## transilient turbulence theory

A method for parameterizing turbulence that allows nonlocal vertical mixing between every pair of grid points in a vertical column, even between nonneighboring points.

This method can account for the advective-like turbulent transport within large coherent turbulence structures such as thermals, where large diameter (1 km) updraft cores transport air from near the surface to the top of the mixed layer with little or no dilution. The method also parameterizes the mixing effects of medium and small size eddies, so it gives a physical-space representation of a spectrum of turbulence wavelengths. The framework for this parameterization is a matrix equation: where

*S*_{j}is the initial value at time*t*of any scalar such as potential temperature, specific humidity, or wind velocity component at any source grid point*j*, and*S*_{i}is the final value after timestep Δ*t*at destination grid point*i*. The matrix*c*_{ij}is called a transilient matrix and indicates the fraction of the air ending at destination grid cell*i*that came from source grid cell*j*. The equation is summed over all grid points*n*representing a column of air. Transilient turbulence theory is called a nonlocal, first-order turbulence closure.*See*nonlocal mixing, nonlocal flux;*compare*K-theory.Stull, R. B. 1993. Review of nonlocal mixing in turbulent atmospheres. Bound.-Layer Meteor.. 62. 21–96.

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