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- W133550479 abstract "We consider the classical Couette-Taylor problem in the limiting case when the radii ratio (( (eta = tfrac{{{{R}_{1}}}}{{{{R}_{2}}}}) )) is very close to 1 and the critical Reynolds number is very large. It is well know that the critical modes which destabilise the Couette flow are either stationary axisymmetric modes or oscillatory non axisymmetric modes with an integer azimutal wavenumber. Langford and al. [1] observe when η tends to 1 that the most critical oscillatory modes come altogether (Figure 4 in [2]). In this paper, our main motivation is to analyse the transition between axisymmetric and non axisymmetric modes at this limit and to determine the selected azimuthal wavelength. By this way, we give some informations on the occurrence of oscillatory motion when the two cylinders move in the opposite direction. The governing equations considered here are deduced from the Navier-Stokes equations by a suitable choice of scale taken at the limit η= 1. The new dimensionless parameters are the inner and outer Taylor numbers T i , and, the basic flow is the planar Couette flow. The linear analysis points out the possibility of oscillatory instabilities for negative value of T 2. The bifurcated structures are studied by means of Ginzburg-Landau type of equations. Thus, we can take into account the interaction between critical modes with spatial wave numbers close to the critical one. In addition, we give precisely the coefficients occuring these equations. At the critical point, these coefficients can be obtained in the same way as those of classical amplitude equations ([3])." @default.
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- W133550479 date "1992-01-01" @default.
- W133550479 modified "2023-09-24" @default.
- W133550479 title "The Couette Taylor Problem in the Small Gap Approximation" @default.
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- W133550479 doi "https://doi.org/10.1007/978-1-4615-3438-9_4" @default.
- W133550479 hasPublicationYear "1992" @default.
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