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Media type:
E-Article
Title:
Statistical non-locality of dynamically coherent structures
Contributor:
Souza, Andre N.;
Lutz, Tyler;
Flierl, Glenn R.
Published:
Cambridge University Press (CUP), 2023
Published in:
Journal of Fluid Mechanics, 966 (2023)
Language:
English
DOI:
10.1017/jfm.2023.467
ISSN:
0022-1120;
1469-7645
Origination:
Footnote:
Description:
We analyse a class of stochastic advection problems by conditionally averaging the passive tracer equation with respect to a given flow state. In doing so, we obtain expressions for the turbulent diffusivity as a function of the flow statistics spectrum. When flow statistics are given by a continuous-time Markov process with a finite state space, calculations are amenable to analytic treatment. When the flow statistics are more complex, we show how to approximate turbulent fluxes as hierarchies of finite state space continuous-time Markov processes. The ensemble average turbulent flux is expressed as a linear operator that acts on the ensemble average of the tracer. We recover the classical estimate of turbulent flux as a diffusivity tensor, the components of which are the integrated autocorrelation of the velocity field in the limit that the operator becomes local in space and time.