Invariant Manifolds in the Taylor Problem
This chapter is devoted to a method for calculating the unstable manifold that arises from the basic flow in hydrodynamical problems, devised by Davey 1962, Davey, DiPrima, and Stuart 1968, and Eagles 1971 for the study of the Taylor problem. Although the results that have been obtained with it so far are rather limited, it is the only method known at present for such problems (but see Hassard 1980 for a similar method in finite-dimensional spaces). Presumably, methods of this sort will be needed to understand the early onset of turbulence in detail.
KeywordsPower series representation of a finite-dimensional manifold in a Hilbert space coordinates in the manifold determination of the expansion coefficients dynamical system in the manifold separation of variables Taylor vortices wavy vortices helical vortices
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