Resonance phenomena in a time-dependent, three-dimensional model of an idealized eddy
Abstract
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Mar 30, 2015
- Source ID
- 10.1063/1.4916086
Entities
People
- I. Mezić
- Irina I. Rypina
- Lawrence J. Pratt
- Pingshan Wang
- Tamay M. Özgökmen
Organizations
- Office of Naval Research
- University of California
- University of Miami
- Woods Hole Oceanographic Institution