Nonlocal flux

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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 i and j need not be neighbors. Using kinematic heat flux as an example,
where n is the total number of grid cells in a vertical column, Δz is the vertical thickness of each grid cell (i.e., spacing between grid points), Δt is the time increment over which eddies transport heat starting from time t, θa is the potential temperature at grid cell a, and cab 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.

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