Statistical non-locality of dynamically coherent structures
Abstract
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jul 06, 2023
- Source ID
- 10.1017/jfm.2023.467
Entities
People
- Andre N. Souza
- Glenn R. Flierl
- Tyler Lutz
Organizations
- National Science Foundation
- Office of Naval Research