Chaotic advection in a steady, three-dimensional, Ekman-driven eddy Pratt, Lawrence J. Rypina, Irina I. Ozgokmen, Tamay M. Wang, P. Childs, H. Bebieva, Y. 2014-04-01T16:01:39Z 2014-12-05T10:02:27Z 2013-12-05
dc.description Author Posting. © Cambridge University Press, 2013. This article is posted here by permission of Cambridge University Press for personal use, not for redistribution. The definitive version was published in Journal of Fluid Mechanics 738 (2014): 143-183, doi:10.1017/jfm.2013.583. en_US
dc.description.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 Ro, 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. en_US
dc.description.embargo 2014-12-05 en_US
dc.description.sponsorship L.J.P., I.I.R., T.M.O. and P.W. have been supported on DOD (MURI) grant N000141110087, administered by the Office of Naval Research. I.I.R. and L.J.P. received additional support from Grant NSF-OCE-0725796 from the National Science Foundation. en_US
dc.format.mimetype application/pdf
dc.identifier.citation Journal of Fluid Mechanics 738 (2014): 143-183 en_US
dc.identifier.doi 10.1017/jfm.2013.583
dc.language.iso en_US en_US
dc.publisher Cambridge University Press en_US
dc.subject Chaotic advection en_US
dc.subject Geophysical and geological flows en_US
dc.subject Ocean processes en_US
dc.title Chaotic advection in a steady, three-dimensional, Ekman-driven eddy en_US
dc.type Article en_US
dspace.entity.type Publication
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