Abstract
The motion of a compressible viscous gas in a rapidly rotating cylinder closed at both ends is investigated by the linear theory. The rigid rotation state is perturbed slightly by source or sinks and by thermal gradients. The method of matched asymptotic expansions is used to find uniform solutions in powers of the Ekman number. In the Stewartson 1/3 layer along the side wall, the Ekman number ε at power 1/3 is taken of the same order of magnitude as the inverse of the square Mach number M; this allows to take correctly into account the radial compressibility effect, contrary to previous works. This method is also applied to detached layers and to Stewartson 1/4 layers with ε 1/4 M 2 = 0 (1). The pattern of the flow in these layers is strongly altered as compared to incompressible case.
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Louvet, P., Durivault, J. (1977). Compressible countercurrent flow in a strongly rotating cylinder. In: Brauner, CM., Gay, B., Mathieu, J. (eds) Singular Perturbations and Boundary Layer Theory. Lecture Notes in Mathematics, vol 594. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086095
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DOI: https://doi.org/10.1007/BFb0086095
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