Upper bound on angular momentum transport in Taylor-Couette flow.
Upper bound on angular momentum transport in Taylor-Couette flow.
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DOI：
10.1103/physreve.100.063109
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发表时间：
2019-12
期刊：
影响因子：
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通讯作者：
Zijing Ding;Elena Marensi
中科院分区：
文献类型：
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作者：
Zijing Ding;Elena Marensi
本文采用一维背景场方法，从理论上和数值上研究了Taylor-Couette流中角动量输运的上界。流的边界在半径为R_{i}的旋转内柱和半径为R_{o}的固定外柱之间。本文提出了一个变分问题，并利用伪时间步进法求解了一个泰勒数为Ta=10^{9}的变分问题。角动量输运以努塞尔数Nu为特征，其边界为Nu≤cTa^{1/2}，其中前因子c取决于半径比η=R_{i}/R_{o}。研究了三种典型的半径比。， η=0.5,0.714和0.909，相应的前因子c=0.0049,0.0075和0.0086改善了Doering和Constantin [c。杜林和P.康斯坦丁，物理学家。中国生物医学工程学报，2009,32 (6):559 - 559 . [P]。Constantin, SIAM Rev. 36,73 (1994)SIREAD0036-144510.1137/1036004]至少一个数量级。此外，我们通过归纳分岔分析表明，考虑三维背景速度场无法降低边界。
We investigate the upper bound on angular momentum transport in Taylor-Couette flow theoretically and numerically by a one-dimensional background field method. The flow is bounded between a rotating inner cylinder of radius R_{i} and a fixed outer cylinder of radius R_{o}. A variational problem is formulated and solved by a pseudo-time-stepping method up to a Taylor number Ta=10^{9}. The angular momentum transport, characterized by a Nusselt number Nu, is bounded by Nu≤cTa^{1/2}, where the prefactor c depends on the radius ratio η=R_{i}/R_{o}. Three typical radius ratios are investigatedi.e., η=0.5,0.714,and0.909, and the corresponding prefactors c=0.0049,0.0075,and0.0086 are found to improve (lower) the rigorous upper bounds by Doering and Constantin [C. Doering and P. Constantin, Phys. Rev. Lett. 69, 1648 (1992)PRLTAO0031-900710.1103/PhysRevLett.69.1648] and Constantin [P. Constantin, SIAM Rev. 36, 73 (1994)SIREAD0036-144510.1137/1036004] by at least one order of magnitude. Furthermore, we show, via an inductive bifurcation analysis, that considering a three-dimensional background velocity field is unable to lower the bound.