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Tertiary and quaternary solutions for plane Couette flow. (English) Zbl 0898.76028
The manifold of the three-dimensional steady solutions is explored in the parameter space of the problem and their instabilities are investigated. These instabilities lead to time-periodic solutions whose properties do not differ much from those of the steady solutions except that the amplitude varies in time. In some cases travelling wave solutions which are asymmetric with respect to the midplane of the layer are found as quaternary states of flow. Similarities with longitudinal vortices recently observed in experiments are discussed.

MSC:
76E05 Parallel shear flows in hydrodynamic stability
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