Chaotic advection in a steady, three-dimensional, Ekman-driven eddy
Chaotic advection in a steady, three-dimensional, Ekman-driven eddy
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埃克曼驱动的稳定三维涡流中的混沌平流
DOI：
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发表时间：
2013
影响因子：
3.7
通讯作者：
Y. Bebieva
中科院分区：
文献类型：
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作者：
Larry J. Pratt;I. Rypina;T. Özgökmen;P. Wang;Hank Childs;Y. Bebieva
摘要我们研究和量化搅拌由于混沌平流内的一个稳定的，三维的，埃克曼驱动的，旋转的圆筒流。流场具有垂直翻转和水平旋转运动，是某些海洋涡旋中观察到的运动的理想化。流动的特点是强烈的背景旋转，我们探讨的变化，埃克曼和Rossby数，$E$和${R}_{o} $，范围内的海洋中尺度和亚中尺度。一个高分辨率的谱元模型与线性分析理论，弱非线性共振分析和运动学模型，以映射出的障碍，流形，共振层和其他对象，提供了一个模板的混沌搅拌。正如预期的那样，当一个径向对称的背景态被一个破缺扰动扰动时，混沌就会出现。在背景状态下，每个轨迹生活在一个环面和一些后者生存的扰动，并作为障碍，混沌运输，结果符合扩展的KAM定理的三维，体积保持流。对于浅涡，其中$E$是$O（1）$，流动是由薄共振层夹在KAM型障碍，搅拌速率是弱的。另一方面，涡流与适度小$E$经验较厚的共振层，更广泛的传播混乱和更迅速搅拌。这种趋势逆转足够小的$E$，对应于深涡，其中的垂直刚性施加强旋转限制搅拌。从被动示踪剂释放估计的散装搅拌速率证实了搅拌速率随E$的非单调变化。这一结果与线性Ekman层理论、共振宽度计算和泰勒-普劳德曼定理相一致。该理论能够粗略地预测搅拌最大时的E$值。对于大的扰动，搅拌速率变得单调的埃克曼数的范围内探索。我们还探讨了涡流展弦比的变化。
Abstract We investigate and quantify stirring due to chaotic advection within a steady, three-dimensional, Ekman-driven, rotating cylinder flow. The flow field has vertical overturning and horizontal swirling motion, and is an idealization of motion observed in some ocean eddies. The flow is characterized by strong background rotation, and we explore variations in Ekman and Rossby numbers, $E$ and ${R}_{o} $ , over ranges appropriate for the ocean mesoscale and submesoscale. A high-resolution spectral element model is used in conjunction with linear analytical theory, weakly nonlinear resonance analysis and a kinematic model in order to map out the barriers, manifolds, resonance layers and other objects that provide a template for chaotic stirring. As expected, chaos arises when a radially symmetric background state is perturbed by a symmetry-breaking disturbance. In the background state, each trajectory lives on a torus and some of the latter survive the perturbation and act as barriers to chaotic transport, a result consistent with an extension of the KAM theorem for three-dimensional, volume-preserving flow. For shallow eddies, where $E$ is $O(1)$ , the flow is dominated by thin resonant layers sandwiched between KAM-type barriers, and the stirring rate is weak. On the other hand, eddies with moderately small $E$ experience thicker resonant layers, wider-spread chaos and much more rapid stirring. This trend reverses for sufficiently small $E$ , corresponding to deep eddies, where the vertical rigidity imposed by strong rotation limits the stirring. The bulk stirring rate, estimated from a passive tracer release, confirms the non-monotonic variation in stirring rate with $E$ . This result is shown to be consistent with linear Ekman layer theory in conjunction with a resonant width calculation and the Taylor–Proudman theorem. The theory is able to roughly predict the value of $E$ at which stirring is maximum. For large disturbances, the stirring rate becomes monotonic over the range of Ekman numbers explored. We also explore variation in the eddy aspect ratio.