The stability of a circular Couette flow with internal heat generation is studied in the region between two coaxial cylinders. The inner cylinder is rotating with constant velocity while the outer one is kept at rest. The investigation is carried out for wide ranges of the Prandtl number and radius ratio R, for the axisymmetric mode (n=0) and the first two asymmetric modes (n=1,2), respectively. For small to large gaps (R=0.95, 0.7, 0.4), axisymmetric perturbations are the single main cause of instability. The growths of the Prandtl and Taylor numbers lead to a decrease of the critical Grashof number. Stabilization of the Couette flow is possible for very large gaps (R=0.1), but the region of stabilization decreases for large Prandtl numbers. The stability boundary is determined by the concurrence of axisymmetric (n=0) and spiral (n=1) modes in the case of very large gaps.

中文翻译：

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非等温圆形库埃特流的稳定性

圆形的稳定性 库埃特流 与内部 发热在两个同轴圆柱体之间的区域进行了研究。内圆柱体以恒定速度旋转，而外圆柱体保持静止。分别针对轴对称模式（n = 0）和前两个非对称模式（n = 1,2）对普朗特数和半径比R的宽范围进行了研究。对于小到大的间隙（R = 0.95、0.7、0.4），轴对称扰动是产生间隙的唯一主要原因。不稳定。Prandtl和Taylor数的增长导致临界Grashof数减少。稳定库埃特流对于很大的间隙（R = 0.1）是可能的，但是对于大的Prandtl数，稳定区域会减小。在间隙非常大的情况下，稳定性边界由轴对称（n = 0）和螺旋（n = 1）模态的同时确定。