摘要：

A series representation of the relation that links the eigenvalues of the Orr-Sommerfeld equation is developed. This enables the complex frequency parameter to be expressed as a double series in terms of the Reynolds number and wavenumber, both of which are treated as complex variables. The complex coefficients arising in this series are determined by contour integration for the case of the eigenfunctions for a Blasius boundary layer profile. A nonlinear transformation is applied to the partial summations formed from the series in order to improve the convergence, and so to enable predictions of high accuracy to be made from only a few terms. Eigenvalues calculated by this technique are compared with those obtained directly from the Orr-Sommerfeld equation. The power of the technique is demonstrated by various graphical displays of the amplification contours for both temporal and spatial modes.

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