Li Zhenyu, Khayat Roger E
Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, Canada N6A 5B9.
Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Apr;69(4 Pt 2):046305. doi: 10.1103/PhysRevE.69.046305. Epub 2004 Apr 27.
Low-inertia vortex formation and pattern selection are examined for axisymmetric Taylor-Couette flow with spatially modulated cylinders. The forcing is arbitrary but remains periodic. The modulation amplitude is assumed to be small, and a regular perturbation expansion is used to determine the flow field at small to moderately large Taylor numbers (below the critical threshold). It is found that the presence of a weak modulation leads unambiguously to the emergence of steady Taylor-vortex flow even at vanishingly small Taylor number. This situation is closely reminiscent of the effect of end plates, and the consequent onset of imperfect bifurcation. The vortex structure is found to have the same periodicity as the forcing when only one of the cylinders is modulated, or when the modulations are commensurate. For incommensurate modulations, the vortex pattern is quasiperiodic, with regions of almost purely azimuthal flow. When the counter-rotation speed of the outer cylinder increases, the original vortices are gradually replaced by new ones that end up spanning the entire gap width, and in turn break up into two vortices resulting in two rows of vortices commensurate with each cylinder modulation. It is also shown that, for any modulation amplitude, the forcing wave number that generates the most intense vortex flow for a given Taylor number varies monotonically with Ta, but always reaches the critical value predicted by linear stability analysis for straight cylinders, regardless of which cylinder is modulated.
研究了具有空间调制圆柱的轴对称泰勒-库埃特流中的低惯性涡旋形成和模式选择。强迫是任意的,但保持周期性。假设调制幅度很小,并使用正则摄动展开来确定小到中等大泰勒数(低于临界阈值)时的流场。结果发现,即使在非常小的泰勒数下,弱调制的存在也明确导致了稳定泰勒涡旋流的出现。这种情况与端板的影响以及随之而来的不完善分岔的开始非常相似。当只有一个圆柱被调制或调制是可公度时,发现涡旋结构与强迫具有相同的周期性。对于不可公度调制,涡旋模式是准周期的,具有几乎纯方位流的区域。当外圆柱的反向旋转速度增加时,原来的涡旋逐渐被新的涡旋取代,新涡旋最终跨越整个间隙宽度,进而分裂成两个涡旋,导致与每个圆柱调制对应的两排涡旋。还表明,对于任何调制幅度,在给定泰勒数下产生最强涡旋流的强迫波数随泰勒数单调变化,但无论哪个圆柱被调制,总是达到直圆柱线性稳定性分析预测的临界值。