The Taylor-Couette problem for a rarefied gas is studied numerically by the direct simulation Monte Carlo method. The gas is supposed to be contained in an annular domain, bounded by two coaxial rotating cylinders and top and bottom (specularly reflecting) boundaries, and the flow is assumed to be steady and axisymmetric. Special attention is focused on the effect of rotation of the outer cylinder on the type of the induced Taylor-vortex flow. It is shown that different types of flow can coexist stably in a wide range of speeds of rotation of the inner and outer cylinders unless the outer cylinder is rotating fast in the opposite direction to the inner.
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