# Mixing and diffusion in coherent vortices

Lead Research Organisation:
University of Exeter

Department Name: Engineering Computer Science and Maths

### Abstract

Mixing is an important process in fluid flows. The flow of a fluid, be it the sea or atmosphere, can enhance the mixing of tracers such as plankton or pollutants by many orders of magnitude. This has important implications for industrial processes and the natural environment. For example mixing speeds up chemical reactions and combustion. In oceans and lakes mixing affects the distribution of nutrients and so the distribution of plant and animal life. On the scale of the atmosphere, mixing is important in determining the dispersal of pollutants and the destruction of ozone in the South Polar vortex. Many fluid flows are dominated by coherent vortices: long-lived regions of swirling fluid flow. These have particularly interesting and subtle mixing properties, because mixing affects the structure of the fluid flow (through the mixing of a quantity called the `vorticity', which may be thought of as the local angular momentum of fluid). This leads to complex mixing, with some regions being well-mixed, and others very poorly. This is seen in large-scale numerical simulations, for example of the atmosphere, but is not well-understood mathematically. The aim of the proposed research is to investigate the mixing properties of vorticity and other tracers in coherent vortices, and to determine the different regimes, using combination of numerical and analytical techniques.

### Publications

TURNER M
(2009)

*Spreading of two-dimensional axisymmetric vortices exposed to a rotating strain field*in Journal of Fluid Mechanics
Turner M
(2009)

*The influence of periodic islands in the flow on a scalar tracer in the presence of a steady source*in Physics of Fluids
Turner M
(2011)

*A study of mixing in coherent vortices using braiding factors*in Fluid Dynamics Research
TURNER M
(2008)

*Thresholds for the formation of satellites in two-dimensional vortices*in Journal of Fluid Mechanics
TURNER M
(2009)

*Diffusion and the formation of vorticity staircases in randomly strained two-dimensional vortices*in Journal of Fluid Mechanics
TURNER M
(2009)

*Analysis of the unstable Tollmien-Schlichting mode on bodies with a rounded leading edge using the parabolized stability equation*in Journal of Fluid Mechanics
Turner M. R.
(2008)

*Effective diffusion of scalar fields in a chaotic flow*in Physics of Fluids
Turner M. R.
(2008)

*Neutral modes of a two-dimensional vortex and their link to persistent cat's eyes*in Physics of Fluids
Turner, M.R.
(2009)

*Spreading of two-dimensional axisymmetric vortices exposed to a rotating strain field*in Journal of Fluid Mechanics
Turner, M.R.
(2007)

*Linear and nonlinear decay of cat's eyes in two-dimensional vortices, and the link to Landau poles*in Journal of Fluid MechanicsDescription | The aim of the research project was to understand the interaction of vortex dynamics and mixing. A two-dimensional vortex may be described by its flow field, or more conveniently by the vorticity field, which is a scalar quantity. What is intriguing is that the distribution of vorticity, for example the profile of the vortex, determines the fluid flow and so its mixing properties. On the other hand this vorticity is itself transported by the fluid flow and so the profile can evolve in time through mixing processes. Thus, the problem of the interaction of dynamics and mixing is subtle; it is also nonlinear and nonlocal. In this research we studied a number of fundamental problems in this area, based on coherent vortices, and broadly relevant to many astrophysical and geophysical flows, as well as turbulence. |

Exploitation Route | Mixing is an important process in fluid flows. The flow of a fluid, be it the sea or atmosphere, can enhance the mixing of tracers such as plankton or pollutants by many orders of magnitude. This has important implications for industrial processes and the natural environment. For example mixing speeds up chemical reactions and combustion. In oceans and lakes mixing affects the distribution of nutrients and so the distribution of plant and animal life. On the scale of the atmosphere, mixing is important in determining the dispersal of pollutants and the destruction of ozone in the South Polar vortex. Dissemination via: Journal articles, Presentations at scientific conferences. |

Sectors | Other |

URL | http://emps.exeter.ac.uk/mathematics/research/cgafd/interests/theoreticalfluiddynamics/vortices/ |