Source Themes

This paper examines why turbulent tracer fluxes can depend on gradients elsewhere in space and earlier in time. It develops a formal expression for that dependence as a nonlocal functional of the mean tracer gradient. Two-dimensional turbulence simulations, stochastic velocity fields, and iterated maps reveal the extent and structure of the resulting transport kernels. The analysis identifies circumstances in which a local eddy diffusivity is a reasonable approximation and cases where it misses important transport effects. Readers get a framework for diagnosing nonlocality and using it to guide the design of physically informed, data-driven mixing parameterizations.

This paper studies how persistent flow structures make turbulent tracer transport depend on conditions at other locations and earlier times. It conditions the tracer equation on the flow state and describes changes between flow states with continuous-time Markov processes. That construction produces a transport operator whose form depends on the spectrum of the flow statistics. The familiar local diffusivity tensor emerges as a limiting case, while progressively richer Markov descriptions approximate more complicated transport. Readers get a theoretical route from coherent flow dynamics to nonlocal mixing closures and a precise account of the assumptions behind ordinary eddy diffusivity.