Connection between encounter volume and diffusivity in geophysical flows

• Published in: Nonlinear Processes in Geophysics
• Main Authors: Rypina, Irina I., Llewellyn Smith, Stefan, Pratt, Lawrence J.
• Format: Article in Journal/Newspaper
• Language: English
• Published: Copernicus Publications on behalf of the European Geosciences Union 2018
• Subjects: North Atlantic
• Online Access: https://hdl.handle.net/1912/10300

© The Author(s), 2018. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Nonlinear Processes in Geophysics 25 (2018): 267-278, doi:10.5194/npg-25-267-2018. Trajectory encounter volume – the volume of fluid that passes close to a reference fluid parcel over some time interval – has been recently introduced as a measure of mixing potential of a flow. Diffusivity is the most commonly used characteristic of turbulent diffusion. We derive the analytical relationship between the encounter volume and diffusivity under the assumption of an isotropic random walk, i.e., diffusive motion, in one and two dimensions. We apply the derived formulas to produce maps of encounter volume and the corresponding diffusivity in the Gulf Stream region of the North Atlantic based on satellite altimetry, and discuss the mixing properties of Gulf Stream rings. Advantages offered by the derived formula for estimating diffusivity from oceanographic data are discussed, as well as applications to other disciplines. This work was supported by NSF grants OCE-1558806 and EAR-1520825, and NASA grant NNX14AH29G.