A new look at Lagrangian diffusivity and its relation to irreversible mixing

中国科学院南海海洋研究所

"Shiqiu Peng and Yukun Qian
State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou, China.
Abstract
Traditional Lagrangian diffusivity is defined as the growth rate of particle dispersion, in which dispersion is measured using Eulerian displacement. Here it is proposed that particle spreading should be measured using ‘contour-distance’, or equivalently, displacement in contour-based coordinate. Isopycnal vertical coordinate is a well-known example. In such coordinate, Lagrangian particle motions obey a transformed zeroth-order stochastic (i.e., random-walk) model with the diffusivity replaced by the effective diffusivity (lateral case) or diapycnal diffusivity (vertical case). In the absence of small-scale diffusion, particles do not disperse at all in the contour-coordinate. The resulting instantaneous horizontal or vertical Lagrangian spreading rate is conceptually identical to the effective diffusivity or diapycnal diffusivity that only measures the irreversible mixing. In these regards, the present study provides a new look at particle dispersion in contour-based coordinates and sheds light on developing new mixing parameterization schemes in the ocean circulation models regarding to the irreversible mixing."