On the non-linear stability of plane Couette flow

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Abstract
In the present paper the stability of plane Couette flow is studied. The stream function and distribution of vorticity and the Reynolds stresses for the linearized solution are computed. The stability effect of the non-linear terms are also discussed and it is found that for small amplitudes, the non-linear terms are destabilizing. A neutral curve determining the necessary amplitude in order to get instability, is found. The convergence of the expansion in the latter case is, however, somewhat uncertain and the result should therefore only be considered as a first, rough approximation.