On the transition from the laminar to disordered flow in a precessing spherical-like cylinder
On the transition from the laminar to disordered flow in a precessing spherical-like cylinder
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关于进动类球形圆柱体中从层流到无序流的转变
DOI：
10.1080/03091929.2014.976214
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发表时间：
2014-11
影响因子：
1.3
通讯作者：
Zhang, Keke
中科院分区：
文献类型：
--
作者：
Kong, Dali;Cui, Zhen;Liao, Xinhao;Zhang, Keke
我们调查，通过渐近分析和直接数值模拟，进动驱动的流动的均匀流体被限制在一个充满流体的圆柱体，快速旋转的对称轴和进动的不同的轴，是固定在空间中。一个特别的重点是放在一个球形的圆柱体，其直径几乎是相同的长度。在这个特殊的长宽比，最强的直接共振之间发生的空间最简单的惯性模式和岁差庞加莱强迫。在渐近小Ekman数的地幔参考系中，导出了描述弱旋进流的封闭形式的渐近解析解。我们还构建了一个非线性三维有限元模型-这是验证对渐近解和构造的精确解-阐明的非线性过渡导致无序流动的旋进类球柱。借助完全非线性解的完全惯性模态分解，研究了弱旋进流和强旋进流的性质。尽管做了大量的努力，著名的三阶共振没有发现在旋进类球柱。包含在岁差强迫惯性模式中的能量主要通过粘性边界层中的非线性效应转移到地转流，当岁差庞加莱力足够大时，地转流成为主导。结果表明，随着旋进力的增加，非线性流动逐渐从层流向无序流动演化。
We investigate, through both asymptotic analysis and direct numerical simulation, precessionally driven flow of a homogeneous fluid confined in a fluid-filled circular cylinder that rotates rapidly about its symmetry axis and precesses about a different axis that is fixed in space. A particular emphasis is placed on a spherical-like cylinder whose diameter is nearly the same as its length. At this special aspect ratio, the strongest direct resonance occurs between the spatially simplest inertial mode and the precessional Poincaré forcing. An asymptotic analytical solution in closed form describing weakly precessing flow is derived in the mantle frame of reference for asymptotically small Ekman numbers. We also construct a nonlinear three-dimensional finite element model – which is validated against both the asymptotic solution and a constructed exact solution – for elucidating the nonlinear transition leading to disordered flow in the precessing spherical-like cylinder. Properties of both weakly and strongly precessing flows are investigated with the aid of a complete inertial-mode decomposition of the fully nonlinear solution. Despite a large effort being made, the well-known triadic resonance is not found in the precessing spherical-like cylinder. The energy contained in the precessionally forced inertial mode is primarily transferred, through nonlinear effects in the viscous boundary layers, to the geostrophic flow that becomes predominant when the precessional Poincaré force is sufficiently large. It is found that the nonlinear flow evolutes gradually and progressively from the laminar to disordered as the precessional force increases.
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影响因子：
3.7
作者：
Rainer Hollerbach
通讯作者：
Rainer Hollerbach
影响因子：
3.7
作者：
J. J. Kobine-J.
通讯作者：
J. J. Kobine-J.
影响因子：
3.7
作者：
Liao, Xinhao;Zhang, Keke
通讯作者：
Zhang, Keke
影响因子：
3.7
作者：
H. Greenspan
通讯作者：
H. Greenspan
影响因子：
1.3
作者：
Cheng-Chin Wu;P. Roberts
通讯作者：
Cheng-Chin Wu;P. Roberts