Abstract
Abstract. 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.
Highlights
Chaotic advection (Aref, 1984; Shepherd et al, 2000) is a process by which rapid stirring, as manifested by the stretching and folding of material, is produced within a smooth and well-organized Eulerian velocity field
The answer is that chaotic advection can be relevant, and in some cases dominant, within certain regions of the flow field and over certain time intervals
The region most likely to feel the effects of chaotic advection is the extensive chaotic sea that exists in all simulations, and this is especially pronounced when the eddy is shallow
Summary
Chaotic advection (Aref, 1984; Shepherd et al, 2000) is a process by which rapid stirring, as manifested by the stretching and folding of material, is produced within a smooth and well-organized Eulerian velocity field. In most cases the flow fields are two-dimensional and timedependent, and when observed, they often occur at the sea surface or within the stratosphere (Polvani et al, 1995; Ngan and Shepherd, 1997). Three-dimensional examples exist (e.g., Fountain et al, 2000; Rypina et al, 2015; Solomon and Mezic, 2003; Yuan et al, 2004; Branicki and Kirwan Jr., 2010, and Pratt et al, 2014, hereafter P2014) and often involve numerically modeled velocity fields, due to the limitations of observational methods. The chaotic regions are rapidly stirred as a result of the signature rapid separation of nearby tra-
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
