# Nonlocal flux

From AMS Glossary

## nonlocal flux

The vertical turbulent transport of a quantity such as heat per unit area per time across any height index

*k*, between source heights*j*to destination heights*i*, where*i*and*j*are on opposite sides of*k*vertically.It is nonlocal because where

*i*and*j*need not be neighbors. Using kinematic heat flux as an example,*n*is the total number of grid cells in a vertical column, Δ*z*is the vertical thickness of each grid cell (i.e., spacing between grid points), Δ*t*is the time increment over which eddies transport heat starting from time*t*, θ_{a}is the potential temperature at grid cell*a*, and*c*_{ab}is the transilient matrix specifying the fraction of air that ended in destination cell*a*originated at source cell*b*, for*a*and*b*dummy indices.*See*transilient turbulence theory, nonlocal mixing.