracy of the method is confirmed.