Competition between chaotic advection and diffusion: Stirring and mixing in a 3-D eddy model.

© The Author(s), 2019. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Brett, G. J., Pratt, L., Rypina, I., & Wang, P. Competition between chaotic advection and diffusion: Stirring and mixing in a 3-D eddy model. Nonlinear Processes in Geophysics, 26(2), (2019):37-60, doi:10.5194/npg-26-37-2019.
The importance of chaotic advection relative to turbulent diffusion is investigated in an idealized model of a 3-D swirling and overturning ocean eddy. Various measures of stirring and mixing are examined in order to determine when and where chaotic advection is relevant. Turbulent diffusion is alternatively represented by (1) an explicit, observation-based, scale-dependent diffusivity, (2) stochastic noise, added to a deterministic velocity field, or (3) explicit and implicit diffusion in a spectral numerical model of the 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 depend 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 Lagrangian Batchelor scale, 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 turbulent diffusion for more realistic models.
This work was supported by DOD (MURI) grant no. N0004110087 as well as the US National Science Foundation grants OCE-1154641 and OCE-1558806 and the National Aeronautics and Space Administration (NASA) grant no. NNX14AH29G. Genevieve Jay Brett received additional support from the Woods Hole Oceanographic Institution Academic Programs Office. We also thank Marianna Linz, Dan Collura, and four anonymous reviewers for their constructive input on how to present this material.