# Transilient turbulence theory

From Glossary of Meteorology

## 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.

Copyright 2022 American Meteorological Society (AMS). For permission to reuse any portion of this work, please contact permissions@ametsoc.org. Any use of material in this work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act (17 U.S. Code § 107) or that satisfies the conditions specified in Section 108 of the U.S.Copyright Act (17 USC § 108) does not require AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a website or in a searchable database, or other uses of this material, except as exempted by the above statement, require written permission or a license from AMS. Additional details are provided in the AMS Copyright Policy statement.