Resonance phenomena in a time-dependent, three-dimensional model of an idealized eddy.
We analyze the geometry of Lagrangian motion and material barriers in a time-dependent, three-dimensional, Ekman-driven, rotating cylinder flow, which serves as an idealization for an isolated oceanic eddy and other overturning cells with cylindrical geometry in the ocean and atmosphere. The flow is forced at the top through an oscillating upper lid, and the response depends on the frequency and amplitude of lid oscillations. In particular, the Lagrangian geometry changes near the resonant tori of the unforced flow, whose frequencies are rationally related to the forcing frequencies. Multi-scale analytical expansions are used to simplify the flow in the vicinity of resonant trajectories and to investigate the resonant flow geometries. The resonance condition and scaling can be motivated by simple physical argument. The theoretically predicted flow geometries near resonant trajectories have then been confirmed through numerical simulations in a phenomenological model and in a full solution of the Navier-Stokes equations.
Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543, USA.
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Rypina
Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543, USA.
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LJ
Pratt
Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida 33149, USA.
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Wang
Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida 33149, USA.
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TM
Özgökmen
Department of Mechanical Engineering and Center for Control, Dynamical Systems and Computation, University of California, Santa Barbara, California 93106, USA.
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Mezic
D008962:Models, Theoretical; D009716:Numerical Analysis, Computer-Assisted; D012212:Rheology; D013997:Time Factors; D014872:Water Movements