On the basis of the Meksyn-Stuart method, nonlinear instability of the plane Couette flow is investigated. The perturbed stream function and the mean flow field are determined by the Galerkin method. A neutral surface is obtained in a three-dimensional space of the Reynolds number, wave-number, and amplitude. The critical Reynolds number based on the width and the relative velocity is estimated to be about 190 000.
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S. Kuwabara (1967) studied this question.