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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Discussion papers
https://doi.org/10.5194/npg-2018-54
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/npg-2018-54
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 04 Dec 2018

Research article | 04 Dec 2018

Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Nonlinear Processes in Geophysics (NPG).

Competition between Chaotic Advection and Diffusion: Stirring and Mixing in a 3D Eddy Model

Genevieve Jay Brett1, Larry Pratt2, Irina Rypina2, and Peng Wang3 Genevieve Jay Brett et al.
  • 1IPRC, University of Hawaii Manoa, Honolulu, HI, USA
  • 2Woods Hole Oceanographic Institution, Woods Hole, MA, USA
  • 3University of California, Los Angeles, CA, USA

Abstract. The importance of chaotic advection relative to turbulent diffusion is investigated in an idealized model of a 3D swirling and overturning ocean eddy. Various measures of stirring and mixing are examined in order to determine when and where chaotic advection is relevant. Turbulence is alternatively represented by: 1) an explicit, observation–based, scale–dependent eddy diffusivity, 2) stochastic noise, added to a deterministic velocity field, or 3) explicit and implicit diffusion in a spectral numerical model of Navier–Stokes equations. Lagrangian chaos in our model occurs only within distinct regions of the eddy, including a large chaotic ‘sea’ that fills much of the volume near the perimeter and central axis of the eddy, and much smaller ‘resonant’ bands. The size and distribution of these regions depends on factors such as the degree of axial asymmetry of the eddy and the Ekman number. The relative importance of chaotic advection and turbulent diffusion within the chaotic regions is quantified using three measures: the ratio of the tracer filament arrest scale to the width of the chaotic region, the rate of dispersal of closely spaced fluid parcels, and the Nakamura effective diffusivity. The role of chaotic advection in the stirring of a passive tracer is generally found to be most important within the larger chaotic ‘seas’, at intermediate times, with small diffusivities, and for eddies with strong asymmetry. In contrast, in thin chaotic regions, turbulent diffusion at oceanographically relevant rates is at least as important as chaotic advection. Future work should address anisotropic and spatially–varying representations of turbulence for more realistic models.

Genevieve Jay Brett et al.
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Genevieve Jay Brett et al.
Data sets

Rotating Cylinder Eddy Data G. J. Brett and P. Wang https://doi.org/10.5281/zenodo.1560204

Model code and software

Rotating Cylinder Eddy Codes G. J. Brett https://doi.org/10.5281/zenodo.1560663

Genevieve Jay Brett et al.
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Latest update: 13 Dec 2018
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Short summary
The relative importance of chaotic stirring and smaller-scale turbulent mixing for the distribution of dye in an idealized ocean flow feature is quantified using three different methods. We find that stirring is the dominant process in large areas with fast stirring, while mixing dominates in small fast-stirring regions and all slow-stirring regions. This quantification of process dominance can help oceanographers think about when to model stirring accurately, which can be costly.
The relative importance of chaotic stirring and smaller-scale turbulent mixing for the...
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